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Design of a submillimeter gas laser Sahay, Vishnu 1967

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THE DESIGN OF A SUBMILLIMETER GAS LASER Toy VISHNU SAHAY B . A . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1965 A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l E n g i n e e r i n g We accept t h i s t h e s i s as conforming t o the s t a n d a r d s r e q u i r e d from c a n d i d a t e s f o r the degree o f Master of A p p l i e d S c i e n c e Members o f t h e Department of E l e c t r i c a l E n g i n e e r i n g THE UNIVERSITY OF BRITISH COLUMBIA June, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n -t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a D a t e 4ou/v 3-S>, V^fcr" ABSTRACT A gas l a s e r has been designed :.to 'lase over the e n t i r e f a r i n f r a - r e d spectrum. T h i s t h e s i s d i s c u s s e s the t h e o r e t i c a l and p r a c t i c a l c o n s i d e r a t i o n s t h a t a r e i n v o l v e d i n such a d e s i g n . The t h r e e a s p e c t s of d e s i g n t h a t are d i s c u s s e d a r e the l a s e r c a v i t y , the e x c i t a t i o n mechanism, and the d e t e c t i o n a p p a r a t u s . E v e r y e f f o r t i s made throughout t o keep the system as s i m p l e as p o s s i b l e . Water vapor i s used i n the l a s e r as a t e s t gas, s i n c e i t i s known t o have t r a n s i t i o n s i n the f a r i n f r a - r e d r e g i o n . I t was found t o l a s e i n s e v e r a l l i n e s most of whi c h have been i d e n t i f i e d w i t h l i n e s d i s c o v e r e d by o t h e r workers. Two l i n e s , however, appear t o be new: 133.65P-, and 145.75m w i t h a p o s s i b l e e r r o r of - 1.65u. C h a r a c t e r i s t i c v a r i a t i o n s of output power w i t h p r e s s u r e and c u r r e n t d e n s i t y have been o b t a i n e d f o r the l a s e r u s i n g water vapor. Attempts a t o b t a i n i n g l a s e r a c t i o n w i t h acetone and a l c o h o l proved u n s u c c e s s f u l . TABLE OP CONTENTS Page ABSTRACT i i TABLE OP CONTENTS i i i LIST OP ILLUSTRATIONS i v LIST OP TABLES v i ACKNOWLEDGEMENTS v i i 1. INTRODUCTION 1 2. LASER MECHANISM 5 2 .1 P o p u l a t i o n I n v e r s i o n 5 2.2 E x c i t a t i o n of Gas L a s e r s 10 2.3 L i n e w i d t h 17 2.4 Gaseous D i s c h a r g e 21 3. RESONATOR DESIGN 23 3 .1 I n t r o d u c t i o n 23 3.2 Resonator Tube 33 3.3 M i r r o r s and t h e i r Mountings..... 45 3.4 E x t e r n a l M i r r o r s 49 3.5 Mode S e l e c t i o n 50 4. COUPLING AND DETECTION 55 4 .1 C o u p l i n g 55 4.2 Measurement of Output S i g n a l I n t e n s i t y . . 65 4.3 Frequency Measurements 73 5. TESTS ON LASER. 82 5 .1 T e s t s on L a s e r 82 5.2 Test Data 82 5.3 D i s c u s s i o n o f R e s u l t s 86 6. CONCLUSIONS 95 REFERENCES 97 i i i LIST OF ILLUSTRATIONS F i g u r e Page 2.1 Three L e v e l l a s e r 7 2.2 H y p o t h e t i c a l P o t e n t i a l Energy Curves.. 16 3.1 D i f f r a c t i o n Loss of Low Order Modes... 26 3.2 Medium-Mode C o u p l i n g 30 3.3 Alignment T o l e r a n c e o f Double Concave C a v i t y 34 3.4 Ali g n m e n t T o l e r a n c e of Piano-Concave C a v i t y 34 3-5 S t a b i l i t y Diagram 36 3.6 R e l a t i v e L o c a t i o n o f Modes 42 3.7 C a v i t y S t r u c t u r e 44 3.8 F i x e d M i r r o r Housing 46 3.9 T r a n s m i s s i v i t y of P o l y e t h y l e n e 47 3.10 Movable M i r r o r Arrangement 47 3.11 M i r r o r Alignment Procedure 48 3.12 A p e r t u r e L i m i t e d C a v i t y C o n f i g u r a t i o n . 52 3.13 Spot S i z e of Concave C a v i t y 52 4.1 F i e l d I n t e n s i t y f o r 00, 01, 02 Modes, N=1.6 58 4.2 F i e l d I n t e n s i t y f o r 10, 11 Modes, N=l .6 58 4.-3 F i e l d I n t e n s i t y f o r 20, 30 Modes, N=1.6 59 4.4 F i e l d I n t e n s i t y f o r Low Loss Modes With C o u p l i n g A p e r t u r e , N=1.6 and N q=0.01.. 60 4.5 C r i t i c a l A p e r t u r e F r e s n e l Numbers 61 4.6 Golay C e l l D e t e c t i o n Apparatus 68 4.7 Golay C e l l D e t e c t o r 70 4.8 E b e r t - F a s t i e Monochromator 74 i v 4.9 J a r r e l - A s h Mono chroma t o r 76 5.1 T o t a l Output Power, N e a r - C o n f o c a l C a v i t y 84 5.2 Output Power i n 118u L i n e , Near Con-f o c a l C a v i t y 85 5.3 T o t a l Output Power, Piano-Concave C a v i t y , 1mm C o u p l i n g A p e r t u r e 85 5.4 T o t a l Output Power, Plan-Concave C a v i t y , 2mm C o u p l i n g A p e r t u r e 86 v LIST OF TABLES Table Fage 2- 1 Af vs M o l e c u l a r Weight 20 3 - 1 S u b m i l l i m e t e r Gas L a s e r s 39 3-2 Low D i f f r a c t i o n Loss Modes 43 3 - 3 Modes E x c i t e d by 118u, L i n e 43 4 - 1 C r i t i c a l F r e s n e l Numbers 62 4-2 T r a n s m i s s i o n C o e f f i c i e n t s w i t h a 2 mm C o u p l i n g Hole 64 4 - 3 Water Vapor T r a n s i t i o n L i n e s 80 5- 1 Monochromator Scans 91 5-2 Wavelength A n a l y s i s 92 v i ACKNOWLEDGEMENT The f o l l o w i n g f i n a n c i a l support i s gratefully-acknowledged : 1. N a t i o n a l Research Council Block Grants, NRC-A68 f o r 1965-66 and NRC-A3287 f o r 1966-67-2. B r i t i s h Columbia Graduate Student Scholarship f o r 1965-66. 5- U n i v e r s i t y of B r i t i s h Columbia Fellowship f o r 1966-67. I would l i k e to express my sincere thanks to Dr. D.P.' A k i t t f o r h i s inv a l u a b l e guidance during the e n t i r e p r o j e c t . I would also l i k e to thank Dr. L. Young f o r reading the manuscript and h i s u s e f u l comments. :.. Thanks are due to Mr. C. S h e f f i e l d f o r h i s t e c h n i c a l assistance w i t h the c i r c u i t r y , and to Miss D. Mackenzie f o r typing the manuscript of t h i s t h e s i s . Further thanks are given to my f e l l o w students who helped proof-read and assemble the t h e s i s . THE DESIGN OP A SUBMILLIMETER GAS LASER 1. INTRODUCTION One of the few regions of the e l e c t r o magnetic spectrum that remains unexplored i s the f a r i n f r a - r e d or the suhmillimeter region. The frequency range i s from 0.3 to 3 te r a h e r t z . I n t e r e s t i n developing t h i s r egion has been mounting because i t o f f e r s p o t e n t i a l b e n e f i t s which combine those of the microwave and of the o p t i c a l regions. These b e n e f i t s w i l l p a r t i c u l a r l y be f e l t i n the f i e l d s of m i l i t a r y communications, astronomy and spectroscopy. Two aspects of the development of t h i s region are the generation and the detection of suhmillimeter r a d i a t i o n . Development of one leads to the development of the other. At the present time much of the research e f f o r t i s d i r e c t e d towards developing suhmillimeter sources. I t i s i n t h i s effort..that l a s e r s are proving themselves. Attempts have been made, l a r g e l y unsuccessful, to develop these sources :by extending the p r i n c i p l e s behind conventional microwave generators. The shortest wavelength-k l y s t r o n that has been made i s one by Varian Associates of Canada Limited and- i t operates at 1.76 mm (.170 GHz). The only-present non-laser source of suhmillimeter waves i s developed by CFS of P a r i s , c a l l e d the Carcinotron. I t y i e l d s output-powers of m i l l i w a t t s - f o r wavelengths as short as 400p. (750 GHz). However, Carcinotrons are extremely expensive devices and t h e i r l i f e t i m e s are short. Therefore, the phenomenon of stimulated emissions i s being e x p l o i t e d f o r f a r i n f r a - r e d sources. 2 The phenomenon of s t i m u l a t e d e m i s s i o n o f R a d i a t i o n was p r e d i c t e d and e x p l a i n e d hy E i n s t e i n 1 i n 1917, who used 2 thermodynamical arguments, and hy D i r a c i n 1927, who used the t h e e r y of quantum mechanics. However, i t was o n l y i n 1 9 5 3 "that a p p l i c a t i o n f o r the phenomenon was proposed i n the •5 4 microwave r e g i o n hy Weber , Townes et a l and by Basov and 5 Prokhorov . S i n c e t h e n , e f f o r t s to a p p l y i t i n o t h e r r e g i o n s of" the e l e c t r o m a g n e t i c spectrum have proved s u c c e s s f u l . Maiman^, i n I 9 6 0 , a p p l i e d i t t o the o p t i c a l r e g i o n u s i n g a ruby c r y s t a l . S u b s e q uently, more and more l a s e r m a t e r i a l s have been found and used f o r the g e n e r a t i o n of r a d i a t i o n . I n f a c t , so much work has been done i n t h i s f i e l d t h a t i t i s now p o s s i b l e t o c l a s s i f y l a s e r s i n f o u r c a t e g o r i e s a c c o r d i n g t o t h e ' m a t e r i a l s used. (a) ": S o l i d S t a t e L a s e r s such as t h e Ruby L a s e r (b) Organic L a s e r s (c) " S e mi-conductor L a s e r s (d) Gas L a s e r s To d a t e , gas l a s e r s have been the most p o p u l a r f o r r e s e a r c h purposes. T h i s i s l a r g e l y because l a s e r a c t i o n i n gas l a s e r s can be s t i m u l a t e d by a l a r g e v a r i e t y of methods and the output beam can be s t a b i l i z e d t o a h i g h degree, i n so f a r as f r e q u e n c y and power a r e concerned. 7 S i n c e l a t e 1961, when Javen e t a l d i s c o v e r e d the Helium-Neon L a s e r , a h o s t of gaseous m a t e r i a l s have been used f o r l a s e r s . L a s e r s u s i n g these m a t e r i a l s can be c l a s s i f i e d i n t o t h r e e t y p e s , a c c o r d i n g t o the type of gas used. 3 (a) Neutral Atom Gas l a s e r s (b) I o n i c Gas Lasers (c) Molecular Gas Lasers The generation of r a d i a t i o n at f a r i n f r a - r e d frequencies i s , at present, the sole province of molecular gas l a s e r s . I n v e s t i g a t i o n of these l a s e r s has only l a t e l y begun. The f i r s t observation of stimulated emission i n the f a r i n f r a - r e d g spectra of molecules was made i n 1964 , u s i n g water vapour and deuterium oxide. Since then, research f o r more and more molecular gases with stimulated emission at f a r i n f r a - r e d frequencies has proved f r u i t f u l . However, no d e t a i l e d a n a l y s i s has as yet been undertaken to determine the exact mechanisms involved i n the phenomenon. In t h i s .thesis'',-a. .gas l a s e r i s designed'' which '•'. can ,be used to continue the search f o r hew molecular gas : m a t e r i a l s usable f o r l a s e r a c t i o n at f a r i n f r a - r e d frequencies. I t s h a l l then be tested using water vapour which i s known to have t r a n s i t i o n s w i t h i n t h i s region. The range of wavelengths over which the l a s e r so designed w i l l a c t u a l l y operate can only be' determined by a c t u a l experimentation. To determine t h i s range, other m a t e r i a l s which are known to have t r a n s i t i o n s i n t h i s region must be used i n the l a s e r . Whether any given m a t e r i a l w i l l have t r a n s i t i o n s i n the f a r i n f r a - r e d region cannot be predicted. Nor can i t be predicted whether the l a s e r designed i n t h i s p r o j e c t w i l l e x c i t e a l l the t r a n s i t i o n s w i t h i n t h i s range since some of these t r a n s i t i o n s may not be strong enough to overcome the l o s s e s i n h e r e n t i n the l a s e r . However, t h e r e i s l i t t l e doubt t h a t w i t h t h i s l a s e r c e r t a i n new t r a n s i t i o n s can be d i s c o v e r e d . The t h e s i s i s d i v i d e d i n t o f o u r p a r t s : (1) the e x c i t a t i o n mechanism, i n which the pr o c e s s of s t i m u -l a t e d e m i s s i o n and t h e pr o c e s s e s t h a t are i n v o l v e d i n o b t a i n i n g t h i s i n a gas are d e s c r i b e d , (2) the r e s o n a t o r d e s i g n , i n which the t h e o r e t i c a l and p r a c t i c a l c o n s i d e r a t i o n s i n v o l v e d i n the d e s i g n of the r e s o n a t o r a re d e s c r i b e d , ( 3 ) the d e t e c t i o n p r o c e d u r e , i n which t h e d e t e c t i o n mechanism used f o r power and f r e q u e n c y measurements, and how the r e s u l t s can be i n t e r p r e t e d a re described:, . (4) r e s u l t s and c o n c l u s i o n s , i n which' t h e r e s u l t s from the e x p e r i m e n t a l d a t a are d e r i v e d and comments made on them. The r e s o n a t o r d e s i g n i s chosen as s i m p l e as p o s s i b l e and no attempt i s made t o o p t i m i z e output power and f r e q u e n c y s t a b i l i t y . 5 2. LASER MECHANISM Be f o r e a t t e m p t i n g t o d e s i g n the l a s e r c a v i t y , i t i s e s s e n t i a l t o understand the mechanisms whereby l a s e r a c t i o n i s o b t a i n e d . I n t h i s c h a p t e r , a q u a l i t a t i v e summary of these mechanisms i s g i v e n as a p r e l i m i n a r y t o d e s c r i b i n g the method used t o e x c i t e the l a s e r . F urthermore, c e r t a i n items are i n t r o d u c e d w h i c h may i n some subsequent work l e a d t o p r e d i c t i o n s o r h y p o t h e t i c a l e x p l a n a t i o n s of the phenomena t h a t a r e observed. 2.1 P o p u l a t i o n I n v e r s i o n I n a g i v e n system- of p a r t i c l e s , each p a r t i c l e can e x i s t i n one o f s e v e r a l quantum s t a t e s c h a r a c t e r i z e d by energy l e v e l s . The number of s t a t e s h a v i n g the same energy i s c a l l e d the m u l t i p l i c i t y of t h a t energy l e v e l . A p a r t i c l e can jump from one energy l e v e l to another by a b s o r b i n g or e m i t t i n g energy e q u a l t o the energy d i f f e r e n c e between the l e v e l s i n v o l v e d . The t r a n s i t i o n can take p l a c e i n two ways:-(a) by y i e l d i n g energy t o or a b s o r b i n g i t from o t h e r p a r t i c l e s , (b) by e m i t t i n g o r a b s o r b i n g a photon of r a d i a t i o n energy whose f r e q u e n c y , V , i s g i v e n by h . where h = P l a n c k ' s c o n s t a n t E^= energy of h i g h e r energy l e v e l E 2= energy o f l o w e r energy l e v e l There i s a c e r t a i n p r o b a b i l i t y t h a t r a d i a t i o n a t f r e q u e n c i e s s u r r o u n d i n g v" can be absorbed or e m i t t e d when a 6 t r a n s i t i o n occurs. This p r o b a b i l i t y i s determined by a f u n c t i o n known as the l i n e Shape, g ( ^ ) , which has the general shape of a resonance curve. Each t r a n s i t i o n has i t s own c h a r a c t e r i s t i c l i n e w i d t h and t h i s determines the p r o b a b i l i t y that a p a r t i c l e w i l l undergo that t r a n s i t i o n . A p a r t i c l e can undergo a t r a n s i t i o n e i t h e r spontaneously or i t can he stimulated to do so by i n c i d e n t r a d i a t i o n of an appropriate frequency. Spontaneous t r a n s i t i o n s can occur only when a p a r t i c l e drops from a higher to a lower l e v e l . R a d i a t i o n from "such t r a n s i t i o n s w i l l emerge from the v a r i o u s p a r t i c l e s i n the system i n random phase and i s . t h e r e f o r e incoherent. Stimulated t r a n s i t i o n s , on the other hand, can he upward or downward and w i t h equal p r o b a b i l i t y , the p r o b a b i l i t y being dependent on the d e n s i t y of the s t i m u l a t i n g r a d i a t i o n . The r a d i a t i o n emitted by stimulated downward t r a n s i t i o n s i s always coherent w i t h the incident r a d i a t i o n and i s the basis f o r l a s e r a m p l i f i c a t i o n . I f a system of p a r t i c l e s can be i n one of two energy l e v e l s i n thermal e q u i l i b r i u m at temperature, T, the p a r t i c l e s w i l l populate these l e v e l s according to Maxwell-Boltzmann s t a t i s t i c s i n such a way that the population of the lower l e v e l , \N-^ , i s greater than that of the upper l e v e l , Ng. There are, t h e r e f o r e , more p a r t i c l e s a v a i l a b l e f o r upward t r a n s i t i o n s than there are f o r downward. This would r e s u l t i n a. net absorption of the s t i m u l a t i n g energy. However, i f thermal e q u i l i b r i u m could be disturbed by some means and the upper l e v e l population, H 9, was caused to exceed the lower l e v e l 7 p o p u l a t i o n , N^, i n c i d e n t r a d i a t i o n of the a p p r o p r i a t e f r e q u e n c y would s t i m u l a t e more downward than upward t r a n s i t i o n s . The net r e s u l t i s t h a t r a d i a t i o n would he e m i t t e d w i t h i n t e n s i t y which depends b o t h on the p o p u l a t i o n d i f f e r e n c e , and on the Q i n t e n s i t y o f the i n c i d e n t r a d i a t i o n . There i s , t h e r e f o r e , a net g a i n g i v e n ; b y : Gain- = (^-n-^) u quanta/second where u = i n c i d e n t r a d i a t i o n i n t e n s i t y ~&2\ = E i n s t e i n c o e f f i c i e n t f o r s t i m u l a t e d e m i s s i o n between l e v e l s 2 and 1. T h i s c o n d i t i o n , where the p o p u l a t i o n of the upper l e v e l i s h i g h e r t h a n t h a t of the low e r l e v e l i s c a l l e d "Popu-l a t i o n I n v e r s i o n " . The e x t e n t t o which p o p u l a t i o n i n v e r s i o n can be a c h i e v e d determines t h e s u i t a b i l i t y of a m a t e r i a l f o r use i n l a s e r a c t i o n . I n o r d e r t o d i s c u s s the v a r i o u s c o n d i t i o n s and parameters t h a t l e a d t o p o p u l a t i o n i n v e r s i o n , i t i s i n s t r u c -t i v e to,-study the si m p l e system w i t h t h r e e energy l e v e l s . The p e r t i n e n t l e v e l s a r e shown i n f i g u r e 2.1 and the f o l l o w i n g a n a l y s i s o f the system can be made. \ £ E 2 "=1 \ \ \ \ E i \ • ^ 3 N n. n 1 x3 2 P o p u l a t i o n (a) E q u i l i b r i u m C o n d i t i o n n x,n^- n, P o p u l a t i o n (b) E x c i t e d C o n d i t i o n F i g u r e 2.1 Three L e v e l L a s e r 8 A t e q u i l i b r i u m , a Boltzmann p o p u l a t i o n d i s t r i b u t i o n o b t a i n s f o r the energy l e v e l s E-^, Eg, E . The p o p u l a t i o n s are g i v e n by? TS. -(E.-E.)/kT _x = e v x 2 • N. 2 assuming u n i t m u l t i p l i c i t y . P o p u l a t i o n i n v e r s i o n between l e v e l s Eg and can be a c h i e v e d by d e p o p u l a t i n g E-^  so t h a t ng> n-^. I n the case o f the Three L e v e l - , l a s e r , i n c i d e n t r a d i a t i o n a t f r e q u e n c y = E^-E.^ w i l l l e a d t o the f o l l o w i n g p r o c e s s e s ; h ( l ) s t i m u l a t e d a b s o r p t i o n w i t h atoms i n l e v e l E^ r i s i n g t o l e v e l E^, (2) s t i m u l a t e d e m i s s i o n w i t h atoms i n l e v e l E^ d e c a y i n g . t o l e v e l E-^, and ( 3 ) random spontaneous e m i s s i o n from l e v e l E^ t o l e v e l E^. A l l t h e s e are r a d i a t i v e t r a n s i t i o n s , and w i l l proceed u n t i l n-^  = n^. W i t h t h i s s i t u a t i o n , ng may be g r e a t e r than = E 2 " E 1 n-^  and a weak s t i m u l a t i n g r a d i a t i o n a t f r e q u e n c y V - ^ h w i l l r e s u l t i n coherent e m i s s i o n of r a d i a t i o n a t f r e q u e n c y ^ -y^-The s t i m u l a t i n g f i e l d may be p r o v i d e d by the spontaneous e m i s s i o n a t a n d a l s o by p r e v i o u s l y s t i m u l a t e d e m i s s i o n . I n a l a s e r , m i r r o r s r e f l e c t t h i s r a d i a t i o n back i n t o the e x c i t e d gas volume p r o d u c i n g f u r t h e r s t i m u l a t e d e m i s s i o n . A f a s t t r a n s i t i o n between l e v e l s E„ and E„ ensures 3 2 t h a t the p o p u l a t i o n i s g r e a t e r t h a n n-^. Such a t r a n -s i t i o n t a k e s p l a c e by y i e l d i n g the energy (E^ - E^) t o the c r y s t a l l a t t i c e , i n t h e case of s o l i d s , o r . b y v a r i o u s ' c o l l i s i o n s i n the case o f gases and o t h e r f l u i d s . W ith t h e elementary p i c t u r e p r e s e n t e d i n the preceding;.-paragraphs, i t i s now p o s s i b l e t o make some statements c o n c e r n i n g the a t t a i n m e n t o f p o p u l a t i o n i n v e r s i o n . ll) The l e v e l must have a wide l i n e w i d t h . T h i s i s necessary. ..... - s j _ n c e t h e r e i s u s u a l l y not enough energy a v a i l a b l e from o r d i n a r y s o u r c e s of r a d i a t i o n i n a na r r o w . f r e q u e n c y band. I t s h o u l d be noted t h a t r a d i a t i v e t r a n s i t i o n s from l e v e l E^ t o l e v e l 'E^ may n o t always he p o s s i b l e due to t h i s r e q u i r e m e n t , as i n the case o f gas l a s e r s . A l t e r n a t e -methods, t o be d i s c u s s e d l a t e r , musx then be adopted. (2) While the t r a n s i t i o n 3-2 may or may not be r a d i a t i v e , the i m p o r t a n t f a c t i s t h a t i t be f a s t compared t o the t r a n -s i t i o n 2-1. T h i s would l e a d t o a p o p u l a t i o n o f l e v e l i n excess of t h a t of E-^  and a p o p u l a t i o n i n v e r s i o n i s then -achieved. Note t h a t t h i s i m p l i e s t h a t a f a s t t r a n s i t i o n ' 3-2 has a narrow bandwidth, a c c o r d i n g t o the U n c e r t a i n t y P r i n c i p l e AE.. AT^ h where AE = bandwidth and AT = l i f e t i m e o f l e v e l E^. (3) I n a d d i t i o n t o t h i s , l e v e l E-^  must decay f a s t e r t h a n l e v e l E^. T h i s may be done by d i r e c t t r a n s i t i o n , r a d i a t i v e or o t h e r w i s e , t o l e v e l E^ as i n f i g u r e 2.1 or t o an even "lower energy l e v e l whence p a r t i c l e s a r e t r a n s f e r r e d ~ u p t o l e v e l E,,. i. 10 2.2 E x c i t a t i o n o f Gas L a s e r s 2 . 2 . 1 I n t r o d u c t i o n Except f o r the t r a n s i t i o n i n which s t i m u l a t e d e m i s s i o n i s d e s i r e d , none need n e c e s s a r i l y he r a d i a t i v e . T h i s i s p a r t i c u l a r l y i m p o r t a n t i n the case of gas l a s e r s , s i n c e r a d i -a t i v e a b s o r p t i o n s are d i f f i c u l t , though not i m p o s s i b l e , t o o b t a i n i n gaseous media. I n gas l a s e r s , p o p u l a t i o n i n v e r s i o n can be a c h i e v e d i n s e v e r a l ways, a l l of which may c o n t r i b u t e t o the i n v e r s i o n p r o c e s s t o some degree. T h i s i s because of the ease w i t h which n o n - r a d i a t i v e t r a n s i t i o n s , caused by the f r e q u e n t i n t e r - a t o m i c c o l l i s i o n s , a r e o b t a i n e d . I n gases t h e n , i n t e r - e n e r g y - l e v e l t r a n s f e r s can be a c h i e v e d i n any of the f o l l o w i n g ways 1^: ( i ) O p t i c a l or R a d i a t i o n E x c i t a t i o n ( i i ) E l e c t r o n Impact ( i i i ) I n e l a s t i c Atom-Atom C o l l i s i o n ( i v ) M o l e c u l a r D i s s o c i a t i v e E x c i t a t i o n T r a n s f e r I n each of t h e s e methods, the S e l e c t i o n R u l e s a r e observed and t h e r e e x i s t f o r b i d d e n t r a n s i t i o n s . These r u l e s are u s e f u l i n d e t e r m i n i n g whether l a s e r a c t i o n i s p o s s i b l e a t c e r t a i n f r e q u e n c i e s . However, t o a p p l y them, the s p e c t r o s c o p i c c o n f i g u r a t i o n must be known, as t h e y are i n the c l a s s i c a l example of the Helium-Neon Gas L a s e r . However, i n t h e s e a r c h f o r new l a s e r t r a n s i t i o n s , these are n o t known and the e x a c t mechanism whereby p o p u l a t i o n i n v e r s i o n i s a c h i e v e d i s open t o s p e c u l a t i o n . C e r t a i n l y , a l l of the above f o u r w i l l be c a l l e d i n t o p l a y , but the degree of t h e i r u s e f u l n e s s cannot be p r e d i c t e d . I n o r d e r 11 to obtain some i n s i g h t i n t o t h i s , a c l o s e r look at each e x c i -t a t i o n mechanism w i l l prove p r o f i t a b l e . 2.2.2 R a d i a t i v e E x c i t a t i o n As mentioned on page 9, r a d i a t i v e t r a n s i t i o n s stimu-l a t e d by an e x t e r n a l source require a wide l i n e w i d t h . In the case of a gas at low pressure, the l i n e w i d t h i s l a r g e l y deter-mined by the Doppler e f f e c t - a phenomenon r e s u l t i n g from the r e l a t i v e motion of the gas p a r t i c l e s with respect to the obser-ver. (A q u a l i t a t i v e d i s c u s s i o n of l i n e w i d t h s i s given at the end of t h i s chapter.) Ordinary sources of r a d i a t i o n r a d i a t e i n a wide range of frequencies - wide compared to the l i n e w i d t h determined by t h i s e f f e c t . Therefore, the i n t e n s i t y of i n c i d e n t r a d i a t i o n w i t h i n the l i n e w i d t h , i s i n s u f f i c i e n t t o r a i s e enough p a r t i c l e s from the ground l e v e l to l e v e l E^ to permit the f o r -mation of population i n v e r s i o n . Therefore, r a d i a t i o n from ordinary sources cannot be the main source of e x c i t a t i o n f o r a gas l a s e r . R a d i a t i v e e x c i t a t i o n does occur to a very small extent, however, owing to spontaneous emission at ^ ^he extent to which t h i s i s u s e f u l cannot be determined. A second l a s e r of appropriate frequency may, however, be used to e x c i t e the gas l a s e r . Since the output power of t h i s l a s e r i s contained w i t h i n a narrow frequency band, i t i s s u f f i c i e n t l y intense to cause appreciable population i n v e r s i o n . I f the spectroscopic c o n f i g u r a t i o n of the gas i s known and i f a 1 l a s e r o f appropriate frequency;.:c :ahl vhei ; foHhd, R a d i a t i v e - e x c i -t a t i o n can then be the main method of e x c i t a t i o n . In attempting 12 to discover new t r a n s i t i o n s i n various gases, p a r t i c u l a r l y those whose spectroscopic c o n f i g u r a t i o n i s unknown, a second l a s e r can he u s e f u l only hy chance. A given l a s e r may or may not stimulate the new t r a n s i t i o n s . Therefore, a more general form of e x c i t a t i o n i s required which can simultaneously e x c i t e a l l the detectable t r a n s i t i o n s . 2.2.3 E l e c t r o n Impact This i s the most general form of e x c i t a t i o n used f o r atomic gases. Population i n v e r s i o n by t h i s means occurs due to the e x c i t a t i o n of atoms by c o l l i s i o n s with electrons of high k i n e t i c energy. In an e l e c t r i c discharge of a gas, ions and f r e e electrons are formed. These are a c c e l e r a t e d by the f i e l d that created the discharge and the electrons acquire the necessary high k i n e t i c energy. In a discharge, the f o l l o w i n g energy exchange processes take place': ( i ) ^electron c o l l i s i o n s of the f i r s t kind i n which an atom gains energy from an electron., ( i i ) e l e c t r o n c o l l i s i o n s of the second kind i n which an ex c i t e d atom loses energy to an e l e c t r o n , ( i i i ) spontaneous emission of r a d i a t i o n from an e x c i t e d atom., ( i v ) absorption of r a d i a t i o n by an atom, (v) stimulated emission of r a d i a t i o n by an atom. The advantage that these processes o f f e r over the r a d i a t i v e method of o b t a i n i n g population i n v e r s i o n i s that the e l e c t r o n e x c i t a t i o n c r o s s - s e c t i o n i s much wider than the absorption l i n e w i d t h of gases. Thus, although the S e l e c t i o n 13 R u l e s remain the same f o r t r a n s i t i o n s , an atom i s more l i k e l y to~-he e x c i t e d t o a p e r m i s s i b l e l e v e l hy e l e c t r o n impact than hy i n c i d e n t r a d i a t i o n . However, the s i t u a t i o n i s now more c o m p l i c a t e d t h a n t h e sim p l e p i c t u r e presented, e a r l i e r , owing tro the h i g h e r p r o b a b i l i t y o f v a r i o u s t r a n s i t i o n s . I n orde r t o o b t a i n p o p u l a t i o n i n v e r s i o n u s i n g a s i n g l e gas, some a d d i t i o n a l r u l e s must be observed. Suppose t h a t l a s e r a c t i o n i s r e q u i r e d between l e v e l s E^ and E 2„ Under t h e r m a l e q u i l i b r i u m c o n d i t i o n s , the popu-l a t i o n s a r e g i v e n b y 1 1 ; _2 _2, exp ( - 3 2 ) H 2 T 2 9j± kT where 1*. = Spontaneous r a d i a t i o n l i f e t i m e o f t r a n s i t i o n s between l e v e l E^ and the ground l e v e l ( i=3,2 ). = T r a n s i t i o n l i f e t i m e of an atom g o i n g from l e v e l E^ t o the ground l e v e l when the atom i s s u b j e c t e d o n l y t o c o l l i s i o n s w i t h e l e c t r o n s of a g i v e n d e n s i t y i n e q u i l i b r i u m amongst themselves a t temperature T. T h i s f o r m u l a assumes t h a t t h e r e i s no d i r e c t i n t e r -a c t i o n between l e v e l s E^ and E 2 , but between these l e v e l s and the ground l e v e l , E.^. F o r the p o p u l a t i o n of E^ t o exceed t h a t of E 2 , i . e . H 2 ?21 > f 2 i '(2.D 72^ T 3 14 I n t h e case of t r a n s i t i o n s a l l o w e d by t h e S e l e c t i o n Q R u l e s , the r a t i o • i l i s the same f o r a l l i * . C l e a r l y t h e n , r i i n a s i n g l e " gas, p o p u l a t i o n i n v e r s i o n i s i m p o s s i b l e t o o b t a i n u n l e s s t h e l e v e l E g i s not r a d i a t i v e l y connected t o ground by p e r m i t t e d t r a n s i t i o n s . I n such an event, T cannot be a f f e c t e d by r e a b s o r p t i o n of spontaneous e m i s s i o n . T^, on the o t h e r hand, can s t i l l be so a f f e c t e d . I f the gas d e n s i t y were i n c r e a s e d , r e a b s o r p t i o n due t o s t i m u l a t i o n by photons e m i t t e d by o t h e r gas can become im p o r t a n t enough t o decrease T-^. Thus, i n o r d e r t o get N^>Ng, a h i g h d e n s i t y o f gas i s r e q u i r e d . I n a r e a l gas, the presence of o t h e r energy l e v e l s b e s i d e s the t h r e e u s e d - f o r the above elementary a n a l y s i s can l e a d t o c o m p l i c a t i o n s . Atoms u n d e r g o i n g t r a n s i t i o n s from these l e v e l s can p o p u l a t e t h e lower l e v e l i n p r e f e r e n c e t o E^. The p o p u l a t i o n i n v e r s i o n w i l l t h e n be l o s t . F o r t h i s r e a s o n , gas d i s c h a r g e l a s e r s i n v o l v i n g a monatomic gas i n w h i c h p o p u l a t i o n i n v e r s i o n i s t o be a c h i e v e d s o l e l y be e l e c t r o n impact are c o m p a r a t i v e l y r a r e . I n a few n o t a b l e c a s e s , Neon, K r y p t o n , 12 Argon and Xenon , t r a n s i t i o n s have indeed been observed. With two gases p r e s e n t i n the d i s c h a r g e , and i f an energy l e v e l of one gas i s n e a r l y the same as an energy l e v e l o f t h e o t h e r , p o p u l a t i o n i n v e r s i o n i s more r e a d i l y o b t a i n e d . *A c o n c l u s i o n drawn by B.A. Lengyal"*""'" from the Quantum Theory of T r a n s i t i o n s . 15 F o r a mixture- of two gases, a and b, the energy l e v e l s a r e : gas a: E l = 0 , Eg, E^. gas b: E-^  = 0 , E^ = E^ o f gas a. The c o n d i t i o n f o r p o p u l a t i o n i n v e r s i o n is"*""*": > T 32 where the 9's a r e s t i m u l a t e d t r a n s i t i o n l i f e t i m e s and the T's are spontaneous t r a n s i t i o n l i f e t i m e s , and 1 = _1_ + _1_ ^3 ~^ 31 ^32 t, = l i f e t i m e of t r a n s i t i o n s a t l e v e l E^ between the ba 3 two gases. The Helium-Neon l a s e r i s a t y p i c a l example o f such 7 a system . 2.2.4 I n e l a s t i c Atom-Atom C o l l i s i o n " * " ^ I n a d i a t o m i c gas, p o p u l a t i o n i n v e r s i o n may-be o b t a i n e d i n one atom, Y, w i t h l a s e r a c t i o n a p p r o p r i a t e t o the s p e c t r o -s c o p i c c o n f i g u r a t i o n of t h a t atom. The p r o c e s s may s t a r t w i t h the o t h e r atom, X, i n an e x c i t e d s t a t e , X*, and t h i s e x c i t a t i o n may be t r a n s f e r r e d t o Y by c o l l i s i o n s . X* + Y Y* + X + AE 16 The energy d i f f e r e n c e , - AE, may he absorbed by the w a l l s or i n f u r t h e r c o l l i s i o n s . The p r o c e s s i s net w e l l known, but may he., e x p l a i n e d i n terms of the p o t e n t i a l energy c u r v e s . u ( R ) X* ,Y AE X , Y * R o D i s t a n c e between atoms, R F i g u r e 2 . 2 H y p o t h e t i c a l P o t e n t i a l Energy Curves The p o t e n t i a l energy c u r v e s of the two system (X*,Y) and (X,Y*)" are shown i n f i g u r e 2 . 2 . A t some c r i t i c a l d i s t a n c e R Q between the"" two atoms,- t h e r e i s a c e r t a i n p r o b a b i l i t y t h a t the system" (X*,Y) can s w i t c h over t o the system (X,Y* ) . The atom Y* w i l l t h e n r e v e r t t o i t s u n e x c i t e d s t a t e w i t h the e m i s s i o n o f r a d i a t i o n . Note t h a t t h e atom X* may a l s o y i e l d l a s e r a c t i o n i n r e v e r t i n g t o an u n e x c i t e d s t a t e , but the output may not f a l l w i t h i n t h e d e s i r e d d e t e c t i o n range of f r e q u e n c i e s . Otherwise, i t s i m p l y r e v e r t s by n o n - r a d i a t i v e t r a n s i t i o n s . F o r "new" gases t h i s phenomenon cannot be p r e d i c t e d , s i n c e the p o t e n t i a l energy c u r v e s are not known. 2.2.5 D i s s o c i a t i v e E x c i t a t i o n T r a n s f e r 17 T h i s c o n s i s t s of an e x c i t e d atom c o l l i d i n g w i t h a m o l e c u l e , r a i s i n g the molecule t o an e x c i t e d s t a t e , which sub-s e q u e n t l y f l i e s a p a r t w i t h t h e e m i s s i o n o f energy, r a d i a t i v e or o t h e r w i s e . X* + Y 2 ~ Y* + Y + X + AE The e x c i t e d atom Y* w i l l y i e l d the d e s i r e d l a s e r a c t i o n . A g a i n , v e r y l i t t l e i s known about t h i s mechanism and when e x a c t l y i t i s a p p l i c a b l e . I t c e r t a i n l y w i l l be i n v o l v e d when a m o l e c u l a r gas i s . e x c i t e d by a d i s c h a r g e . 2.3 L i n e w i d t h The l a s e r system c o n s i s t s o f the i n t e r a c t i o n between two reson'ant systems: the t r a n s i t i o n s and the c a v i t y . Each o f thes e has i t s own c e n t e r f r e q u e n c y and resonance c u r v e s . The resonance of the t r a n s i t i o n system i s c h a r a c t e r i z e d by the fr e q u e n c y of t r a n s i t i o n and the l i n e w i d t h . E v e r y t r a n s i t i o n has a n a t u r a l l i n e w i d t h . T h i s f o l l o w s as a r e s u l t o f the U n c e r t a i n t y P r i n c i p l e AE . At £s _h 2at where AE = spread of.energy l e v e l s due t o l i n e w i d t h , At - l i f e t i m e i n a g i v e n s t a t e , = _ 1 _ Amn A = spontaneous e m i s s i o n c o e f f i c i e n t , mn ^ 18 T h e r e f o r e , Af = AE = fmn h 2* - l i n e w i d t h The n a t u r a l l i n e w i d t h i s g e n e r a l l y v e r y s m a l l , of the o r d e r of a few h e r t z . I n a gas, the m o l e c u l e s a re i n p e r p e t u a l m o t i o n and t h i s has the e f f e c t of b r o a d e n i n g t h i s l i n e w i d t h . There are two mechanisms which a c h i e v e t h i s : (a) Doppler B r o a d e n i n g and (b) P r e s s u r e Broadening. D o p p l e r B r o a d e n i n g i s a consequence of the random r e l a t i v e m o t i o n o f t h e m o l e c u l e s , o f m o l e c u l a r w e i g h t , M, w i t h 13 r e s p e c t t o the o b s e r v e r . T h i s g i v e s a l i n e w i d t h : Af = 1.48 v f = 7.15 x 10"7/TY f (2.2) - mn \m) m n A s m a l l m o d i f i c a t i o n t o t h i s can be made i f t h e mole-c u l e s a r e i o n i z e d and a c c e l e r a t e d by t h e e x c i t i n g p o t e n t i a l . P r e s s u r e B r o a d e n i n g i s a g e n e r a l term f o r b r o a d e n i n g caused by i n t e r - m o l e c u l a r c o l l i s i o n s . A t low p r e s s u r e , .Af = _ l where. T = mean time between c o l l i s i o n s , = 1 nv N = m o l e c u l a r d e n s i t y , v = mean v e l o c i t y of c o l l i d i n g m o l e c u l e s , a - = c o l l i s i o n c r o s s s e c t i o n , 2 •-= Ttb h = m o l e c u l a r d i a m e t e r . T h e r e f o r e , A-f = Hvb 2 (2.3) At a f i x e d temperature,- N v a r i e s w i t h p r e s s u r e and v and b are c o n s t a n t . Hence, Af i s p r o p o r t i o n a l t o p r e s s u r e . 19 With v a r y i n g temperature, t h e v a r i a t i o n o f Af i s c o m p l i c a t e d s i n c e n-^, v and even b are temperature dependent. C o l l i s i o n s w i t h tube w a l l s a l s o have a b r o a d e n i n g e f f e c t i f the dimensions of the tube a re o f the o r d e r o f the mean f r e e p a t h . The l i n e w i d t h i s g i v e n by Af = 20 (TV KHz (2.4) r \Mj where r = tube r a d i u s , i f the mean f r e e p a t h , 1, i s s m a l l compared t o r . The mean f r e e p a t h , 1, i s g i v e n by I = 1 2jtb2R where N = m o l e c u l a r dens i t y = % P, (2.5) RT 23 where N = A v o g a d r o 1 s number = 6.023 x 10 , P = P r e s s u r e , R = U n i v e r s a l gas c o n s t a n t , = 8.32 j o u l e s / m o l e °k, T = Temperature o f gas 400 °k, y i e l d s N = 3.21 z 1 0 1 6 molec/cnr 5, f o r P = 1mm I f t he m o l e e u l a r d i a m e t e r s a re o f t h e o r d e r of an Angstrom, I = 7.2 x 10" 2 cm. I f the tube r a d i u s i s o f the o r d e r of a few c e n t i m e t e r s , i t i s .much l a r g e r t h a n I . I n such a case, the l i n e w i d t h due t o c o l l i s i o n s w i t h w a l l s w i l l be s m a l l e r t h a n g i v e n by e q u a t i o n (2 .4) . The v a r i o u s l i n e w i d t h s g i v e n by eq u a t i o n (2 .2) , (2 .3) , (2.4) are g i v e n i n Ta b l e 2-1, showing l i n e w i d t h s v e r s u s mole-c u l a r w e i g h t. C o l l i s i o n l i n e w i d t h s are o b t a i n e d assuming r = 4 cm. 20 Table 2-1 l i n e w i d t h v s M o l e c u l a r Weight, M M < A f'walls ( A f ) p r e s s ^A f ^ D o p p l e r (approx) f =3xl0 1 I L mn f =10 1 2 mn (KHz) (KHz) (MHz) (MHz) 5 46.5 319 1.92 19-15 10 .32.1 240 1.36 13-55 15 27 . 0 196 1.11 11.05 20 23.4 170 0.97 9.68 25 20.9 152 0.86 8.57 30 19.1 139 0.78 7.83 35 17.7 130 0.74 7.36 40 16 . 5 120 0.68 6.78 45 15.6 113 0.64 6.38 50 14. 8 112 0.61 6.06 Note: ( A f ) i s a t p=l T o r r . F o r l o w e r p, ( A f ) v p r e s s * ^' 'pres i s p r o p o r t i o n a t e l y d ecreased. F o r H 20, f m n = 2.54 x 1 0 1 2 , ( A f ) d o p p = 8.55 MHz. f = 1.37 x 1 0 1 2 , ( A f ) , = 4.6 MHz. mn ' v ydopp From Table 2-1, i t i s apparent t h a t the Doppler e f f e c t i s the predominant l i n e b r o a d e n i n g e f f e c t i n gases o p e r a t i n g at low p r e s s u r e s . A t h i g h e r p r e s s u r e s , N i n e q u a t i o n (2.3) would i n c r e a s e t o f u r t h e r broaden the l i n e . There a r e o t h e r b r o a d e n i n g mechanisms which a r e weak 15 i n gases, but are predominant i n s o l i d s . The s p i n - s p i n i n t e r -a c t i o n and d i p o l e - d i p o l e i n t e r a c t i o n can broaden the l i n e much more t h a n can the Do p p l e r e f f e c t and make the s o l i d m a t e r i a l 21 s u i t a b l e f o r r a d i a t i v e pumping. These e f f e c t s f a l l o f f r a p i d l y as t h e p a r t i c l e s p a c i n g s i n c r e a s e . " The e f f e c t of the D oppler w i d t h on the l a s e r output w i l l be d i s c u s s e d l a t e r . At t h e moment, i t s u f f i c e s t o say t h a t the o r d i n a r y sources o f r a d i a t i o n cannot s u p p l y s u f f i c i e n t i n t e n s i t y w i t h i n a range o f f r e q u e n c i e s e q u a l t o the Doppler w i d t h t o i n c i t e l a s e r a c t i o n . The o n l y way t o i n c i t e l a s e r a c t i o n i s t h e n by a gaseous d i s c h a r g e . 2.4 G-aseous D i s c h a r g e W i t h one n o t a b l e e x c e p t i o n , t h a t of Cesium"""'"', l a s e r a c t i o n i n gases has been o b t a i n e d u s i n g a gaseous d i s c h a r g e . A l l -of the e x c i t a t i o n mechanisms d e s c r i b e d above have beepi c a l l e d i n t o p l a y t o v a r y i n g e x t e n t s and s t i m u l a t e d e m i s s i o n has been a c h i e v e d a t a l a r g e number of f r e q u e n c i e s . I t i s t h e r e -f o r e s a f e t o say, t h a t i f l a s e r a c t i o n i s g o i n g t o be o b t a i n e d from some gas w i t h unknown s p e c t r o s c o p i c c o n f i g u r a t i o n , i t w i l l c e r t a i n l y be o b t a i n e d i n a gaseous d i s c h a r g e . The frequency o f the e m i t t e d r a d i a t i o n i s of .course unknown, but i t can be determined u s i n g a p p r o p r i a t e d e t e c t i n g d e v i c e s . A gas can be caused t o d i s c h a r g e by a p p l y i n g a p o t e n t i a l a c r o s s the tube, c a u s i n g the gas t o break down i n t o a plasma s t a t e . The p o t e n t i a l can be i n one of t h r e e forms: (1) r f (2) dc (3) P u l s e d As a r e s u l t of t h e s e , a c u r r e n t i s caused t o pass t h r o u g h t h e d i s c h a r g e , and energy i s absorbed by t h e gas system. 22 Of the t h r e e methods of i n d u c i n g a d i s c h a r g e , the p u l s e method i s p r e f e r r e d s i n c e i t has t h e p o t e n t i a l o f g r e a t e r e x p e r i m e n t a l v e r s a t i l i t y . I f a p u l s e of s h o r t d u r a t i o n i s a p p l i e d , i t i s p o s s i b l e " t o o b t a i n the v a r i a t i o n of output power a f t e r the a p p l i -c a t i o n of the p u l s e w i t h the h e l p o f a f a s t - r e s p o n s e d e t e c t o r , (See s e c t i o n on d e t e c t o r s ) . T h i s would y i e l d i n t e r e s t i n g i n f o r -m a t i o n of l i f e t i m e s o f t r a n s i t i o n s and the e f f e c t of the i n t e r -a c t i o n between th e atoms or m o l e c u l e s of the gas. There a r e c e r t a i n t r a n s i t i o n s w i t h h i g h g a i n t h a t can be e x c i t e d o n l y by p u l s e d d i s c h a r g e . These a r e c a l l e d S e l f - T e r m i n -a t i n g t r a n s i t i o n s . T h e s e a r e t r a n s i t i o n s t h a t occur somewhat c l o s e r t o the ground than t h e u s u a l l a s e r t r a n s i t i o n s , and t h e l o w e r l e v e l may be m e t a s t a b l e ( i . e . , l o n g l i v e d ) . L a s e r a c t i o n i s o b t a i n e d by momentary i n v e r s i o n among low energy l e v e l s d u r i n g a f a s t p u l s e , and t h e n t e r m i n a t e d as soon as the l o w e r s t a t e b u i l d s up an a p p r e c i a b l e p o p u l a t i o n . Because o f the p r o x i m i t y of t h e ground s t a t e , and because of f a v o r a b l e e x c i t a t i o n f u n c t i o n s t o the l a s e r l e v e l from t h e ground s t a t e , a v e r y h i g h p o p u l a t i o n i n v e r s i o n c a n be b u i l t up i n a s h o r t t i m e . 23 3. RESONATOR DESIGN 3•1 I n t r o d u c t i o n I n the p r e v i o u s c h a p t e r i t was shown t h a t t h e l a s e r gas medium i s an a m p l i f i e r . I t has a c e n t e r f r e q u e n c y of operation., where t h e g a i n i s a maximum, and a bandwidth. W i t h an a p p r o p r i -a t e feedback system, t h i s a m p l i f i e r can be caused t o operate as an o s c i l l a t o r . Such a feedback system can be f u r n i s h e d by con-t a i n i n g "the gas i n a g l a s s tube and p l a c i n g m i r r o r s a t e i t h e r end. . R a d i a t i o n w h i c h t r a v e r s e s t h e l e n g t h of t h e tube would be a m p l i f i e d by the gas, and r e f l e c t e d by the m i r r o r s , and would t r a v e r s e the medium once a g a i n . I n the p r o c e s s the r a d i a t i o n would be f u r t h e r a m p l i f i e d . At the same time i t would i n c u r l o s s e s . A f t e r a f i n i t e number of r e f l e c t i o n s , a s t e a d y s t a t e f i e l d p a t t e r n w i t h i n the tube would be e s t a b l i s h e d . T h i s c h a p t e r w i l l d i s c u s s the e f f e c t o f the m i r r o r s , and how the s e can be used t o d e s i g n a l a s e r which would operate w i t h i n the f a r i n f r a - r e d r e g i o n . The c h a p t e r d e a l s f i r s t w i t h the t h e o r y and t h e n w i t h the p r a c t i c a l d e s i g n of. the c a v i t y . The t h e o r e t i c a l p a r t i s l a r g e l y q u a l i t a t i v e and o n l y those f o r m u l a s which, are. i n v o l v e d , in.' the c a v i t y des ign-.;are - quoted. 3.1.1 O r t h o g o n a l Modes and Resonance C o n d i t i o n s The l a s e r tube may be regard e d as a resonant c a v i t y i n the same sense as a c l o s e d copper box w i t h p o l i s h e d i n n e r w a l l s i s a microwave c a v i t y . The d i f f e r e n c e i s t h a t whereas t h e l a t t e r i s o f t h e o r d e r of a few wavelengths l o n g , the former i s of t h e o r d e r o f many thousands. An e x t r e m e l y l a r g e number 24 of c a v i t y resonances may c o n s e q u e n t l y be i n v o l v e d i n a l a s e r c a v i t y . These resonances a r e s u s t a i n e d by t h e presence o f the a m p l i f y i n g medium,, which c o u n t e r b a l a n c e s the l o s s e s i n h e r e n t i n the system. The l o s s e s a r e caused by i n h o m o g e n e i t i e s i n the medium, r e f l e c t i o n o f f m i r r o r s w i t h f i n i t e c o n d u c t i v i t y ; , and d i f f r a c t i o n over the edges of t h e m i r r o r s . 16 Pox and L i showed t h a t a s t e a d y s t a t e c o n d i t i o n i s reached a f t e r many r e f l e c t i o n s . I n t h i s s t a t e , the r a d i a t i o n f i e l d e x i s t s i n an i n f i n i t y o f near o r t h o g o n a l modes c a l l e d TEM modes. These modes a r e c h a r a c t e r i s e d by t h e i r t r a n s v e r s e f i e l d p a t t e r n s and a r e a s s i g n e d s u b s c r i p t s m and n, which a r e i n t e g e r s . The modes are t h e n n o t a t e d TEM modes. The f i e l d ° mn of the l o w e s t mode, TEMQQ, i s c o n c e n t r a t e d n e a r e r t o t h e a x i s t h a n a r e the f i e l d s o f h i g h e r o r d e r modes. Hence,, w i t h m i r r o r s of f i n i t e d i m e n s i o n s , energy l o s s e s due t o d i f f r a c t i o n over m i r r o r edges, i s l o w e s t f o r the TEM^Q mode. The o t h e r l o s s e s a re e q u a l l y h i g h f o r a l l modes w i t h i n a wide f r e q u e n c y range.-D i f f r a c t i o n l o s s e s i n a l l modes depend on the a c t u a l c a v i t y c o n f i g u r a t i o n , namely t h e s i z e of the tube and the shape of the m i r r o r s o There a r e s e v e r a l m i r r o r shape c o n f i g u r a t i o n s t h a t can be and have been used f o r l a s e r c a v i t i e s . Among t h e s e are b o t h m i r r o r s p l a n e ; b o t h concave; one plane and one concave or convex; one concave and t h e o t h e r convex. Of these c o n f i g u -r a t i o n s , the concave-concave i s known t o have the minimum d i f f r a c t i o n l o s s e s f o r the dominant mode (TEMQQ u s u a l l y ) , f o r the same i n t e r - m i r r o r d i s t a n c e and m i r r o r s i z e . Pox and L i 17 and D.E, McCumber have computed d i f f r a c t i o n l o s s e s f o r some low o r d e r modes i n c o n f o c a l c a v i t i e s • ( c a v i t i e s whose m i r r o r 25 spacing equals the radius of curvature of t h e i r m i r r o r s ) . McCumher's r e s u l t s are reproduced i n the graph on page.26, f i g u r e 3°1* The graph shows that the d i f f r a c t i o n l o s s e s decrease wi t h i n c r e a s i n g F r e s n e l Number N. For the symmetrical confocal cavity," N is..given" by N = _a£ (3.1) b\ where a = radius of mi r r o r apertures b = radius of curvature of the mirror s = length of tube A. = wavelength This inverse dependence of d i f f r a c t i o n l o s s on Fr e s n e l number i s confirmed by other workers, such as Boyd and 18 Gordon . F i e l d amplitudes and f i e l d i n t e n s i t i e s f o r v a r i o u s modes f o r .different.values of 'N have beer., evaluated by authors of references 16, 17 and 18. As N increases, the mode f i e l d i s compressed nearer the a x i s . This r e s u l t s i n a decrease i n losses over the mi r r o r edges, ( i . e . d i f f r a c t i o n l o s s e s ) . Figure 3.1 can al s o be used to determine d i f f r a c t i o n l o s s e s i n a non-confocal c a v i t y . Boyd and Gordon have defined an equivalent confocal c a v i t y f o r a non-confocal c a v i t y . They base t h e i r d e f i n i t i o n on a quantity c a l l e d the "Spot S i z e " . At any c r o s s - s e c t i o n of the tube and w i t h i n a radius small compared to the mir r o r r a d i u s , the r a d i a t i o n amplitude drops e x p o n e n t i a l l y away from the tube a x i s . The: .spot s i z e i s defined as the •.:.;.<:• distance from the a x i s t o the point where the amplitude f a l l s to l / e of i t s value at the a x i s . For symmetrical, concave, non-confocal c a v i t i e s , the spot s i z e at the mirror w i s 26 F i g u r e 3.1 D i f f r a c t i o n Losses f o r Low Order Modes 27 g i v e n by: w = s it 2d - [d b lb 2' (3.2) where b = r a d i u s of c u r v a t u r e of both m i r r o r s d = s e p a r a t i o n of m i r r o r s and b ^  d„ E q u a t i o n (3.2) i s v a l i d o n l y i f w «.'a. s Wi t h a g i v e n d, w i s a minjjnum. for . :.the- c o n f o c a l case s (b=d) and i s g i v e n bys w = bA (3.3) • s * Since w i s a" minimum ,.-f orhthe. c o n f o c a l case i/.the..'.dif-s • ' f r a c t i o n l o s s e s a r e a l s o s m a l l e s t f o r t h a t case. For the n o n - c o n f o c a l c a v i t y , an e q u i v a l e n t P r e s n e l Number can be d e r i v e d so t h a t N = a l a 2 |~2d - |d\ 2~|^ ' (3.4) d\ \ b j J where, a,-^,^ = r a d i i of m i r r o r a p e r a t u r e s d = m i r r o r s e p a r a t i o n b = r a d i u s of c u r v a t u r e of the two m i r r o r s . The d i f f r a c t i o n l o s s can then be determined from f i g u r e 3.1 u s i n g t h i s v a l u e of N» A s i d e from i n c u r r i n g d i f f r a c t i o n l o s s per r e f l e c t i o n , t h e r a d i a t i o n s u f f e r s a phase s h i f t . Here a l s o t h e modes are i n v o l v e d . Boyd and Gordon show t h a t the c o n d i t i o n f o r resonance i s t h a t the round t r i p phase s h i f t be 2it times an i n t e g e r . q w hich has v a l u e s z e r o t h rough i n f i n i t y . T h i s c o n d i t i o n imposes a r e l a t i o n s h i p between mP n, q and the wavelength. A...... A g a i n , t h i s phase r e l a t i o n s h i p depends on the c a v i t y c o n f i g u r a t i o n . 28 For the general concave-concave case, the phase r e l a t i o n ship i s : 4_d = 2q + (1 + m + n ) ( l - 4 t a n " 1 h^d) (3.5) A. % h+d From equation(3.5 ;) »it i s found that the various modes do not, i n general, operate at the same frequency. Two modes would operate at the same wavelength, A., i f A. = 4d = 4d 2 q^+ (l+m^+n-j^ ) K 2^TTl+m^+n^7K K= 1 - 4_ t a n - 1 b^d (3.6) Tt h+d (q!-<l 2) = 4-K (-(m2+n2) - ( m ^ ^ ) ) = iK(A(m + n))(3.7) Since q^ and q 2 are i n t e g e r s , the q u a n t i t y , -£-K(A(m+n)) must also he an in t e g e r . I f A(m+n) i s an odd i n t e g e r , then K must he an even i n t e g e r . However, f o r K to he even, b=0 or.d=0, n e i t h e r of which cases are i n t e r e s t i n g . Therefore, i t i s not pos s i b l e f o r two modes whose A(m+n) i s an odd intege r to be resonant at the same frequency. On the other hand, two modes whose A(m+n) i s an even integ e r may be. simultaneously resonant, since now K i s permitted to be an odd i n t e g e r . When K has the odd inte g e r v a l u e s , l - 4 r , ( r=0,l,2 53. . . . , ) „ then, d=b', .which i s , course, the confocal case. Thus, i n the confocal case, a l l transverse modes (TEM ) whose (m+n) i s even operate at one mn * frequency, while those whose (m+n) i s odd a l l operate at some crther frequency. I f K were to d i f f e r s l i g h t l y from an i n t e g e r , as i t does i n the non-confocal case, two modes would not operate at the same frequency, unless t h e i r (m+n)'s were the same. Their 29 frequencies, however, may he very close to each other, the proximity being determined by the f a c t o r b-d. Thus, the modes b+d may be regarded as i n d i v i d u a l resonators, each operating at some c e n t r a l frequency, f n« The Q's of these resonators are given by: Q = 2fffmn E '(3.8) Pd where E = energy stored i n the mode, P^= rate of energy d i s s i p a t i o n i n mode per t r a n s i t . Note that the mode resonators a l s o have harmonic frequencies, owing to the i n t e g e r , q. These are spaced by: (from equation (3.2)) Af = c_- , c = speed of l i g h t i n a vacuum (3.9) " 2d 3.1.2 I n t e r a c t i o n between Ca v i t y Modes and Am p l i f y i n g Medium 'In the l a s e r c a v i t y , a complicated i n t e r a c t i o n takes place between the a m p l i f y i n g medium and an i n f i n i t y of resonant modes with''"characteristics f and Q . The medium has charac-- mn mn t e r i s t i c s f ^ and l i n e w i d t h Af^. Prom equation ( 3 . 8 ) , the, Q's of s e v e r a l modes are very high, p a r t i c u l a r l y the lower order modes. The l i n e w i d t h of the gas i s determined by the Doppler e f f e c t and t h i s i s g e n e r a l l y much wider than Af . There i s mn hence a complicated coupling among the. various.resonant systems ( i . e . , the medium and the modes) i n which energy i s given up by the system w i t h the greater energy and lower Q to those with l e s s energy and higher Q. Thus the modes are fed with energy by the medium. The mathematics of the coupling 19 between resonant systems, obtained by Wagner and Birnbaum, , 30 describes the manner i n which energy i s fed i n t o the v a r i o u s modes. A q u a l i t a t i v e a n a l y s i s w i l l s u f f i c e here. z Medium Resonance Curve Mode Resonance Curves fmn f o Figure 3-2 Medium-Mode Coupling In f i g u r e 3.2, the resonance curves of s e v e r a l modes are shown. Assuming that coupling among the orthogonal modes i s n e g l i g i b l e , the modes w i l l be coupled to the medium. Energy w i l l be coupled from the medium to a mode, depending on the Q m n of that mode as w e l l as the d i f f e r e n c e , |^o~^mnl " R e f e r r i n g to equation (3.8) t h i s means that most of the energy i s fed i n t o the modes which already store most of the energy. This increases t h e i r Q with the r e s u l t that more energy i s coupled i n t o these modes. F i n a l l y , a l l the energy goes i n t o those modes which i n i t i a l l y had the highest Q and whose frequencies are nearer f o .,; The mode w i t h the highest Q i s the dominant mode, u s u a l l y TEMQQ^, since the d i f f r a c t i o n l o sses are smallest f o r 31 that mode. However, i t i s p o s s i b l e that of the t o t a l l o s s , the d i f f r a c t i o n l o s s i s n e g l i g i b l e f o r s e v e r a l modes as w e l l as, and other than, the TEM^Q^ mode. The Q's of these modes w i l l then be nearly as high as that of the dominant mode. The resonant frequencies may also be very close t o the resonant frequency of the dominant mode. Thus, the energy w i l l be coupled i n t o s e v e r a l modes and a l l of these may operate. R e f e r r i n g again to equation (3«5)» i n the confocal case,- KS=1, h=d and hence, A. = 4d (3.10) 2q +(1 + m + n) I t can he seen that s e v e r a l modes,: i n c l u d i n g the dominant mode, have the same .-..resonant frequency.- i n other words, the resonant frequency i s "mode degenerate". A f i n a l r e s u l t of the medium-mode-coupling a n a l y s i s i s that the smaller the gain, .of the medium., the fewer the] number of modes e x c i t e d . I t i s , t h e r e f o r e , p o s s i b l e to excite only the dominant mode i n both the confocal and the non-confocal cases simply by l i m i t i n g the o v e r - a l l gain experienced by the in c i d e n t r a d i a t i o n . The o v e r - a l l gain that the r a d i a t i o n w i l l experience depends on the leng t h of the tube. Thus, the le n g t h can be chosen so as to excite s e v e r a l modes, or else .only-the dominant mode. I t can be appreciated that i f the length i s too small, no modes at a l l w i l l be excited. This i s c l e a r from the view-p o i n t , mentioned e a r l i e r , that the gain must counterbalance the l o s s e s . The leng t h of the tube must, th e r e f o r e , be greater than some, minimum value. The simple a n a l y s i s above must be modified when con-s i d e r a t i o n i s given to the e f f e c t s that the presence of the am p l i f y i n g medium has on the modes. The degree of m o d i f i c a t i o n depends on the gain and the l i n e w i d t h of the t r a n s i t i o n and can be considered a source of e r r o r i n the determination of t r a n -s i t i o n frequency. Mode-pulling, f o r example, i s an e f f e c t due to the v a r i a t i o n of r e f r a c t i v e index with frequency and i t leads to modes w i t h i n the l i n e w i d t h being p u l l e d c l o s e r toward the centre frequency. The r e s u l t i s that the spacing between a x i a l modes i s no longer c / 2 b . Furthermore,, e f f e c t s such as ""hole-burning" lead to anomalous v a r i a t i o n s of power i n a given mode as the mode frequency i s s h i f t e d (by a l t e r i n g • the. m i r r o r separation) through the l i n e center. N o n - l i n e a r i t y and s a t u r a b i l i t y of gain lead t o an e f f e c t which almost c o n t r a d i c t s the simple a n a l y s i s of f i g u r e 3 - 2 . 20 21 W.W. Rigro.d found and Fox and L i confirmed that the dominant output transverse mode i s the highest order mode permitted by a near conf ocal c o n f i g u r a t i o n . The reason f o r t h i s , as given by Fox and L i i s that higher order modes have l a r g e r beam diameters than lower order modes. Thus, modes of a l l orders compete f o r molecules i n the c e n t r a l regions of the beam,, but the higher order modes can stimulate and receive energy from molecules outside the diameter of the lower order modes. I f the higher gain o f f -sets the higher l o s s , the higher order modes may not only be able to o s c i l l a t e , but may succeed i n suppressing the lower order modes by s a t u r a t i n g the gain i n the c e n t r a l region. This e f f e c t may not he v a l i d f o r i n f r a - r e d m a t e r i a l s , but even i f i t was i t i s impossible to p r e d i c t whether domination can be so 33 complete t h a t a l l l o w e r o r d e r modes w i l l he s uppressed. I t i s l i k e l y t h a t s e v e r a l modes are e x c i t e d s i m u l t a n e o u s l y , w i t h d i f f e r e n t r e l a t i v e magnitudes. Fox and L i make t h e p o i n t t h a t the t h e o r y of p a s s i v e r e s o n a t o r s gives, l o s s . v a l u e s which-.canobeausediin;;^ r e s o n a t o r . Thus i t i s p o s s i b l e t o d e s i g n a l a s e r u s i n g t h i s t h e o r y , always r e a l i z i n g t h a t the output w i l l be determined by the t h e o r y o f a g a i n - m o d i f i e d c a v i t y . The l a s e r should be s u f f i c i e n t l y l o n g t o p r o v i d e enough g a i n t o overcome l o s s e s i n a t l e a s t one mode. I t may be t h a t the a c t u a l g a i n w i l l be s u f f i c i e n t l y h i g h t o provoke e x c i t a t i o n of s e v e r a l modes s i m u l t a n e o u s l y , and i f so, the output power w i l l be -; d i s t r i b u t e d among t h e s e modes. 3.2 Resonator Tube 3.2.1 G e n e r a l C o n s i d e r a t i o n s The c a v i t y c o n s i s t s o f a c y l i n d r i c a l g l a s s tube w i t h m i r r o r s a t e i t h e r end. The parameters i n v o l v e d i n d e s i g n i n g t h i s c a v i t y are t h e l e n g t h and d i a m e t e r of the tube and the shape and dimensions of the m i r r o r s . These are c l o s e l y i n t e r -r e l a t e d and each must be designed w i t h the o t h e r s i n mind. The p r i m a r y concern i s t h a t the g a i n i n t h e medium exceed the l o s s e s i n h e r e n t i n t h e c a v i t y . However, s i n c e i t i s not p o s s i b l e t o p r e d i c t the g a i n of a g i v e n medium, the o n l y a l t e r n a t i v e i s t o draw on the e x p e r i e n c e of o t h e r e x p e r i m e n t e r s . I t w i l l be s u f f i c i e n t t o keep the l o s s e s t o a minimum and t e s t t o see i f t h e g a i n was indeed h i g h enough t o c o u n t e r these l o s s e s . The r e f l e c t i o n l o s s e s can be m i n i m i z e d by a p p r o p r i a t e c h o i c e of m i r r o r m a t e r i a l . The d i f f r a c t i o n l o s s e s can be m i n i -34 mized by u s i n g the c o n f o c a l c o n f i g u r a t i o n . There i s another v e r y v a l i d r e a s o n f o r c h o o s i n g t h i s c o n f i g u r a t i o n . T h i s i s the i m p o r t a n t p r a c t i c a l c o n s i d e r a t i o n o f m i r r o r a l i g n m e n t . I n a l a s e r c a v i t y , i t i s n e c e s s a r y t h a t the a x i s of the m i r r o r s pass t h r o u g h the l a s e r tube and t h a t i t be f a r enough away from t h e tube w a l l s t o a l l o w the TEM^Q 22 mode-room!to operat e . The e x t e n t t o which the m i r r o r a x i s can be r o t a t e d w h i l e s t i l l f u l f i l l i n g t h i s r equirement d e f i n e s t h e "Alignment T o l e r a n c e " of the m i r r o r system. D.C S i n c l a i r has used t h i s d e f i n i t i o n t o show t h a t Alignment T o l e r a n c e i s h i g h e s t f o r a c o n f o c a l m i r r o r system. The t o l e r a n c e o f t h e plan e p a r a l l e l m i r r o r system i s o f t h e o r d e r o f a hundred times worse t h a n t h a t of the c o n f o c a l c a v i t y . S i n c l a i r ' s r e s u l t s a re shown i n F i g u r e s 3-3 and 3 -4 . 0 o !H Q) H o E H CD • H O i d u H o -P • H 5! lm 100m M i r r o r Radius lm 100m Radius of Concave M i r r o r F i g u r e 3.3 Double Concave C a v i t y ( M i r r o r S e p a r a t i o n = lm) F i g u r e 3.4 Flano-Concave C a v i t y ( M i r r o r S e p a r a t i o n = lm) 35 There are, however, certain disadvantages to using a confocal cavity. One of them is that it has a very low mode volume. This is defined by: mode volume = j j rdrdedz (3.11) where w(zj = spot size at any point, z, z l ' z2 = a n y ^ W 0 P o i n ^ s o n l a s e r a x i s between which the mode volume is desired, r,9,z = are cylindrical cordinates. S i n c l a i r shows that power obtainable from the cavity depends on this mode volume. Hence, to obtain maximum power output, a cavity with maximum mode volume is desired. The smal mode volume of the confocal cavity is, therefore,, a dis-advantage. The seriousness of. this shortcoming is reduced by the requirements of this experiment - namely that the output power should merely be high enough that it can be detected. ,-, A far more critical disadvantage appears when the 23 s t a b i l i t y of the cavity is considered. Boyd and Kogelnik have defined "unstable regions" as the ranges of mirror .sepa-r a t i o n , d, in which the diffraction losses are high. . They have proved the existence of these ranges. Their stability diagram is reproduced in figure 3-5. In figure 3-5, it is apparent that the confocal point, d=b-^ =b2 is one of critical stability. An error in the radius of curvature of either mirror can prohibit laser action due to high diffraction loss. Hence, the mirror separation for a system with identical mirrors should have d^b. However, the Reparation (d-b) should not be too large, since the confocal 36 system s t i l l y i e l d s minimum d i f f r a c t i o n l o sses as w e l l as maximum alignment tolerance,, Figure 3.5 S t a b i l i t y Diagram I t has now been resolved that the m i r r o r c o n f i g u r a t i o n should be near-confocal. I t remains to determine the a c t u a l dimensions of the tube. As was stated e a r l i e r , these can only a r b i t r a r i l y be chosen, on the experience of others„ However, some d i s c u s s i o n of the f a c t o r s involved i s useful,. 1. Lengths In s e c t i o n 3 ° l ° l s > i t was stated that the gain was p r o p o r t i o n a l to the tube length. A l s o , from \. McCumber's r e s u l t s ( f i g u r e 3-1), the d i f f r a c t i o n losses i n -crease as the Fre s n e l Number, B, decreases, H i s given f o r a symmetrical confocal system by: N = a£ ' (3.1) b\ 2a = diameter of m i r r o r b = distance between m i r r o r s . 37 I f the m i r r o r d i a m e t e r , 2a, i s chosen the same as the tube d i a m e t e r , and t h e i n t e r - m i r r o r d i s t a n c e about the same as the tube l e n g t h , t h e n , c l e a r l y , the d i f f r a c t i o n l o s s e s a r e r o u g h l y p r o p o r t i o n a l t o the tube l e n g t h . Hence t h e tube l e n g t h must be a compromise between g a i n and d i f f r a c t i o n l o s s , 2o Diameter: The tube d i a m e t e r can be determined i f the l e n g t h o f t h e tube and the p e r m i s s i b l e d i f f r a c t i o n l o s s e s are known. I n d e t e r m i n i n g the p e r m i s s i b l e d i f f r a c t i o n l o s s , i t must be remembered t h a t the l a s e r c a v i t y i s r e q u i r e d t o s e r v e over the wavelength range of 0,1 mm t o 1,0 mm. D e s i r a b l y , >the•: d i f -f r a c t i o n l o s s e s should, be w e l l below th e m i r r o r r e f l e c t i o n l o s s e s over t h i s range, so as not t o add a p p r e c i a b l y t o the o v e r -a l l l o s s of the c a v i t y . Prom the e x p r e s s i o n , (3.1), f o r t h e F r e s n e l Number, i t i s seen t h a t the l o s s e s decrease w i t h i n -c r e a s i n g m i r r o r r a d i u s , a. However, the m i r r o r r a d i u s , a, cannot be chosen to be of an i n d e f i n i t e l y l a r g e s i z e , L a s e r a c t i o n depends on the number of p a r t i c l e s t h a t can be i n d uced i n t o an i n v e r t e d popu-l a t i o n s i t u a t i o n , which depends on the c u r r e n t d e n s i t y o f the discharge., w h ich, i n t u r n , i s i n v e r s e l y p r o p o r t i o n a l t o the a r e a o f c r o s s - s e c t i o n o f the tube, . I t i s , t h e r e f o r e , d e s i r a b l e t o keep t h i s a r e a t o a minimum. Thus the r a d i u s ? a, s h o u l d be chosen as a compromise between c u r r e n t d e n s i t y and d i f f r a c t i o n l o s s , 3. C o u p l i n g s Output c o u p l i n g e n t e r s i n t o the d e s i g n o f t h e c a v i t y because i t r e p r e s e n t s a source of l o s s . F u r t h e r d i s c u s s i o n o f t h i s i s g i v e n i n the next c h a p t e r 9 b u t , f o r the 3§ p r e s e n t , l e t i t be s t a t e d t h a t a s m a l l a p e r t u r e i n one of the m i r r o r s w i l l a l l o w some of the power t o emanate from t h e c a v i t y to a d e t e c t i n g a p p a r a t u s . The e f f e c t of t h i s a p e r t u r e w i l l be t o d i s t u r b the mode f i e l d c o n f i g u r a t i o n i n s i d e the c a v i t y . 17 However, a c c o r d i n g t o D.E. McCumber, i f t h i s a p e r t u r e i s kept s m a l l compared t o m i r r o r s i z e , . t h e ' e f f e c t ' w i l l ' be a small, p e r -t u r b a t i o n . The t r a n s m i s s i o n c o e f f i c i e n t w i l l t h e n s i m p l y he t h e r a t i o o f t h e a p e r t u r e a r e a t o the a r e a determined by t h e spot s i z e , i . e . T = ( r / w ) 2 (3.12) where T = t r a n s m i s s i o n c o e f f i c i e n t , r = r a d i u s o f a p e r t u r e . a ' w = spot s i z e , s E q u a t i o n (3.12) i s p r i m a r i l y a p p l i c a b l e t o the dominant mode. C e r t a i n modes may not even be t r a n s m i t t e d . T h i s i s because of the p a r t i c u l a r f i e l d p a t t e r n o f t h e s e modes, as w i l l be f u r t h e r mentioned i n the c h a p t e r on c o u p l i n g and d e t e c t i o n . 24-E q u a t i o n (3.12) was f i r s t used by P a t e l e t a l . 3.2.2 Dimensions I n the p r e v i o u s s e c t i o n , the t h e o r e t i c a l c o n s i d e r a t i o n s i n the c h o i c e of dimensions were g i v e n . S i n c e the g a i n c h a r a c t e r i s t i c s of any g i v e n l a s e r gas medium a r e unknown, the d e s i g n c o n s i d e r a t i o n s reduce t o c h o o s i n g a c o n v e n i e n t l a s e r l e n g t h and thence d e t e r m i n i n g the o t h e r l a s e r parameters. I n o r d e r t o s t a r t from some base, a l o o k a t works done by o t h e r e x p e r i m e n t e r s i s h e l p f u l . 25 A k i t t et a l have d e s c r i b e d a water vapor l a s e r 39 2 6 o p e r a t i n g a t 118 micr o n s wavelength. F l e s h e r and M u l l e r have a l s o d e signed a l a s e r w i t h which t h e y obtained:.::laserqactiohnin water vapor a t wavelengths 79m 118u, and 2 20u. They a l s o were a b l e t o d e t e c t s u h m i l l i m e t e r l i n e s i n D^O a t 84M., 108p,, and 117 and i n CH^CN a t 313^ and 337(i. T able 3-1 g i v e s a summary-comparison o f the two l a s e r s o I n t h i s t a b l e , d i f f r a c t i o n l o s s e s are i n d i c a t e d w i t h a dash i f t h e y a r e n e g l i g i b l e (<0v01%) compared t o the r e f l e c t i o n l o s s e s (~2%). Table 3-1 S u h m i l l i m e t e r Gas L a s e r s Reference R e f e r e n c e P r e s e n t 25: 26 Desig] Tube Length •3.66 m 2. 15: im 2.44; ii Tube Diameter 10.15 cm 7. 5 cm 7.62 < M i r r o r Diameter 10.15 cm 5. 73 cm 7.62 < M i r r o r Radius o f 4.0 m 2. 69 m 3.0 i Cu r v a t u r e P r e s n e l Number ( E q u a t i o n 2.10), =100u 6,9 3. 77 5.85 =118-1 5.85 3. 19 4.96 =220u 3.14 1. 71 2.66 =337(i 2.05 1. 12 1.74 =500\x 1.38 0. 76 1.17 =600u 1.05 0. 63 0,98 =700p. 0.98 0. 54 0,84; =800u 0.86 0. 47 0.732 =900u 0.78 0. 42 0.65 =1 mm. 0.69 0. 38 0.59 D i f f r a c t i o n Loss I n TEM n Mode, u u =100u — -=118u - -=220p. - -=337^ -=500|i — 0. 6% 0.01% =600u 0.02% 1. 5% 0.08% =700u. 0.05% 4. 5% 0.25% =800u 0.20% 8 % 0.9 % =900u 0.45% 10 % 2.5 % =1 mm 1.10% 30 % 6 % 40 Table 3-1 shows t h a t a l a s e r w i t h F r e s n e l Number between 3 = 77 and 6.9 a t A. = lOOu- can s u s t a i n l a s e r a c t i o n up t o a wavelength of a t l e a s t 400u i n H 2 © , D 20 and CH^CN. I f a gas i s suspected t o have l i n e s beyond 400p,, a F r e s n e l Number n e a r e r 6.9 a t lOOp. i s needed and whether l a s i n g w i l l o c c u r w i l l s t i l l depend on the g a i n c h a r a c t e r i s t i c s of the medium,, With the above a n a l y s i s , a l a s e r w i t h N=6 a t X - lOOp, was aimed f o r . A heavy g l a s s tube, 3 i n c h e s i n s i d e d i a m e t e r and 72 i n c h e s l o n g , was r e a d i l y a v a i l a b l e and was c o n s i d e r e d to be a c o n v e n i e n t s i z e f o r t h e l a b o r a t o r y o p e r a t i o n s . A l o n g w i t h g l a s s Tees connected t o the ends of t h i s t u b e , t h e m i r r o r s p a c i n g can be a r r a n g e d t o be 96 i n c h e s or 2.44 meters. A n e a r - c o n f o c a l m i r r o r system i s d e s i r e d and a c o n v e n i e n t m i r r o r r a d i u s o f c u r v a t u r e i s t h r e e meters. Consequently, two concave m i r r o r s , 3 i n c h e s i n diameter and 3 meters r a d i u s of c u r v a t u r e were o b t a i n e d . They are made o f q u a r t z and aluminum s u r f a c e s which r e f l e c t 9&f° of i n c i d e n t r a d i a t i o n i n the w a v e l e n g t h range 4(i t o 900)io The d i f f r a c t i o n l o s s e s a r e shown i n Table 3-1, t h i r d columno The l a s e r so d e s i g n e d w i l l now s u s t a i n l a s e r a c t i o n f o r t r a n s i t i o n s up t o 500|_i wavelength, p r o v i d e d t h a t t h e s e t r a n -s i t i o n s have t h e same g a i n f e a t u r e as t h e 118u- l i n e o f watejr vapor. H i g h e r wavelength a c t i o n w i l l , o f c o u r s e , a l s o be s u s t a i n e d i f the g a i n i s c o r r e s p o n d i n g l y h i g h e r f o r t h i s wave-l e n g t h . For t h e l a s e r , t h u s c o n s t r u c t e d , c e r t a i n q u a n t i t i e s of i n t e r e s t can be d e r i v e d . 41 The s e p a r a t i o n between a x i a l modes i s o f i n t e r e s t i n o r d e r t o determine the number of modes t h a t can be s i m u l t a n e o u s l y e x c i t e d i n the l a s e r . The l i n e w i d t h of the t r a n s i t i o n s was determined i n s e c t i o n 2.3. S e p a r a t i o n between modes whose (m+n) are d i f f e r e n t by one i s o b t a i n e d from e q u a t i o n (3 .5) . M f m n = 2q + (l+m+n)K (3.5) c K = IU4_ t a n " l b^d = 0.869 % b+d fm r, - f = cK = 27 MHz, m +n -m+n = 1 I'. 1 > 4d S e p a r a t i o n between the harmonics of a g i v e n TEM mode * ° mn i s g i v e n by e q u a t i o n (3-9): f » , n t < l + l " f m , n , q - J j = The c h a r t , f i g u r e 3-6, shows the r e l a t i v e p o s i t i o n s of the v a r i o u s modes w i t h r e s p e c t t o some harmonic, q, of the TEMQQ, mode. I t i s a m a t t e r of some i n t e r e s t t o see how many of t h e s e modes can be e x c i t e d a t the same time as the TEM^Q mode. Table 3-2 l i s t s modes w i t h d i f f r a c t i o n l o s s e s n e g l i g i b l e compared t o the m i r r o r r e f l e c t i o n l o s s of 2$. D.E. McCumber's graph of f i g u r e 3.1 showing power l o s s per pass due t o d i f f r a c t i o n f o r s e v e r a l modes i s used. S i n c e h i s graph shows l o s s v a l u e s down t o o n l y 0.1$ and F r e s n e l numbers up t o 2.25, Table 3-2 i s o b t a i n e d by e x t r a -p o l a t i o n . The " n e g l i g i b l e " v a l u e of d i f f r a c t i o n l o s s i s ta k e n a r b i t r a r i l y as 0.01$. Table 3-3 shows t h e number of modes t h a t can be e x c i t e d s i m u l t a n e o u s l y w i t h the T E M ^ mode f o r v a r i o u s l i n e w i d t h s , assuming A. = 118u-. 3.2.3 S t r u c t u r e of C a v i t y With the dimensions o f the c a v i t y tube determined, (oo) (01) (10) (02)(11) (30)(12) - (2Q) (03)(21) {^}{}l}{22) (50) (41) (32) (60)(51)(42)(33) -(04)(31) . (05)(14)(23) (06 ) ( 1 5)(24) (60 ) (51)(42)(33)" c o m b i n a t i o n s ? ^ ^ • (06)(15)(24). o f m> n» ^ J 8 9 10 1 1 12 13 * i o K H Z _ Figure 3.6 Re l a t i v e - l o c a t i o n of Modes 4 ^ ro 43 Table 3-2 Low D i f f r a c t i o n Loss Modes* N LOW D i f f r a c t i o n Loss Modes 100 5.85 00, 10, 20, 01, 30, 11, 40, 21, 02, 50, 31, 60, 12, 70, 22, 03, 51, 32, 13 118 4.96 -do- except 13 220 2.66 00, 10, 20, 01, 30, 11, 40, 21, 02, 50 337 1.74 00, 10, 20,' 01 500 1.17 00 600 0.975 -** 700 0.835 -** 800 0.732 -** 900 0.65 -** 1000 0.59 -** *Reference D.E. McCumber **See Table 3-1 Table 3-3 Modes excited, by 118u l i n e * Doppler Modes E x c i t e d (Aside from (00)) Width ' (MHz) 10 n i l 15 " 70 20 20, 11, 02, 70 25 -do-30 -do- plus 40, 50, 31, 22 35 -do-40 a l l low loss(modes except 10, 01 55 a l l low l o s s modes *Refer to Table 3-2 44 i t now remains to solve the p r a c t i c a l problems of i n s e r t i n g the l a s i n g gas and of e x c i t i n g l a s e r a c t i o n . Gas i n s e r t i o n can be achieved by usi n g a c o n t r o l l i n g valve and a vacuum pump. The l a s e r i s e x c i t e d by having discharge electrodes at e i t h e r end. A l l these are in s e r t e d i n t o the mouth of glass Tees which are attached to the ends of the 72 inch tube. See f i g u r e 3-7 f o r d e t a i l s . Power Input Electrode Zl -Mirror Power Ground E l e c t r o d [ Gas Input Valve-Coupling Hole Pigure 3.7 Ca v i t y Structure A few words about the var i o u s components are i n order. The vacuum pumping i s done i n two stages i n i t i a l l y . The f i r s t one uses a d i f f u s i o n pump to evacuate the system down to approximately 2x10"^ Torr. This i s necessary i n order to detect leaks i n the tube and thereby prevent a i r from contami-n a t i n g the l a s i n g gas. The second stage uses an ordinary r o t a r y pump so as to maintain the gas at l a s i n g pressures. Lasing pressures are of the order of 0.5 Torr to 1.0 Torr. (See reference 25 and 26.) The discharge i s caused by a 5022-line type pulse modulator whose output i s fed through polished aluminum electrodes 45 The modulator can d e l i v e r 2 microsecond pulses up to 200 times per second, with a peak voltage of 7 kv and current, 280 amps. Coupling i s achieved hy a small aperture i n the grounded end m i r r o r . The aperture i s 2mm i n diameter, and the through tunnel i s l i m i t e d to 3mm long i n an e f f o r t to reduce the wave-guide e f f e c t that such a tunnel would cause. No attempt i s made here to determine q u a n t i t a t i v e l y the matching problem due to the waveguide e f f e c t . The mountings of the mirror s are a very important part of the design and the next s e c t i o n w i l l be devoted to t h i s . 3.3 M i r r o r s and t h e i r Mountings 3.3.1 Mountings The mi r r o r s must be mounted so that there i s great f l e x i b i l i t y i n t h e i r s e t t i n g . The axes of the two mirrors must not only be al i g n e d w i t h •each': other,- they must a l s o be c o i n c i - ... dental with the a x i s of the tube. This means that the mirrors must be able to ro t a t e about any a x i s i n the transverse plane. The spacing between the two mirrors a l s o determines the resonant frequency of the c a v i t y , i n accordance w i t h equation (3.5). By a d j u s t i n g the i n t e r - m i r r o r distance, d, the resonant frequency of the dominant mode can be made to coincide w i t h the tr a n s i t i o n - f r e q u e n c y . This would ensure maximum power i n t h i s mode. (See s e c t i o n 3.1.1.) Hence, the mirror mountings must be such that the m i r r o r spacing i s adjustable. This means that at l e a s t one of the mirrors should be able to move a x i a l l y . These requirements are met by the use of bellows, two micrometers and a screw, as i n fig u r e 3.8. The f i g u r e shows a 46 mechanism f o r r o t a t i n g the mirr o r s about any a x i s i n the t r a n s -verse plane. Figure 3.8 Fixed M i r r o r Housing The m i r r o r i s a f f i x e d to ( l ) , w ith p r o v i s i o n s f o r the c o u p l i n g hole. A window f i x t u r e over t h i s hole provides a s e a l i n g f o r vacuum purposes. The window m a t e r i a l can be changed so as to be transparent to the operating frequency. High density polyethylene i s used i n the f a r i n f r a - r e d . The window i s 1/8 i n . t h i c k . From Figure 3•9,.this corresponds to 50$ l o s s between lOOu- and 600p.. Lines below t h i s , down to 22\x s u f f e r s i m i l a r l o s s e s . I t i s to be recognized that the .atmosphere, mayiabsorbycertaih l i n e s l a t l i n f r a ^ r e d i i f r e q u e n -c i e s . The spacing can be a l t e r e d by moving the m i r r o r which does not have the coupling aperture. This m i r r o r i s housed i n the same way as the other. The d i f f e r e n c e i s that the m i r r o r 47 T 100 r e i i o 0* — . — — — . . , 1 . » n . 0 100 200 300 400 500 600 700 Wavelength (u) Figure 3.9 T r a n s m i s s i v i t y of Polyethylene 2mm T h i c k 2 7 i s no longer mounted on the end p l a t e , hut on a separate p l a t e which i s attached to a plunger. The plunger i s mounted on the end p l a t e as i n f i g u r e 3.10. I t can be moved i n and out at a steady r a t e by use of a motor. A d i f f e r e n t i a l micrometer plunger i s placed i n bearing contact with t h i s plunger and the. micrometer screw i s turned with a synchronous motor. Figure 3.10 Moveable M i r r o r Arrangement 48 With t h i s mounting i n place, the l a s e r c a v i t y i s complete. A l l j o i n t s are vacuum-sealed wi t h 0 - r i n g s . I t remains to a l i g n the mirrors and then to perform the t e s t s on the l a s e r . 3.3.2 M i r r o r Alignment ;The m i r r o r s are mounted so that t h e i r o r i e n t a t i o n i s f l e x i b l e , p r i m a r i l y to f a c i l i t a t e t h e i r alignment. I t i s desired that the axes of the two m i r r o r s be c o - l i n e a r and the common a x i s should coincide w i t h the a x i s of the l a s e r tube. The alignment procedure which f o l l o w s i s based on the f a c t that f o r s p h e r i c a l m i r r o r s a beam which t r a v e l s along the mirror a x i s i s a l s o r e f l e c t e d along that a x i s . Sheet Sheet Figure 3.11 M i r r o r .Alignment Procedure. In f i g u r e 3.11, an aluminum sheet i s placed i n f r o n t of m i r r o r #1. The sheet has a small aperture i n i t at the ax i s of the tube. A sheet of polystyrene i s placed i n f r o n t of m i r r o r #2. A He-Ne Laser beam i s caused to pass along the 49 tube a x i s v i a the coupling hole and through the hole i n the aluminum sheet. Where the beam h i t s the polystyrene a red spot i s seen. The beam i s r e f l e c t e d o f f m i r r o r #1 and, i f the mirror a x i s does not coincide w i t h the tube a x i s , i s blocked by the aluminum sheet. Using the micrometer, the m i r r o r i s oriented so that the r e f l e c t e d beam passes through the hole i n the aluminum and forms a second spot::on the polystyrene. This spot i s then caused to coin c i d e w i t h the f i r s t . The a x i s of mi r r o r #1 i s now aligned w i t h the tube a x i s . The beam now h i t s m i r r o r # 2 , with the c e n t r a l part of i t shooting, out .the coupling hole and ' an , annular' ringgis r,-reflecked back to the polystyrene sheet. This annular r i n g i s caused to coincide w i t h the o r i g i n a l spot. Now mir r o r #2 i s also a l i g n e d . Note that with very s l i g h t misalignment, many spots w i l l be seen on the polystyrene, owing to o f f - a x i s r e f l e c t i o n s from both m i r r o r s . When the aluminum and the polystyrene sheets are removed,"the alignment can be checked when the l a s e r i s l a s i n g . A t w i s t on one of the micrometers w i l l r e s u l t i n .a sharp decrease i n output s i g n a l l e v e l . 3.4 E x t e r n a l M i r r o r s A simple c a v i t y design that was considered along with the design j u s t described c o n s i s t s of having the mirrors outside the tube. The tube would contain the l a s e r gas, the discharge electrodes and the gas-pumping mechanisms, while the concave mirro r s are mounted outside. The ends of the tube are g l a s s -sealed at the Brewster angle. This "Brewster Angle Configu-50 28 r a t i o n " was f i r s t introduced by Rigrod et a l . In s p i t e of the very simple s t r u c t u r e , t h i s configu-r a t i o n i s not f e a s i b l e f o r a multi-frequency l a s e r i n the f a r i n f r a - r e d region. The s e a l i n g ends are e l l i p t i c a l p l a t e s whose areas are: A = Jtp£ = 3tX9_ = 56.5 i n 2 . Cos 9 ~0.5 This area i s so large that i t i s d i f f i c u l t to maintain u n i f o r m i t y over the surface of the glass end p l a t e s . A l s o , to keep the ends sturdy, the glass has to be very t h i c k . This causes d i e l e c t r i c " l o s s , which i s very high f o r submillimeter wavelengths. .:ho ."H..' The Brewster Angle Co n f i g u r a t i o n i s s u i t a b l e f o r tubes of smaller diameter, but i s not f e a s i b l e f o r the wide f a r i n f r a -red tube. 3.5 Mode S e l e c t i o n For s e v e r a l reasons, such as stable s i n g l e frequency operation, i t i s d e s i r a b l e to operate a l a s e r i n a s i n g l e mode. 29 30 31 Several ways have been suggested f o r t h i s , ' ' and the matter has been subjected t o i n c r e a s i n g i n t e r e s t over the years. The techniques, however, are rather s o p h i s t i c a t e d and involve exten-s i v e m o d i f i c a t i o n on the simple l a s e r system designed i n t h i s chapter. The simplest way of e l i m i n a t i n g a l l but a s i n g l e mode i s by i n c r e a s i n g the d i f f r a c t i o n l o s s e s of a l l modes. A com-promise must, of course, be reached between mode s e l e c t i v i t y and output power, and precautions must be taken that l o s s i s not high enough t o preclude l a s e r a c t i o n altogether. 51 E s s e n t i a l l y , the problem reduces to decreasing the Fr e s n e l Number of the l a s e r . According to the previous d e f i n i -t i o n of " n e g l i g i b l e d i f f r a c t i o n l o s s " , £j«0.01%, the d e s i r a b l e Eresnel Number, from f i g u r e 3.1, i s N=1.2, since the TEMQQ mode w i l l be the only mode with n e g l i g i b l e d i f f r a c t i o n l o s s . This i m p l i e s , from equation (3.1) , that a long, narrow l a s e r i s required. However, the present l a s e r i s meant to s u s t a i n o s c i l l a t i o n s over a wide frequency range and hence the l a s e r s i z e must remain constant. S u b s t i t u t i n g mirrors of d i f f e r e n t s i z e s f o r d i f f e r e n t wavelengths i s u n f e a s i b l e from the point of view of the "near-confocal" requirement, and of expense. Therefore, the f o l l o w i n g two simple methods may be adopted. 3.5.1. Aperture L i m i t i n g Prom equation? (3 .4) , N can be reduced simply by reducing a-^  or a^ or both. Since reduction of the mi r r o r s i z e i s not f e a s i b l e , a^ can be' reduced by b l o c k i n g o f f the outer edges of the m i r r o r . I n the l a s e r of f i g u r e 3-7, a diaphragm can be i n s e r t e d through one mouth of the Tee on the grounded end. The c o n f i g u r a t i o n would be as i n f i g u r e 3.12. , I n t h i s f i g u r e , i f d'^< d, the mi r r o r aperture ban be taken as ag. Prom f i g u r e 3.1, N=1.2 w i l l lead.to s i g n i f i c a n t l o s s i n a l l but the (00) mode. To obtain N=1.2, a p = N a = 1.8/N (3.13) N 0 o where N = Pres n e l Number of the c a v i t y with no diaphragm. Y1;.^ :,.-tiv,.'-52 Figure 3.12 Aperture Limited C a v i t y C o n f i g u r a t i o n 3.5.2 Piano-Concave Ca v i t y D i f f r a c t i o n l osses can al s o Toe increased by r e p l a c i n g one m i r r o r by a f l a t m i r r o r . Ah added b e n e f i t o f f e r e d by the plano-concave c a v i t y i s that a wider mode volume i s a v a i l a b l e so that molecules i n a wider beamwidth contribute toward the gain of the lower order modes. 32 Eogelnik and L i ^ show that i n a symmetrical concave l a s e r with m i r r o r r a d i i of curvature, R, the spot s i z e of the beam v a r i e s as i n f i g u r e 3.13-Figure 3.13 Spot Size of Concave C a v i t y 53 For a symmetrical c a v i t y , "2 w ~ % V 2R-D/ 2d R —, _ 2 (3.14) 2 w o = X\ 2 d 4 —i 1 2 (2R-d) ' \ 2 '? \dV R 2rc \d R 2 at d 2d 2 U 2d R (3.15) From equation (3-4), 2 w o = N 2 a 2d d\ R 2 a 2d N R 2JCW a 2 R 2 d 2d R R 2red 2 2d R (3.16) By symmetry, a f l a t m i rror placed at d/2 w i l l not a l t e r the beamwidth. Hence, a plano-concave c a v i t y w i t h m i r r o r separa-t i o n , d may be regarded as a concave-concave c a v i t y w i t h mirror separation, d' = 2d and aperture, a, and r a d i i of curvature, R=b. S u b s t i t u t i n g i n t o equations (3.15) and (3.16), and remembering that d i s replaced by 2d, and c a n c e l l i n g out w Q i n equation (3.16) the F r e s n e l Number of the plano-concave c a v i t y becomes 2d R , 2 n i J a 2 I d _ 2d\ R 2 a c 1 ~ d\ R (3.17) With respect to the o r i g i n a l c a v i t y of Fre s n e l Number, N , o' 54 N = H d R - IRI 2d -R N = F_ dR 2dR - d' Note that now, d must he less than 1. R cavity, with d=2.44m and R=3m, N = 0.4N (3-18) In the present (3-19) 55 4. COUPLING AND DETECTION The previous two chapters dealt with the design and the e x c i t a t i o n of the l a s e r . I t now remains to couple out the s i g n a l generated by the l a s e r and then to measure the frequency and i n t e n s i t y of t h i s s i g n a l . This chapter discusses the various coupling and de t e c t i o n mechanisms that can he used and in d i c a t e s the ones best s u i t e d f o r the present experimental set-up. 4•1 Coupling 4.1.1 Types of Coupling: The three most common ways of coupling the l a s e r power to an outside system are Transmission Coupling, D i f f r a c t i o n Coupling and Aperture Coupling. Each of these types o f f e r s i t s own advantages to a given l a s e r system and the choice of which to incorporate depends on the system i t s e l f . Transmission Coupling i s achieved by designing one mir r o r of the l a s e r to be p a r t i a l l y transparent. The Ruby Laser^ i s a notable example of a l a s e r u s i n g t h i s type of coupling. The p a r t i a l transparency of the m i r r o r does not i n t e r f e r e w i t h the mode patterns of the l a s e r resonator and i t i s expected that most of the output power would be contained w i t h i n the spot s i z e of the c a v i t y . For the c a v i t y Resigned, from equation (3.2^, the spot s i z e s are l a r g e over the e n t i r e wavelength range, A.=100p, to \=1000u. Transmission c o e f f i c i e n t s are kept low ( t y p i c a l l y 10-25%) so as not to stop l a s e r a c t i o n i n the c a v i t y . Therefore, i n order to have appreciable output power, the poly-ethylene window described i n s e c t i o n 3.3-1 should be at l e a s t 5 6 of the same diameter as the spot s i z e . The window s i z e would then be rather l a r g e and hence inconvenient i n a vacuum system,. An a d d i t i o n a l o b j e c t i o n to Transmission Coupling i s that the p a r t i a l l y transparent m i r r o r i s constructed using d i e l e c t r i c l a y e r s , since p a r t i a l l y s i l v e r e d m i r r o r s have a p p r e c i -able ohmic l o s s . The p r o p e r t i e s of d i e l e c t r i c m i r r o r s are, however, frequency dependent. Thus, s e v e r a l m i r r o r s may be needed to cover the e n t i r e submillimeter range. This i s obviously unfeasable from the point of view of p r a c t i c a b i l i t y and cost. A l s o , such a d i e l e c t r i c has to be positioned outside the d i s -charge tube so as to protect i t from the l a s i n g gas. The m i r r o r may be c o r r o s i o n r e s i s t a n t to most gases, but s i n c e the l a s e r i s intended f o r use with v a r i o u s d i f f e r e n t gases, i t i s s a f e s t to keep them away. Such a precautionary measure re q u i r e s the use of the Brewster Angle C o n f i g u r a t i o n which has already been deemed unsuit a b l e f o r the present l a s e r . 33 D i f f r a c t i o n Coupling was proposed by Latourette et a l . They designed one m i r r o r smaller than the other and the output c o n s i s t s of the r a d i a t i o n that d i f f r a c t s over the small mirror edge. The d i f f r a c t i o n losses i n a l l the operating modes i n the l a s e r were thus increased and the r e s u l t of t h i s was to cause the output to be contained i n a s i n g l e mode. However, s i n g l e mode operation i s not the prime c r i t e r i a of 'the present l a s e r . A l s o , design d i f f i c u l t i e s would be encountered, since a means must be e s t a b l i s h e d to c o l l e c t the d i f f r a c t e d r a d i a t i o n . This would complicate the simple m i r r o r housing design described i n s e c t i o n 3 . 3 . 1 w i t h a system of f o c u s s i n g lenses. The Brewster Angle C o n f i g u r a t i o n w i l l e l i m i n a t e the housing problem, but w i l l 57 lead to losses as mentioned i n s e c t i o n 3.4. Therefore, D i f -f r a c t i o n Coupling i s not considered appropriate f o r the present l a s e r . Aperture Coupling i s achieved by p u t t i n g a small hole i n the center of one mirror. I t i s the simplest to incorporate in•the present l a s e r . The small hole does, however, e f f e c t the mode patterns w i t h i n the l a s e r , and may even change it's operating modes. I t i s a matter of some importance to know the operating modes since t h i s w i l l f a c i l i t a t e the determination of the t r a n -s i t i o n frequencies of the m a t e r i a l s . The next s e c t i o n i s , there-f o r e , devoted to Aperture Coupling and i t s i n f l u e n c e on the out-put mode patterns. 3.1.2 Aperture Coupling Due to the f a c t that the d i f f e r e n t modes of the o s c i l -l a t i o n system have d i f f e r e n t f i e l d p atterns, an aperture i n a mi r r o r w i l l couple out power more i n some modes than i n others. Furthermore, the presence of the aperture w i l l a f f e c t the f i e l d c o n f i g u r a t i o n w i t h i n the c a v i t y and thereby a f f e c t the l a s e r out-17 put. D.E. McCumber has made an a n a l y s i s of the e f f e c t of an aperture i n both mirrors of a c o n f o c a l , symmetric c a v i t y with F r e s n e l Numbers ranging from 0.6 to 2.0. He bases h i s a n a l y s i s on the f a c t that the apertures are perturbations on the non-aperture case. McCumber's r e s u l t s do not apply d i r e c t l y to the present l a s e r since t h i s has a non-confocal c a v i t y w i t h only one aperture and the F r e s n e l Number range i s 0.595 t o 5.95 f o r wave-lengths 0.1 mm to 1.0' mm. However, i n the absence of l i t e r a t u r e a n a l y z i n g s i t u a t i o n s d i r e c t l y a p p l i c a b l e t o t h i s l a s e r , h i s r e s u l t s can be used to obta i n a q u a l i t a t i v e p i c t u r e of the e f f e c t of the aperture on the mode patterns. Figures 4 .1 to 4.3 show the f i e l d i n t e n s i t y of some low l o s s modes i n the unperturbed system. 2.0 Figure 4.1 F i e l d I n t e n s i t y f o r 00, 01, 02 modes, N = 1.6 59 2.0 r m 1.5 1.0 0.5 0 0 0.2 0.4 0.6 0.8 1.0 1.2 Figure 4-3 F i e l d I n t e n s i t y f o r 20, 30 modes, N = 1.6 At f i r s t glance, i t would appear that an aperture centred at r=0 w i l l couple out most power i n the (00) mode. However, as the aperture s i z e i s increased, the t o t a l d i f f r a c -t i o n l o sses of the (00) mode, i n c l u d i n g those over the mirror edge and those through the aperture, equal those of the (01) mode. Furthermore, mode mixing begins to become s i g n i f i c a n t . Mode mixing may be regarded as. an attempt by the f i e l d i n the low l o s s (00) mode to reduce i t s i n t e n s i t y at r=0 and thereby reduce the t o t a l (00) l o s s . The excess f i e l d i n t e n s i t y i s d i s t r i b u t e d amongst the other modes, p a r t i c u l a r l y the (02) mode. mostly (02) modes along w i t h some (01), (03), (00) and also other higher order modes. The l a t t e r w i l l be involved to a greater extent i f the aperture s i z e i s increased f u r t h e r . Thus, as the aperture s i z e i s increased, the l a s e r output should change For McCumber's system, the new f i e l d i n t e n s i t y i s shown i n f i g u r e 4.4. An aperture of radius r Q w i l l i n t h i s case output 60 f o r a given m i r r o r F r e s n e l Number from the (00) mode to the (01) and then to the (02) modes and subsequently to modes of higher 4.0 Figure 4.4 F i e l d I n t e n s i t y f o r low l o s s modes wi t h Coupling Aperture, N = 1.6 and N q = 0.01 order. There are, t h e r e f o r e , c r i t i c a l values of aperture F r e s n e l Numbers, N , f o r which these t r a n s i t i o n s occur. o The c r i t i c a l F r e s n e l Number f o r t r a n s i t i o n to the (01) mode i s derived by McCumber and h i s r e s u l t s are shown i n f i g u r e 4-5. For a given m i r r o r F r e s n e l Number, i f N -is below the o curve i n f i g u r e 4-5, the dominant mode i s the (00) mode. For values above, i t i s the (01) j or, depending upon the extent to which they are above, the (02) mode. As was stated e a r l i e r , the f i g u r e s i n t h i s s e c t i o n are d i r e c t l y a p p l i c a b l e .• to the confocal c a v i t y w i t h apertures i n both m i r r o r s and F r e s n e l Numbers ranging from 0.6 to. 2.0. 61 0.6 0.8 1.0 1.2 1.4 1.6 F r e s n e l Number N m Figure 4.5 C r i t i c a l aperture F r e s n e l Number N q c f o r which d i f f r a c t i o n l o sses of (00) mode equal those of (01) mode/versus F r e s n e l Number N . A p p l i c a t i o n to systems with non-confocal c o n f i g u r a t i o n w i t h an aperture i n only one m i r r o r can then only be done as a crude estimate. For the l a t t e r system, the curve of f i g u r e 4.5 can be s h i f t e d to the r i g h t since the l o s s e s through a s i n g l e aperture would be smaller than through two such apertures. With t h i s i n mind, the a 2 mm aperture system can be s t u d i e d . A table of C r i t i c a l F r e s n e l Numbers i s shown i n Table 4-1. 62 Table 4-1 C r i t i c a l F r e s n e l Numbers A, (mm) N m N 0 N o c ( A P p ; 0.1 5.7 0.0042 I O " 1 1 0.2 2.85 0.0021 I O - 8 0.3 1.9 0.0014 IO" 6 0.4 1.43 0.0011 0.00001 0.5 1.14 0.00084 0.00015 0.6 0.95 0.0007 0.001 0.7 0.81 0.0006 0.005 0.8 0.71 0.00055 0.015 0.9 0.63 0.00047 0.025 1.0 0.57 0.00042 0.03 The c r i t i c a l aperture F r e s n e l Numbers are read d i r e c t -l y from f i g u r e 4.5. An examination of Table 4-1 would i n d i c a t e that the dominant output mode w i l l be the (00) mode from about A, = 0.5mm to longer wavelengths, i f allowance i s . made f o r the r i g h t - s h i f t of the curve i n f i g u r e 4.5. Below that wavelength, the (01) mode and subsequent higher modes become dominant. Bennett 1*^ has derived a formula f o r the optimum t r a n s -mission c o e f f i c i e n t , T ^, which w i l l y i e l d the maximum output power i n the (00) mode. T o p t = t 4 - 1 * where G- = gain per pass of the system L = d i f f r a c t i o n l o s s per pass. This formula assumes that the (00) mode I s the domi-63 nant mode. This requires that the coupling aperture, he small enough that the l a s e r o s c i l l a t i o n s are not pushed i n t o the (01) or higher modes. An aperture of diameter 2mm w i l l f u l f i l t h i s requirement f o r A,<0.5mm. Below t h a t , a higher order mode w i l l dominate. I t i s not p o s s i b l e to determine the optimum aperture s i z e f o r a gas whose gain, G , i s not known when the l a s e r i s being designed. Furthermore, since the d i f f r a c t i o n l o s s e s , L, depend upon the frequency of o s c i l l a t i o n s , so does the optimum transmission c o e f f i c i e n t , as seen i n equation (4.1). There-f o r e , there i s l i t t l e to be gained by aiming f o r optimal coupling at any one frequency i n a l a s e r designed to be used over a wide range of frequencies. In designing the c a v i t y , i t i s safest to use a small aperture and t o check experimentally i f an output s i g n a l i s obtained. I f no s i g n a l i s detected, a l,arger aperture i s required. This was the b a s i s f o r the choice of a 2mm aperture. The gain can be determined i f the output power, P , i s measured e x a c t l y from Bennett's formula: P = ( G ^ I - T) T p0 P t w-ji)2- L-;:-where P Q P T = C(V& and C = constant, assuming that the output power i s p r o p o r t i o n a l to the net gain of the medium, • ' G - ( I J - T). Again, the constant C i s an unknown quantity. The transmission c o e f f i c i e n t can roughly be estimated f o r a given hole s i z e by t a k i n g the r a t i o of the aperture area to the spot s i z e areas 2 T = r a (3.12) This formula was suggested and used by P a t e l et a l A table of transmission c o e f f i c i e n t s i s given below ( r e f e r to equation (3.2)) f o r an aperture 2mm i n diameter. Table 4-2 Transmission Coupling Hole C o e f f i c i e n t s with a 2mm A. (mm) 2 r (mm ) 2 w s ? T 0.1 1.0 7.8xl0 2 0.13% 0.2 1.0 1 5.6xl0 3 0.064% 0 .3 1.0 23.4xl0 3 0.043% 0.4 1.0 3 1.2xl0 5 0.032% 0.5 1.0 3.9xl0 5 0.026% 0.6 1.0 4.7xl0 3 0.021% 0.7 1.0 5.5xl0 5 0.018% 0.8 1.0 6.2xl0 5 0.016% 0.9 1.0 7.0xl0 5 0.014% 1.0 1.0 7.8x10 3 0.013% Note that the transmission c o e f f i c i e n t s given i n the above t a b l e are f o r the undisturbed (00) mode. The t o t a l out-put power w i l l c o n s i s t of those modes whose f i e l d i n t e n s i t y i s not zero at the mir r o r center. Furthermore, the spot s i z e formula (3.2) assumes peak f i e l d i n t e n s i t y i n the (00) mode at the m i r r o r centre. The aperture may cause the i n t e n s i t y to change so that t h i s c o n d i t i o n i s no longer f u l f i l l e d . There-f o r e , the transmission c o e f f i c i e n t s i n t h i s t a b l e lose t h e i r v a l i d i t y as the wavelength i s reduced below 0.5mm. For these wavelengths, the modes (01), (02), (03) w i l l also couple out 65 s i g n i f i c a n t amounts of power and i f t h e i r spot s i z e s were known, the o v e r - a l l transmission c o e f f i c i e n t can he determined. No attempt i s made to determine these here, since the problem i s more complex than t h i s report warrants. Besides t h i s , i t w i l l make no major c o n t r i b u t i o n to the object of the present t h e s i s . 4•2 Measurement of Output S i g n a l I n t e n s i t y The f a r i n f r a - r e d r egion of the frequency spectrum., 300 GHz to 3000 GHz has only r e c e n t l y been the subject of i n t e n -s i v e study. The frequency regions surrounding t h i s one, namely the u l t r a v i o l e t , the o p t i c a l , the near i n f r a - r e d and the micro-wave regions, have a l l been w e l l studied and t h e i r p r o p e r t i e s documented. This i s l a r g e l y because 1signals at these frequen-c i e s have been f a i r l y simple to detect. High s e n s i t i v i t y , low noise equivalent power, and f a s t time response have ch a r a c t e r i s e d the d e t e c t i o n methods used i n these regions. With advancing technology, e s p e c i a l l y i n the f i e l d s of semiconductors and of magnetism, these d e t e c t i o n methods have been extended i n t o the submillimeter regions. To date, t h i s extension has been accomplished only at the l a b o r a t o r y l e v e l . A b r i e f account of these techniques i s given below to determine whether they can he of use i n the present p r o j e c t . The paramount c r i t e r i a f o r s u i t a b i l i t y w i l l once again be s i m p l i -c i t y . At the present stage of i n v e s t i g a t i o n , a simple detector i s of greater requirement than a complex one, even though the l a t t e r may have superior s e n s i t i v i t y and noise c h a r a c t e r i s t i c s . 66 4.2.1 Extension of the Microwave and the Near Infra-Red  Detection Techniques The higher frequencies of the microwave spectrum are g e n e r a l l y detected by point contact r e c t i f i e r s . These are f a s t , s e n s i t i v e detectors which operate at room temperature. 34 They are al s o e a s i l y b u i l t . C A . Burrus has given a compre-hensive report on the use of detectors f o r the wavelengths between 1mm and 10mm. Present point contact r e c t i f i e r s - formed by high pressure s p r i n g loaded contact between a metal point and a semiconductor surface - have a lower wavelength l i m i t of 0.5mm. Research i s c u r r e n t l y being conducted u s i n g v a r i o u s semiconductor m a t e r i a l s to extend t h i s to the smaller wavelengths of the sub-m i l l i m e t e r range. Such research has not yet been e n t i r e l y s u c c e s s f u l . Par i n f r a - r e d r a d i a t i o n can a l s o be detected by extending techniques used f o r near i n f r a - r e d r a d i a t i o n . These detectors are f a s t response, high s e n s i t i v i t y and low noise devices and, therefore, very d e s i r a b l e f o r experimentation. Photoconductivity i s the most commonly used phenomenon i n i n f r a - r e d d e t e c t i o n ' ,35,36 37 In 1961, E.H. Putley found that d e t e c t i o n was pos s i b l e w i t h InSb doped w i t h group I I I or V i m p u r i t i e s i n concentrations of 10 1 4 cm^ i f a magnetic f i e l d of 5000 Gauss i s app l i e d . Low temperatures are required - op t i m a l l y 1.8°K, and the d e t e c t i o n range i s 0.2mm to 2mm. The range, 0.1 to 0.2mm must be detected u s i n g a detec t o r which employs a d i f f e r e n t phenomenon - the E l e c t r o n Bolometer or the Hot E l e c t r o n E f f e c t (see Smith ). Here, very pure samples of Ge or InSb at 4°E are used. 67 The above method, using photoconductivity and r e l a t e d phenomena provides a f a s t , s e n s i t i v e and low noise response. However, a combination of two detectors i s r e q u i r e d , both operating at very low temperatures. In the present simple l a s e r system, the advantages i n response offered by t h i s d e t e c t i o n system can be dispensed w i t h i n favor of a simpler detector, i f a v a i l a b l e . Another c l a s s of detectors c o n s i s t s of devices s e n s i t i v e to the heating e f f e c t of r a d i a t i o n . Such thermal detectors are known as Bolometers. The s e n s i t i v i t y of these devices, though i n f e r i o r to the photoconducting devices, i s high. The response time i s , however, r e l a t i v e l y long. (For a comparison of photo-ns • conductive and thermal conductors, see Putley .) The various thermal detectors: the S i n g l e C r y s t a l , Superconducting, Cooled, Carbon and G-ernamium Bolometers are discussed i n the a r t i c l e by 35 Smith and i n Putley's e x c e l l e n t summarising a r t i c l e on f a r i n f r a - r e d d e t e c t i o n . Bolometers are s e n s i t i v e to a wide range of frequencies and t h i s i s a property that i s important f o r an experiment seeking new l a s e r t r a n s i t i o n s . However, these Bolometers l i s t e d above operate at cooled temperatures and, there-f o r e , are here discarded i n favor of a Bolometer which w i l l detect r a d i a t i o n at room temperature. The most s u i t a b l e detector f o r the present e x p e r i -ment i s the Golay C e l l 5 9 , 4 0 . ' I t s main v i r t u e s are that i t operates at room temperature and i t has a' wide bandwidth f o r d e t e c t i o n . I t s s e n s i t i v i t y i s i n f e r i o r to that of the cooled detectors, as i s i t s noise f i g u r e . The time response i s about 68 150 m i l l i s e c o n d s i The main use t o which i t can be put i s t o d e t e c t the t o t a l s i g n a l power emanating from t h e gas l a s e r , i n a l l or any o f the v a r i o u s modes and f r e q u e n c i e s o f the output r a d i a t i o n . Because of i t s slow response, i t cannot be used t o measure time response o f the v a r i o u s t r a n s i t i o n s t o the p u l s e s o f the e x c i t i n g power. T h i s would r e q u i r e some of the more e l a b o r a t e d e t e c t i o n arrangements mentioned e a r l i e r . 4 . 2 . 2 Golay C e l l D e t e c t i o n System 10 Hz and c h a n n e l l e d i n t o the Golay C e l l "eye". The Golay C e l l c o n v e r t s the r a d i a t i o n power t o an e l e c t r i c a l s i g n a l which i s compared t o a r e f e r e n c e s i g n a l of 10 Hz i n a L o c k - i n A m p l i f i e r . The output of t h i s o p e r a t i o n shows the v a r i a t i o n of the Golay C e l l output w i t h r e s p e c t t o the r e f e r e n c e s i g n a l . F i g u r e 4.6 shows a schematic diagram of the d e t e c t i o n a p p a r a t u s . R a d i a t i o n emanating from the l a s e r i s chopped a t R e f e r e n c e S i g n a l Chopper Lock-Ln A m p l i f i e r S i g . Ref. Output L a s e r Beam Golay C e l l R ecorder F i g u r e 4.6 Golay C e l l D e t e c t i o n Apparatus In the f o l l o w i n g paragraphs, the various components of the d e t e c t i o n apparatus are described and t h e i r purposes and p r i n c i p l e s mentioned, ( i ) The Golay C e l l ; . The C-olay C e l l i s a pneumatic detectors that i s , one that depends on the change i n volume of a gas caused by the inc i d e n t r a d i a t i o n . The laser- beam i s caused to f a l l on a r a d i a t i o n absorbing element which i s housed i n a small chamber. One w a l l of the chamber i s a f l e x i b l e m i r r o r w i t h the r e f l e c t i n g surface on the outside. The shape of the w a l l responds to v a r i a t i o n s i n the volume of the gas i n the chamber. A beam of ordinary l i g h t i s r e f l e c t e d o f f the m i r r o r onto a p h o t o c e l l . Interposed i n the path of t h i s beam i s a l i n e g r i d so that the image of one h a l f of the grid i s , upon r e f l e c t i o n o f f the m i r r o r , superimposed on the other h a l f . With the use of lenses, v a r i -a t i o ns i n the bulge of the mirror w i l l determine the amount of l i g h t which w i l l s p i l l over the second h a l f of the g r i d and. reach the p h o t o c e l l . In t h i s way, the l i g h t f l u x i n c i d e n t on the p h o t o c e l l depends on the d i s t e n s i o n of the m i r r o r , which i n tu r n depends on the r a d i a t i o n absorbed by the pneumatic chamber. A sketch showing the p r i n c i p l e of the G-olay C e l l i s shown i n f i gure 4.7. The Golay C e l l used here, f o r suhmillimeter wavelengths, has an aperture of s i z e 1.8 i n . The s e n s i t i v i t y i s approximately 10 +^ v o l t s / w a t t . The p h o t o c e l l i s biassed with +90 v o l t s and the lamp used 2.5 v o l t s at 1.5 amperes. The output of the Golay C e l l i s connected to the Lock-in A m p l i f i e r . 7apere& rfrf/usting Screw Figure 4.7 Golay Infra-Red Detector o 71 ( i i ) Chopper The e l e c t r i c a l s i g n a l from a G-olay C e l l represents the d i f f e r e n c e between the i n c i d e n t r a d i a t i o n and some ambient r a d i a t i o n , such as the l i g h t i n g i n the room. The ambient r a d i a t i o n may d r i f t i n value and thereby cause an erroneous s i g n a l to be read. However, i f the beam i s chopped, t h i s d r i f t w i l l not e f f e c t the Golay C e l l output. Whenever the beam i s i n t e r r u p t e d , the c e l l i s i n e f f e c t reset to a zero va l u e , and the output s i g n a l w i l l represent the r a d i a t i o n that was not blocked by the chopper. I f the beam i s i n t e r r u p t e d f o r a s u f f i c i e n t l y long time, the Golay C e l l output would s t a r t f a l l i n g to the ambient value. Therefore, the rat e of chopping should be such t h a t the beam i s blocked f o r a time l e s s than the time constant of the instrument. This l a s t i s 0 . 15 sec. A c i r c u l a r blade which i s cut such t h a t the a l t e r n a t e quadrants only permit the passage of the beam, and which r o t a t e s at 5 Hz w i l l chop the beam at 10 Hz. The beam i s then blocked f o r 0 . 1 seconds, which i s l e s s than the time constant of the instrument. A 115 v o l t , 60 Hz synchronous motor i s used f o r t h i s purpose. 1 Another advantage of chopping i s that the frequency dependent noise i n the instruments can be reduced. Other sources of noise i n the detec t i o n apparatus are reduced u s i n g a Lock-In A m p l i f i e r . ( i i i ) Lock-In A m p l i f i e r This i s a device that allows d e t e c t i o n of small i n t e n -72 s i t y s i g n a l s buried i n n o i s e 4 1 . Noise enters into the system from v a r i o u s sources. Johnson noise i n the r e s i s t o r s and shot noise i n vacuum tubes and semiconductors produce a white noise spectrum which depends on the bandwidth. Gain modulation or* f l i c k e r noise i s ass o c i a t e d w i t h a m p l i f i e r c i r c u i t s and i t v a r i e s as l / f , i . e . maximum noise at dc. Other sources of noise are power l i n e pick-up and r f i n t e r f e r e n c e . F l i c k e r noise i s reduced because the operating frequency i s 10 Hz rather than dc, Interference can only be eliminated by proper s h i e l d i n g . White noise i s reduced using a l o c k - I n A m p l i f i e r . The bandwidth i s reduced to zero by t h i s device using a harmonic mixer. In t h i s , the chopped s i g n a l i s beat w i t h a reference s i g n a l of the same frequency and the upper side band eliminated by a low pass f i l t e r of a r b i t r a r i l y s m a ll bandwidth. The lower side band i s then a m p l i f i e d w i t h a dc a m p l i f i e r and the output fed to a recorder. ( i v ) Reference S i g n a l The reference s i g n a l i s obtained by chopping a beam of l i g h t i n c i d e n t on a p h o t o r e s i s t o r c i r c u i t u s i n g the same chopper as the output beam of the l a s e r . This ensures that the reference s i g n a l i s of the same frequency (though not neces-s a r i l y the same phase) as the chopped s i g n a l . (v) Light Cone Owing to d i f f r a c t i o n e f f e c t s at the coupling apera-t u r e , the output beam diverges. A l i g h t cone i s necessary to channel t h i s r a d i a t i o n i n t o the Golay C e l l aperture. 1 4-2 D.E. Williamson has shown that the cone must have precise 73 dimensions to ensure that no r a d i a t i o n i s r e f l e c t e d hack o f f the in s i d e surface of the cone. Using an extension of h i s methods, a cone of dimension 1 i n . diameter and 5 i n . l e n g t h ; i s made. The cone i s made of copper and with proper p o l i s h i n g of the i n s i d e w a l l s can transmit 99$ of i n c i d e n t r a d i a t i o n . The mouth of the cone i s covered b y a black high d e n s i t y poly-ethylene sheet which prevents v i s i b l e l i g h t from entering the detector. The polyethylene i s transparent to submillimeter frequencies (see f i g u r e 3.9). 4.3 Frequency Measurements  I t i s now 'possible to use the Golay C e l l apparatus to measure the t r a n s i t i o n frequency, or frequencies, of the l a s e r m a t e r i a l . A monochromator i s interposed between the output hole and the Golay C e l l . By observing the v a r i a t i o n of power as the monochromator i s scanned and a l s o as the m i r r o r separation i s changed while keeping the monochromator set at some valu e , the t r a n s i t i o n frequency can be deduced. The monochromator i s , t h e r e f o r e , an important part of the d e t e c t i o n system. I t i s discussed i n the next s e c t i o n . 4.3.1 Monochromator A simple but adequate monochromator i s the Eb e r t - F a s t i e type monochromator. I t s p r i n c i p l e i s i l l u s t r a t e d i n f i g u r e 4.8. The input and the output s l i t s are i n the f o c a l plane of the l a r g s p h e r i c a l m i r r o r . This causes the g r a t i n g to be i l l u m i n a t e d by p a r a l l e l r a d i a t i o n and a l s o the scattered region of i n t e r e s t i s brought to a focus on the output s l i t . Pigure 4,8 E b e r t - F a s t i e Monochromator The monochromator uses an Echelette g r a t i n g which can he blazed f o r a c e r t a i n frequency i n any order. The blaze a n g l e , i s determined by the order desired and by the design of the monochromator. The input s l i t arrangement i s such that r a d i a t i o n r e f l e c t e d by the concave mirror s t r i k e s the g r a t i n g i n a nearly p a r a l l e l beam at some angle, 0 , w i t h respect to the ax i s of the m i r r o r . The output s l i t i s so positioned i n r e l a t i o n to the concave m i r r o r that those rays scattered o f f the g r a t i n g i n a d i r e c t i o n making an angle, 0 , with the mirror a x i s are focussed to the center of the output s l i t . An Echelette g r a t i n g s c a t t e r s maximum r a d i a t i o n i n the d i r e c t i o n of the specular r e f l e c t i o n o f f the facets of the g r a t i n g . The specular d i r e c t i o n can be caused to coincide w i t h the r e f l e c t e d d i r e c t i o n , 0 , simply by r o t a t i n g the grating so that the fac e t s are p a r a l l e l to the f o c a l plane of the mi r r o r . The angle 0, through which the g r a t i n g must be rot a t e d f o r t h i s c o n d i t i o n to obtain i s equal to 75 the blaze angle,6 , of the g r a t i n g . In the above rotated c o n d i t i o n , the g r a t i n g equation n\ = d ( s i n 9 i - s i n 9 r ) (4.1) becomes nX = 2dco,s0sino (4.2) where X = wavelength,, d = spacing between grooves, 9^ = i n c i d e n t angle w i t h respect to normal to gra t i n g , 9^ = r e f l e c t e d angle with respect to normal to grating,,, and 9^ = 0 + o , 9 = 0 - A . r ^ The g r a t i n g i s s a i d to have been blazed f o r the .A. and n which s a t i s f y equation (4.2). I n the general p o s i t i o n of the g r a t i n g , the g r a t i n g equation (4.1), becomes nX. = 2dcos0sin9 (4-3) Equation (4.3) y i e l d s the wavelength and order which appear at the centre of the output s l i t . Thus, t h i s equation a f f o r d s a means f o r c a l i b r a t i n g the monochromator k In the instrument to be used f o r t h i s experiment, a 0.25 Meter Ebert Monochromator made by the J a r r e l - A s h Company (see f i g u r e 4-9), the c a l i b r a t i o n i s performed f o r a 6000A 0 g r a t i n g i n f i r s t order. This o p t i c a l system can be adapted to the present suhmillimeter system by r e p l a c i n g t h i s g r a t i n g by an appropriate g r a t i n g and c a l i b r a t i n g the monochromator us i n g formula (4.3). The suhmil-l i m e t e r wavelengths are obtained by using the conversion formula? 76 A/F = Entrance/Exit S l i t B/E = Entrance/Exit 45° M i r r o r s C = C o l l i m a t i n g M i r r o r D = Grating Selector Figure 4 . 9 J a r r e l - A s h Monochromator given by: n A d 0 o = _ 0 n A d s s s (4.4) where the sub s c r i p t s "s" and "o" stand f o r submillimeter and o p t i c a l r e s p e c t i v e l y . Equation ( 4 . 4 ) i s derived from ( 4 . 3 ) , assuming that 0 and 9 are the same i n both systems. According to t h i s equation, when \ =0, A g=0. However, i f i n the process of exchanging the g r a t i n g s , the new g r a t i n g i s s l i g h t l y misplaced so that A. ^0 when A =0, the A c a l c u l a t e d by usi n g t h i s equation S O S must be modified by n AA. = 2d cos0cosOA9 (4-5) s s s where AO i s the e r r o r i n placement. The value of AO can be found by a c t u a l experiment u s i n g a known t r a n s i t i o n l i n e . 77 In' tire monochromator, 0 i s estimated to he ~ 8°, so that Cos0~O.99. For the 6000 A 0 blazed g r a t i n g , n =1, d =1/1180 mm, Two suhmillimeter gratings are made on aluminum blanks w i t h d =0.01 i n . and 0.02 i n . r e s p e c t i v e l y . The blaze angle i s 15°. s From equation (4.3 ),these gratings are blazed f o r 131p> and 262\x r e s p e c t i v e l y . The above data can be subsituted i n t o equations (4.4) and (4.5) and a suhmillimeter c a l i b r a t i o n f o r the monochromator w i l l be obtained. For the two g r a t i n g s , then n A. = 300X + 0.5A9xl0 5 |i (4.6) s s o r and n X = 600A. + l.OAQxlO 5 u (4.7) S S 0 R I t was stated e a r l i e r that the concave mirror w i l l focus r a d i a t i o n s t r i k i n g i t at an angle, 0,with respect to the a x i s , at the center of the output s l i t . I n the same manner, r a d i a t i o n that i s scattered at angles s l i g h t l y d i f f e r e n t from 0 w i l l be focussed on e i t h e r side of t h i s center. Thus, when the monochromator i s set f o r a c e r t a i n wavelength, i t w i l l not only show that wavelength at the output s l i t , but a l s o sur-rounding wavelengths w i t h i n a range, dA,. The range dA., c a l l e d the " r e s o l u t i o n " , depends on the s l i t width,, dx as i n equation (4.8). dA. = 2dFcos0d._ (4.8) n where F = f o c a l length of the concave m i r r o r n = order of spectrum For the two g r a t i n g s , the r e s o l u t i o n s are r e s p e c t i v e l y d \ = 2xl0"^dx (4.9) n and dA. = 4xlO~ 3dx (4.10) n 4.3-2 Frequency Measurement Procedures 78 With the a i d of the monochromator, the G-olay C e l l apparatus can he used to measure the t r a n s i t i o n frequencies of the gas. There are two ways i n which t h i s can he done. The f i r s t method i s to scan through 9 with the mono-chromator, and to note the v a r i a t i o n s of power as recorded on the recorder. The process of scanning w i l l d i s t i n g u i s h t r a n -s i t i o n l i n e s which are separated by wavelengths greater than the r e s o l u t i o n of the monochromator. In the search f o r new t r a n s i t i o n l i n e s , i t i s , therefore, advantageous to have a h i g h r e s o l u t i o n u s i n g a narrow s l i t . The s l i t width must, there-f o r e , be a compromise between r e s o l u t i o n and detectable power. I t i s to be r e a l i z e d that the readings given by the c a l i b r a t i o n equations (4.9) and (4.10) y i e l d the product n X . Therefore, any peaks that are observed as a r e s u l t of the mono-chromator scanning may be due t o a higher order of a small wave-length t r a n s i t i o n l i n e . In order to recognize these smaller wavelengths, i t i s advisable,to use s e v e r a l gratings blazed-f o r wavelengths such that the smaller wavelength t r a n s i t i o n l i n e s appear i n s t i l l higher order. Within the l i m i t s of the monochromator r e s o l u t i o n and the v a r i o u s sources of noise, c e r t a i n l i n e s may be i n d i s t i n g u i s h -able from each other. A l l wavelength readings obtained by the scanning method are, t h e r e f o r e , correct only to w i t h i n the r e s o l u t i o n . The second method of measuring the t r a n s i t i o n l i n e s i s by v a r y i n g the m i r r o r separation. Resonances occur only i f 79 e q u a t i o n 3.5 i s s a t i s f i e d : 4d = 2q + (1+m+n) r i - ^ t a n " 1 'bz& \ (3-5) A. V b+d / Si n c e t h e r e may be s e v e r a l t r a n s i t i o n l i n e s f o r a g i v e n m a t e r i a l , as t h e r e a re f o r water v a p o r , the monochromator i s needed so t h a t the s i g n a l d e t e c t i n g a p p a r a t u s "sees" o n l y one l i n e a t a t i m e . I f j u s t one a x i a l mode has a l o s s low enough t o be e x c i t e d , the t r a n s i t i o n wavelength can be deduced by the e q u a t i o n -A = 2Ad ( 4 . H ) where Ad = d i s t a n c e the m i r r o r moves between resonances. There i s a l i k e l y p o s s i b i l i t y t h a t more t h a n one a x i a l mode i s e x c i t e d . E f f o r t s t o m i n i m i z e the l i k e l i h o o d of t h i s were made i n s e c t i o n 3.5. However, i t may be t h a t such e f f o r t s may reduce the output power to the e x t e n t t h a t i t i s . i n d i s t i n g u i s h a b l e from n o i s e . I n such a case, t h e r e i s no s i m p l e a l t e r n a t i v e but t o permit more th a n one a x i a l mode t o be e x c i t e d . When these o t h e r h i g h e r l o s s modes a r e a t l i n e c e n t e r , however, the peak output power s h o u l d be s m a l l e r t h a n i f the dominant mode were t h e r e . . Thus, by measuring the s e p a r a t i o n between these peaks, i t i s p o s s i b l e t o determine the d i s t a n c e the m i r r o r moves between a x i a l r e s o n a n c e s . Prom e q u a t i o n (3-5), A. i s determined from A = 4_d (4.12) KA(m+n) K = 1 - 4 t a n " 1 b-d it b+d where d = d i s t a n c e the m i r r o r moves between a x i a l r esonances. 80 4.3.3 Water Vapor L i n e s I n s e c t i o n 4.3.1 i t was s t a t e d t h a t c a l i b r a t i o n s h o u l d be performed u s i n g a gas w i t h known t r a n s i t i o n s . L a s e r a c t i o n has s u c c e s s f u l l y been o b t a i n e d i n water v a p o r and i t s t r a n s i t i o n l i n e s a c c u r a t e l y measured by s e v e r a l a u t h o r s . Table 4-3 l i s t s l i n e s i n w a t e r v a p o r t h a t have been o b t a i n e d and t h e i r r e l a t i v e output power. Table 4-3 Water Vapor T r a n s i t i o n L i n e s (n) (w) ( c m - 1 ) (W) 1 6 . 9 3 1 0.02 45.523 0.007 23.365 ' 0.1 47.251 0.08 26.666 0.5 47.469 0.06 27.974 3 47.693 0.04 28.054 - 48.677 0.07 28.273 0.6 53.906 0.0008 28.356 0.01 55.077 0.06 32.929 0.4- 57.660 0.02 33.033 7 67.177 0.01 35.000 - 73.402 0.002 35.841 0.1 78.455 0.007 36.619 0.009 79.106 0.006 37.859 0.003 89.775 0.0007 38.094 - 115.42 0.001 39.698 0,1 118.65 -40.629 0.01 120.08 220.34 Table 4-3 c o n t i n u e d on top of page 81. 81 A. i s the wavelength i n vacuum, and p i s the peak output power from the tube. a) The p o s s i b l e e r r o r i s - 0,05 p e r c e n t f o r A,<80|i, and - 0.1 pe r c e n t f o r A>80|-i. b) The power l i e s between 1/3 and 3 times the f i g u r e quoted. c) The 220.34p l i n e was o b t a i n e d by E l e s h e r and M u l l e r 4 4 , and the r e s t by M a t h i a s and Crocker 4''. The l i n e s and t h e i r power were o b t a i n e d by M a t h i a s and Crocker..and were d e t e c t e d u s i n g c o o l e d p h o t o d e t e c t o r s . S i n c e the p r e s e n t system uses l e s s e f f i c i e n t d e t e c t i o n methods,not a l l the t r a n s i t i o n s i n t h e above l i s t w i l l be observed. A l s o , . i t i s not p o s s i b l e t o p r e d i c t whether the r e l a t i v e a m p l i t u d e s a t the v a r i o u s t r a n s i t i o n wavelengths w i l l be e f f e c t e d by u s i n g t h e l o w e r d i s -charge c u r r e n t d e n s i t i e s t h a t are used i n the pre s e n t p r o j e c t . Even i f e v e r y t h i n g i s assumed l i n e a r , the s h o r t e r wavelength l i n e s w i l l appear a t t h e output s l i t i n such a h i g h o r d e r t h a t t h e i r c o n t r i b u t i o n t o t h e t o t a l power r e a c h i n g the G-olay C e l l may be v e r y s m a l l , i f not n e g l i g i b l e . Only a c t u a l e x p e r i m e n t a t i o n c a n d e t e r -mine how s m a l l t h i s c o n t r i b u t i o n i s . A l l t h i n g s c o n s i d e r e d q u a l i -t a t i v e l y , w i t h the 130|i b l a z e d g r a t i n g , the 118u- l i n e s h o u l d appear t o be the most p o w e r f u l . T h i s r e a l i z e d , i t i s p o s s i b l e t o f i n d A9 i n e q u a t i o n (4.7) and thus c a l i b r a t e the monochromator. 5. TESTS ON LASER-82 5 . 1 T e s t s on L a s e r The l a s e r system, as d e s i g n e d , i s meant t o encourage l a s e r a c t i o n i n the f a r i n f r a - r e d r e g i o n of the fr e q u e n c y spectrum. To t h i s end, the l o s s e s due t o the v a r i o u s sourc e s were kept t o a minimum i n the c a v i t y . Any m a t e r i a l w i t h s u h m i l l i m e t e r t r a n - • s i t i o n s which can o b t a i n s u f f i c i e n t i n v e r s i o n of p o p u l a t i o n t o overcome these l o s s e s w i l l y i e l d an output power t o t h e d e t e c t i o n system. I n most gases the e x i s t e n c e of such t r a n s i t i o n s cannot be p r e d i c t e d and can o n l y be determined by a c t u a l e x p e r i m e n t a t i o n . A s i d e from k e e p i n g l o s s e s down, l a s e r a c t i o n can be encouraged by u s i n g the a p p r o p r i a t e gas p r e s s u r e and c u r r e n t den-s i t i e s . F o r a g i v e n t r a n s i t i o n , t h e s e cannot be p r e d i c t e d , and can o n l y be determined by p e r f o r m i n g t e s t s . A l s o , a g i v e n m a t e r i a l may have more t h a n one t r a n s i t i o n , w i t h i n o r w i t h o u t the f a r i n f r a -r e d r e g i o n , each of which have t h e i r own optimum c o n d i t i o n s o f p r e s s u r e and c u r r e n t d e n s i t y . T h e r e f o r e , i t i s i n t e r e s t i n g t o f i n d these c o n d i t i o n s f o r t r a n s i t i o n s w i t h i n t h e r e g i o n o f i n t e r e s t . Once.'it has been determined t h a t l a s e r a c t i o n i s indeed o b t a i n a b l e , the t r a n s i t i o n f r e q u e n c i e s can be determined by one or b o t h of t h e methods d e s c r i b e d i n s e c t i o n 4 . 3 . 5.1.1 T e s t s t o be Performed Pour m a t e r i a l s and d i f f e r e n t c o m b i n a t i o n s o f them a r e used i n the l a s e r t o see i f l a s e r a c t i o n i s o b t a i n a b l e . These a r e : water v a p o r , h e l i u m , acetone and reagent m e t h y l a l c o h o l . Of t h e s e , w a t e r vapor i s known t o have t r a n s i t i o n s t h a t can y i e l d output power under t h e c o n d i t i o n s on the p r e s e n t l a s e r . The o t h e r s a r e t e s t e d r e a l i s i n g t h a t the l a s e r d e s i g n may not he a b l e t o e x c i t e l a s e r a c t i o n i n s u h m i l l i m e t e r t r a n s i t i o n s , even though they may e x i s t . U s i n g water v a p o r , the f o l l o w i n g t e s t s were performed: ( i ) V a r i a t i o n of t o t a l output power w i t h c u r r e n t d e n s i t y and p r e s s u r e . ( i i ) S c anning w i t h the monochromator t o determine t r a n s i t i o n f r e q u e n c i e s . ( i i i ) V a r i a t i o n o f output power i n 118u- l i n e w i t h c u r r e n t and p r e s s u r e . ( i v ) V a r y i n g m i r r o r s e p a r a t i o n f o r a g i v e n mono-chromator s e t t i n g . • ' (v) A l t e r i n g l a s e r c a v i t y c o n f i g u r a t i o n hy r e p l a c i n g one m i r r o r w i t h f l a t m i r r o r s h a v i n g d i f f e r e n t s i z e o u tput h o l e s and r e p e a t i n g ( i ) and ( i v ) . 5.2 Test Data T h i s s e c t i o n c o n t a i n s graphs: r e s u l t i n g from the t e s t s performed. These a r e : ( i ) T o t a l output power o f water vapor u s i n g t h e n e a r - c o n f o c a l l a s e r ( f i g u r e 5.1)-( i i ) Power output i n the 118u l i n e o f water vapor u s i n g the n e a r - c o n f o c a l c a v i t y l a s e r ( f i g u r e 5.2). ( i i i ) T o t a l output power of water vapor u s i n g a plano-concave c a v i t y l a s e r , w i t h a 1mm h o l e i n t h e plane m i r r o r ( f i g u r e 5 - 3 ) . 84 ( i v ) T o t a l output power of water v a p o r u s i n g a piano-, concave c a v i t y l a s e r , w i t h a 2mm h o l e i n the plane m i r r o r ( f i g u r e 5 .4) . (v) T y p i c a l monochromator scans ( f i g u r e s 5.5 and 5 .6) . I n i t e m ( v ) , the two g r a t i n g s were p l a c e d i n the mono-chromator i n such a way t h a t the A© of e q u a t i o n (4.5) i s t h e same f o r b o t h . T h i s was checked u s i n g a He-Ne L a s e r beam, a f l a t m i r r o r and a d i s t a n t w a l l . No l a s e r a c t i o n was o b t a i n e d u s i n g acetone, reagent m e t h y l a l c o h o l or Vat 69 S c o t c h Whiskey. I t was found t h a t the a l c o h o l as w e l l as h e l i u m each decreased the power o u t p u t when added t o water vapor. No power v a r i a t i o n s i n d i c a t i n g resonance were observed when the m i r r o r s e p a r a t i o n was s t e a d i l y a l t e r e d i n each o f the t h r e e c a v i t y c o n f i g u r a t i o n s used. 0,(J> . . . . _ 8 10 12 14 1 6 18 20 22 C u r r e n t (ma) P i g u r e 5.1 T o t a l Output Power, N e a r - C o n f o c a l C a v i t j r 2 mm C o u p l i n g A p e r t u r e o . d • . •  . . . — 8 10 12 14 16 18 20 22 C u r r e n t (ma) F i g u r e 5.2 Output Power i n 118(1 L i n e , Near Conf o c a l Cavity-C u r r e n t (ma) F i g u r e 5.3 T o t a l Output Power, Piano-Concave C a v i t y lmm C o u p l i n g A p e r t u r e £! 8 10 12 14 16 18 20 22 C u r r e n t (ma) H d> F i g u r e 5.4 T o t a l Output Power, Piano-Concave C a v i t y 2mm C o u p l i n g A p e r a t u r e 5.3 D i s c u s s i o n of R e s u l t s 5.3.1 Output Power F i g u r e s 5.1 and 5.2 show t h a t t h e r e i s no d e f i n i t e r e l a t i o n s h i p between t o t a l output power and output power i n the 118u l i n e . Each have independent o p t i m a l c o n d i t i o n s of p r e s s u r e and c u r r e n t . There i s a g e n e r a l tendency i n b o t h , however, f o r the curves t o have narrower peaks a t h i g h e r gas p r e s s u r e s . I n the 118u- l i n e the p = 0.7 curve b e l i e s t h i s o b s e r v a t i o n but t h i s may be because the l a s e r has not y e t reached a p r o p e r o s c i l l a t i o n l e v e l . F i g u r e s 5.3 and 5.4 demonstrate the e f f e c t of the c o u p l i n g h o l e s i z e . The 1mm h o l e system outputs n e a r l y double Figure 5.6 Monochromator Scan, 262|x Blazed Orating 00 00 89 the amount of power of the 2mm hole system. This i s probably because of the mode d i s t o r t i o n s caused by the l a r g e r hole, as discussed i n s e c t i o n 4.2.1. No explanation can be offered here f o r the change i n the c h a r a c t e r i s t i c curve shapes. I t i s i n t e r e s t i n g to note that the plano-concave system wi t h the 1mm coupling hole outputs more power than the near-confocal system, even though i t s d i f f r a c t i o n l o s s e s are l a r g e r . While the aperture s i z e s may have contributed a l a r g e part to t h i s f a c t , the mode volumes probably are the important f a c t o r s in v o l v e d , the mode volume of the plano-concave c a v i t y being much l a r g e r than that >.of ,the near-confocal.cavity. 5.3.2 T r a n s i t i o n Lines Figures 5-5 and 5.6 can be used to determine the t r a n -s i t i o n l i n e s w i t h help of equations (4.6) and (4 .7) . In the 131u blazed g r a t i n g scan, f i g u r e 5-5, the highest peak i s assumed to be the 118u l i n e . I f the c a l i b r a t i o n equation (4.4) i s used, t h i s l i n e corresponds to A. = 114u-, since X i s read from f i g u r e 5-5 to be 3800 A 0 . The e r r o r , A9 can be c a l c u l a t e d f o r the f i r s t g r a t i n g to be: A 9 = n s A X s 2d co~Sj0cos9 . l:' s ^ = (118.65 - 114)u 0.254x0.99x0.974xl0 5u = 0.0095 Cos9 was determined u s i n g equation (4.3). Within the range o f 9 that the monochromator i s r o t a t e d , the denominator 90 can be assumed to be 0.5xl0^p. The Equation (4.6 ) becomes V s = 3 0 0 \) + A ' 7 5 ^ ( 5 , 1 ) The values of n A. are tabulated i n Table 5-1. s s When the 26lp blazed g r a t i n g i s used, the maximum peak occurs at 3820 A 0. Assuming AO = 0.0095 i s the same f o r t h i s g r a t i n g , equation (4.7) i n d i c a t e s that A, = 238.7p. This s looks l i k e the 118.65p l i n e i n second order. The f a c t that the amplitude of the l i n e i s greater than the f i r s t order l i n e may-cause concern. I t may be explained away.by the f a c t that the 26lp g r a t i n g has a lower r e f l e c t i o n l o s s than the 131p g r a t i n g , since the number of l i n e s per i n c h i s smaller. The l a r g e r the number of l i n e s to be drawn on the g r a t i n g , the more the wear on the c u t t i n g t o o l and hence the more i r r e g u l a r the l i n e s . Furthermore, the only known t r a n s i t i o n l i n e i n t h i s region i s the 220p l i n e . Under the assumption that the A,q=3820 A 0 reading corresponds to t h i s l i n e , A9 of the second g r a t i n g would then be -0.019 radians. Such a A9 would have d i r e c t e d the r e f l e c t e d beam 0 .0095-(-0.019)x5 f t . =1 .7 inches away from the o r i g i n a l spot i f a w a l l only 5 feet away i s used i n the simple t e s t described i n s e c t i o n 5.2. The beam width i s considerably l e s s than 0.25 inches i n the distance t r a v e l l e d and hence the non-coincidence would have appeared i n that t e s t . Since i t d i d not, i t i s safe to assume that the 3820 A 0 reading of f i g u r e 5.6 i s not the 220p water vapor l i n e . Using these arguments, equation (4.7) becomes n sA s = 600X Q + 9.5P (5-2) The r e a d i n g s from f i g u r e s 5.5 and 5.6, a l o n g w i t h e q u a t i o n s (5.1) and (5.2) l e a d t o Table 5-1. Table 5-1 Monochromator Scans G r a t i n g Reading n\* E r r o r (|i, b l a z e d ) (A°) (u) 131 3030 95.65 1.65 3080 97.15 ... 1.65 3670 114.85 1.65 3800 118.65 1.65 4300 133.65 1.65 4700 145.75 1.65 262 3580 218.3 2.30 3820 . 238.7 . 2.30 4290 266.9 ...2.3-0 4700 291.5 2.30 * U s i n g e q u a t i o n s (5.1) and (5.2) The r e s o l u t i o n of the monochromator i s 2|i. A l s o , due t o n o i s e e t c . , the peaks can o n l y be determined t o - 1mm of the c h a r t s c a l e , which corresponds t o - 100 A 0. The d i r e c t 6 r e a d i n g s a r e a l s o rounded o f f t o t h e n e a r e s t 10 A , so t h a t the o v e r - a l l e r r o r i n A. i s (- 100 -• 5) A 0. Converted t o X , t h e r e a d i n g e r r o r i s - 0.65u f o r the 131U- b l a z e d g r a t i n g and - 1.3H f o r the 262u b l a z e d g r a t i n g . Thus the t o t a l e r r o r , as shown i n Table 5-1 i s - 1.65H a n d- - 2.30u f o r t h e two g r a t i n g s . The t r a n s i t i o n w avelengths, X, can be determined i n a t a b u l a t e d form. Table 5-2 shows how some of t h e s e can c o r -respond t o c e r t a i n l i n e s i n the i n f r a - r e d r e g i o n , as read i n Table 4-3. 92 According to Table 5-2, most of the l i n e s have been i d e n t i f i e d w i t h respect to Table 4-3. There i s some doubt, however, about the A.=33.033a l i n e . I n the 131a blazed g r a t i n g scan i t appears i n f o u r t h order as 4 A. =133.65a. In the 262p. blazed g r a t i n g scan i t should appear at 6A. = 198,198a ? 7A. = 231.231a I and 8A, = 264.3a. While the l a s t of these three i s observed, the other two are not. In view of t h i s , i t i s concluded that the 33.033a l i n e does not appear i n the two scans. Table' 5-2 T r a n s i t i o n Wavelength A n a l y s i s nA* (a) I d e n t i f i e d w i t h ** 95.65 1. 65 47.251a to 47.693a l i n e s i n second order 97.15 + 1. 65 47.693a to 48,677a l i n e s i n second. order 114.85 + 1. 65 115.42a l i n e i n f i r s t , order, and 57.66a l i n e i n second order 118.65 + 1. 65 118.65a l i n e i n f i r s t order 133.65 + 1. 65 33.033a l i n e i n f o u r t h order 145.75 + 1. 65 -218.3 + 2. 30 220.34a l i n e i n f i r s t order 238.7 + 2. 30 118.65a l i n e i n second order 266.9 + 2. 30 -291.5 + 2, 30 — * As read from Table 5-1 ** As i d e n t i f i e d w i t h l i n e s l i s t e d i n Table 4-3 Thus, there are f o u r u n i d e n t i f i e d values of n.\; 133.65a, 145.75a', 266 .9a, and 291.5a. Of these, the 29-1.5a reading may be the 145.75a l i n e i n second order and the 266.9a may be the 133.65a l i n e i n second order. I t appears, t h e r e f o r e , that two new t r a n s i t i o n l i n e s i n the f a r i n f r a - r e d region have been d i s -93 covered i n water vapor. These are: 133.65p- - 1 . 6 5 m and 1 4 5 . 7 5 - 1 . 6 5 P . A c e r t a i n amount of skepticism of the above r e s u l t i s f a i r l y j u s t i f i e d . Water vapor has been i n t e n s i v e l y studied i n the past w i t h the s p e c i f i c o b j e c t i v e of f i n d i n g a l l of i t s ex-c i t a b l e t r a n s i t i o n s . The d e t e c t i o n methods used were more s o p h i s t i c a t e d than the simple scheme adopted i n t h i s t h e s i s . However, the two l i n e s , p a r t i c u l a r l y the 145^ l i n e , are so pronounced i n f i g u r e s 5»5 and 5 .6 that f u r t h e r i n v e s t i g a t i o n seems worthwhile. More p o s i t i v e i d e n t i f i c a t i o n could be made wit h the use of f i l t e r s and interferometers which were not a v a i l a b l e i n the present stage of t h i s work. . The det e c t i o n arrangement should a l s o be evacuated so as to minimize atmospheric absorption. One check of the r e s u l t s that could, be made i s by scan-ning w i t h the m i r r o r s . This was done using the various c a v i t y c o n f i g u r a t i o n s described i n s e c t i o n 3 . 5 . but i t was found that a s u f f i c i e n t number of modes were e x c i t e d so that no power v a r i a t i o n s were d i s c e r n i b l e from noise. Other mode s e l e c t i o n techniques would have to be employed. 5 . 3 - 4 Hypotheses This project i s i n no way geared to determine the quantum l e v e l s involved i n the l a s e r a c t i o n . The pink colour of the discharge i n d i c a t e s that the water vapor molecules d i s -s o c i a t e to form OH- r a d i c a l s and 0 + ions. In such a case the l a s e r t r a n s i t i o n s can be i n one or both of these and they are stimulated p r i m a r i l y by e i t h e r of the methods described i n : s e c t i o n 3 . 2 . 4 and 3 . 2 . 5 . Witteman and Bleekrode 4^ a t t r i b u t e the a c t i o n 94 to t r a n s i t i o n s between r o t a t i o n s t a t e s i n the OH"" r a d i c a l s . A l c o h o l and helium may have l e v e l s near the upper t r a n -s i t i o n l e v e l s of water vapor so as t o deplete them by n o n - s u b m i l l i -meter t r a n s i t i o n s . 6. CONCLUSIONS 95 The l a s e r c a v i t y as designed i n t h i s t h e s i s i s capable of s u s t a i n i n g l a s e r a c t i o n at l e a s t i n the lower wavelength region of the f a r i n f r a - r e d spectrum. This i s substantiated by the f a c t that water vapor l i n e s were found i n the v i c i n i t y of 120u. The l a s e r was designed to s u s t a i n o s c i l l a t i o n s over the e n t i r e suhmillimeter region, but no t e s t s were performed u s i n g m a t e r i a l s known to l a s e at longer wavelengths. With no d e f i n i t e q u a l i t a t i v e knowledge of the gain values of water vapor as a l a s e r gas, i t i s d i f f i c u l t to state c a t e g o r i c a l l y t h a t l a s e r a c t i o n w i l l be obtained at wavelengths around 1mm.. I t i s pos-s i b l e to say, however, that t r a n s i t i o n l i n e s up to 500u w i l l o s c i l l a t e i n the l a s e r c a v i t y i f the gain for the t r a n s i t i o n i s s i m i l a r to that of the 118u water vapor' l i n e . Beyond 500'd, the gain must be b e t t e r than that of t h i s l i n e . With water vapor i n the l a s e r , the general v a r i a t i o n s of output power wi t h gas pressure and current d e n s i t y were d e t e r -mined. I t was found that as pressure was changed between 0.7 Torr and 1.1 Torr, the maximum value of output power was roughly the same, but the curves were f l a t t e r at lower pressures. A s l i g h t s h i f t i n the value of current f o r which the output was maximum was found as the pressure was changed. The pattern i s not d e f i n i t e enough toi make any f u r t h e r comments. Two t r a n s i t i o n l i n e s were found which were not i d e n t i -f i e d with any found i n the l i t e r a t u r e . These l i n e s may be new l i n e s which were sustained by the present l a s e r . Within l i m i t s of -1.65u, these are: 1"5"5.65|i, and 145.75u. 96 L a s e r a c t i o n was not found u s i n g acetone o r a l c o h o l . E vidence e x i s t s i n the l i t e r a t u r e , however, t h a t "both of t h e s e can l a s e i n the f a r i n f r a - r e d . 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