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Laser scattering with frequency doubled neodymium light Butler, J. Patrick 1977

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LASER SCATTERING WITH FREQUENCY DOUBLED NEODYHIUM LIGHT by J . P a t r i c k B u t l e r B.Sc. , U n i v e r s i t y of Toronto, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR A DEGREE OF MASTER OF SCIENCE . i n THE FACULTY OF GRADUATE STUDIES Ph y s i c s Department U n i v e r s i t y of B r i t i s h Columbia We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER 1977 © J . P a t r i c k B u t l e r 1977 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements f o r an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s t h e s i s for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or p u b l i c a t i o f th i s thes is fo r f inanc ia l gain sha l l not be allowed without my written permission. i on Department of P h y s i c s The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date Augest 25 1977 - i i -ABSTBACT A s e r i e s o f Q - s p o i l e d neodymium g l a s s o s c i l l a t o r s has been c o n s t r u c t e d to produce r a d i a t i o n which, when frequency doubled to 5300 A, can be used i n a o p t i c a l s c a t t e r i n g experiment on a plasma. Though unexpectedly the r e q u i r e d l i g h t power was never obt a i n e d , an exhaustive t h e o r e t i c a l a n a l y s i s has re v e a l e d t h a t t h i s f a i l u r e was due to s u p e r f l u o r e s c e n c e depopulation o f the i n v e r s i o n . When the problem i s c o r r e c t e d by means of a samarium doped g l a s s c l a d d i n g f o r the neodymium g l a s s rods, the power necessary to observe the e l e c t r o n s a t e l l i t e f e a t u r e can e a s i l y be obtained. ACKNOWLEDGEMENTS I would s i n c e r e l y l i k e t o thank Dr.B.A.Nodwell and Dr.Boye A h l b o r n , as w e l l as t h e r e s t of t h e plasma p h y s i c s group, f o r t h e i r h e l p and p a t i e n c e w i t h t h i s p r o j e c t . - i v -TABLE OF CONTENTS i i A b stract i i i Acknowledgements i v Table of Contents v i i i Index of f i g u r e s 1 Chapter 1, I n t r o d u c t i o n Chapter 2, La s e r S c a t t e r i n g 3 S c a t t e r i n g theory 9 C a l c u l a t i o n of the s c a t t e r i n g s i g n a l 12 Background n o i s e Chapter 3, Ths Neodymium Glass Laser 11 I n t r o d u c t i o n -3.1-Laser C o n s t r u c t i o n 16 Layout 17 Lasing medium 17 Flu o r e s c e n c e l i f e t i m e 20 Lower l a s i n g l e v e l 20 C r o s s e c t i o n and l i n e w i d t h 21 E x c i t e d s t a t e a b s o r p t i o n 22 Pumping t r a n s i t i o n s 24 The flashlamp 26 Losses i n the l a s e r g l a s s 27 D i a l e c t r i c c o a t i n g s 28 The powersupply 29 The c a v i t y m i r r o r s - v-30 Q - s p o i l i n g 31 The ble a c h a b l e dye 32 The d y e c e l l 32 The p o l a r i z e r 33 a d d i t i o n a l l o s s e s produced by the p o l a r i z e r 36 Thermal e f f e c t s 37 The c a v i t y end m i r r o r s - 3 . 2 - Q u a n t i t a t i v e Theory 38 I n t r o d u c t i o n 40 Normal mode l a s i n g 40 Q - s p o i l e d mode l a s i n g 44 L a s i n g at t h r e s h o l d 45 Bleachable dye l o s s e s 46 O v e r a l l e f f i c i e n c y 47 The c a v i t y t r a n s f e r c o e f f i c i e n t 48 Numerical e v a l u a t i o n 51 Comparison t o experiment -Normal mode-54 Comparison to experiment - Q - s p o i l e d mode-56 Los energy p u l s e s 57 High power l a s i n g 58 S u p e r f l u o r e s c e n c e emission 60 A d d i t i o n a l a b s o r p t i o n a t 1.06 ji -3.3-Review of the L i t e r a t u r e 61 P u b l i s h e d theory 62 Experimental r e s u l t s - 3 . 4 - Q u a n t i t a t i v e Performance - v i -66 I n t r o d u c t i o n 64 H i s t o r i c a l 66 S p e c i a l techniques 67 Front m i r r o r alignment 67 C a v i t y m i r r o r alignment 68 Laser r od alignment 69 M a t e r i a l s damage 71 I m p l i c a t i o n s o f damage t h r e s h o l d s 71 Pulse shape -3.5-Diagnostics 73 Laser f o o t p r i n t s 73 D e t e c t i o n o f l i g h t at 1.06 jxz the p i n diode 77 The b a l i s t i c thermopile 77 D e t e c t i o n o f l i g h t at .53 jiz the IP21 p h o t o m u l t i p l i e r 79 Summary Chapter 4, Frequency Doubling 80 Theory 81 Q u a n t i t a t i v e theory 82 -4.1-Apparatus 84 Experimental r e s u l t s 87 Doubled energy 87 C o n c l u s i o n s Chapter 5, Co n c l u s i o n s and Design M o d i f i c a t i o n s 89 P r e r e q u i s i t e m o d i f i c a t i o n s 90 O p t i m i z a t i o n o f the f r o n t m i r r o r r e f l e c t i v i t y -vxx-O p t i m i z a t i o n with the i n t e r n a l f l u x f i x e d by damage requirements Other improvements . 1 - F i n a l Summary B i b l i o g r a p h y - v i i i -INDEX OF FIGOSES FIGURE P&GE TITLE 1a 1 O v e r a l l l a y o u t 2a 5 The d e f i n i t i o n s of 0 and <f> 2b 6 C a l c u l a t i o n of Kp 2c 7 The s c a t t e r i n g spectrum f o r 3 t y p i c a l a ngles 2d 10 The monochromator t r a n s m i s s i o n f u n c t i o n versus s l i t width 2e 12 The c o n v o l u t i o n of S(Hp,Kp) with T(W1+S) 3a 16 The neodymium g l a s s o s c i l l a t o r 3b 18 Stat e s o f the neodymium i o n i n g l a s s 3c 23 The output o f the flashlamp versus the a b s o r p t i v i t y of the neodymium g l a s s 3d 24 The pumping pulse 3e-g 25 The fla s h l a m p l i g h t p u l s e : width at h a l f h e i g h t ; width x power; mean l i g h t power 3h 29 The c a p a c i t o r bank 3 i 34 Alignment of the p o l a r i z e r 3 j 42 P a s s i v e decay of a photon c r e a t e d i n s i d e t h e c a v i t y 3k 50 Normal mode l a s i n g 31 52 Laser f o o t p r i n t s on p o l a r o i d f i l m 3m 55 Q - s p o i l e d performance: two rods Q - s p o i l e d performance: one rod The Q - s p o i l e d neodymium l i g h t p u l s e shape as a f u n c t i o n of the i n i t i a l s t o r e d energy (Es (0)) Laser l i g h t monitors The p i n diode s i g n a l versus f i l t e r d e n s i t y . The diode s i g n a l normalized to the sguare r o o t of the doubled l i g h t power The p h o t o m u l t i p l i e r s i g n a l n ormalized t o t h e sguare o f t h e 1.06 jx l i g h t power versus f i l t e r d e n s i t y The frequency doubler: c e l l and hol d e r The d o u b l i n g maximum f o r t u r n i n g about t h e d i r e c t i o n of t h e i n c i d e n t l i g h t ' s p o l a r i z a t i o n The d o u b l i n g e f f i c i e n c y f o r t u r n i n g about the i n c i d e n t beam. CHAPTER 1 INTRODUCTION The advent of g i a n t pulse l a s e r s has made i t p r a c t i c a l to study high d e n s i t y (Ne~10* 6) plasmas through Se v e r a l experiments have been done at 6943 A with ruby l a s e r s and anomalies have been observed, (see r e f . 1 ) To f u r t h e r i n v e s t i g a t e these and to perhaps o b t a i n b e t t e r d e t e c t i o n e f f i c i e n c i e s , i t was f e l t d e s i r a b l e t o develop a s c a t t e r i n g c a p a c i t y at 5300 A. T h i s work d e t a i l s an attempt Thomson s c a t t e r i n g {o*~ 10~ 1 3) at o p t i c a l wavelengths. NEODYMIUM OSCILLATOR ' V,, CHRYSTAL 1o06 JJ I — DOUBLING 1o06 j! PLASMA JET •scatterred light M0N0CHR0MAT0R AND 'HOTOMULTIPLIER FIG 1a OVERALL LAYOUT t o b u i l d such a system f o r s c a t t e r i n g from a plasma j e t . (see r e f . 2 and f i g . l a ) In Chapter 2 we review the s c a t t e r i n g theory and d e r i v e the requirements t h a t t h i s and our d e t e c t i o n system imposes on our l a s e r system.. Re attempt t o meet these c r i t e r a by b u i l d i n g a neodymium g l a s s o s c i l l a t o r l a s i n g a t 1.06 ji and frequency doubling the output to 5300 A. In Chapter 3 we d e s c r i b e the g l a s s l a s e r and the experiments done to t r y to improve i t s performance. Techniques f o r alignment are developed and the unexpected l i m i t to the maximum output power i s d i s c u s s e d . T h i s l i m i t precludes the completion of the s c a t t e r i n g experiment. However, the neodymium l a s e r output was s t i l l freguency doubled and the r e s u l t s of t h i s are d i s c u s s e d i n Chapter 4. Thus, although no s c a t t e r i n g experiments were performed, we have been a b l e t o deduce the changes necessary f o r the s u c c e s s f u l completion o f the experiment..This i s summarized i n Chapter 5. **« 3*** CHAPTER 2 LASER SCATTERING SCATTERING THEORY The c l a s s i c a l theory of Thompson s c a t t e r i n g from a f r e e e l e c t r o n plasma has been d e r i v e d by s e v e r a l authors and i s w e l l summarized by S a l p e t e r 3 or Rosenbluth and Rostoker*. B a s i c a l l y , t h i s theory c o n s i d e r s the e l e c t r o n to be a c c e l e r a t e d by the unperturbed i n c i d e n t l i g h t ' s e l e c t r i c f i e l d . These e l e c t r o n s are then t r e a t e d as r a d i a t i n g d i p o l e s . Thus, the s c a t t e r e d l i g h t ' s e l e c t r i c f i e l d i s the sum o f the d i p o l e f i e l d s a s s o c i a t e d with each e l e c t r o n . C l e a r l y ; t h i s w i l l i n gen e r a l be zero i f s e v e r a l wavelengths o f the i n c i d e n t l i g h t are considered u n l e s s there i s some s p a t i a l or temporal nonuniformity i n the e l e c t r o n s . In r e a l plasmas n o n u n i f o r m i t i e s appear on both the m i c r o s c o p i c and the macroscopic s c a l e s . The former a r i s e because of the f i n i t e s i z e and nonzero temperature of the e l e c t r o n s while the l a t t e r r e p r e s e n t f l u i d waves i n the plasma. In both cases the d e n s i t y f l u c t u a t i o n s may be Fo u r i e r decomposed i n t o a sum of d e n s i t y waves. , The s c a t t e r e d s i g n a l i s then the sum of the s c a t t e r i n g from each of these waves. Thus, i f a plane e l e c t r o m a g n e t i c wave of a n g u l a r f r e q u e n c y S i i s i n c i d e n t on a plasma - o f volume V, we would e x p e c t t o s e e s c a t t e r e d i n t o a s o l i d a n g l e All and a f r e q u e n c y i n t e r v a l dWs {see f i g . 2a) a power P s d E s d J I g i v e n by: *1* Ps{8i,Ks) awsdH=<rVPiS (Hp,Kp) dwsd/l/A where: i r e f e r s t o t h e i n c i d e n t beam s r e f e r s t o t h e s c a t t e r e d beam p r e f e r s t o t h e p l a s m a Ne i s t h e e l e c t r o n d e n s i t y V i s t h e volume o f t h e p l a s m a A i s t h e i n c i d e n t beam a r e a C i s t h e Thompson c r o s s e c t i o n f o r a s i n g l e e l e c t r o n a v e r a g e d o v e r s e v e r a l w a v e l e n g t h s o f t h e i n c i d e n t l i g h t =Ro*cos2<£)/2 Ro i s t h e c l a s s i c a l e l e c t r o n r a d i u s 0 i s t h e a n g l e between K i and K s £ i s t h e a n g l e between t h e d i r e c t i o n o f t h e i n c i d e n t beam p o l a r i z a t i o n and t h e s c a t t e r i n g p l a n e S (»p rKp) i s t h e s p e c t r a l d e n s i t y o f t h e p l a s m a scattering volume Wi,K incident light i v FIG 2a THE DEFINITIONS OF 0 AND $ scattered light In addition the conservation of energy and momentum requires that: *2* Ks=Ki+Kp Ws=«i*Wp To interpret equation 1 we oust r e a l i z e that the f l u c t u a t i o n time of the incident f i e l d i s very much shorter than the o s c i l l a t i o n time of the density fluctuations. Thus, ¥p<<Wi so that WssWi and thus |Ks|«r|Kif. T h i s and equation 2 i m p l i e s that | Kp| =2 f K i | s i n (d/2) . (see fig.2b) Thus, S(flp,Kp) i s a f u n c t i o n of Wi and Ks and, i f we determine the s c a t t e r i n g a t some f i x e d angle 0, we have measured the frequency spectrum o f the plasma at constant Kp. S p e c i f i c a l l y , f o r s m a l l angle s c a t t e r i n g )ip>2;iAd (where Ad i s the e l e c t r o n Debye length) or e g u i v a l e n t l y o^=1/Kp>Xd>1 and we would expect to see most of the Ap p e r i o d i c energy i n the form of i o n and e l e c t r o n a c o u s t i c waves. The former are low frequency and w i l l produce s c a t t e r i n g almost at S i while the l a t t e r o s c i l l a t e e s s e n t i a l l y at We (the e l e c t r o n plasma frequency) and w i l l produce s p i k e s a t : H=Hi±(Wez + 3Kp2KTe/Me)-s where Te i s the e l e c t r o n temperature. He the e l e c t r o n mass and K the Boltzman constant, as we move away from s m a l l 9, of gets s m a l l e r , ^p approaches the Debye l e n g t h and, on t h i s s c a l e , the e l e c t r o n s appear t o be more randomly d i s t r i b u t e d . T h i s produces a qaussian p r o f i l e centered on H i . (see f i g . 2 c ) FIG. 2c THE SCATTERING SPECTRUM FOR 3 TYPICAL ANGLES To a c t u a l l y c a l c u l a t e the s p e c t r a l d e n s i t y of the plasma, (equation 1) we must r e a l i z e that i t i s simply the wave amplitude d e n s i t y i n frequency and momentum space necessary to reproduce the d e n s i t y f l u c t u a t i o n s p r e s e n t i n the plasma as f u n c t i o n s o f space and time. In other words, S<Kp,Wp) i s simply the F o u r i e r transform of the a u t o c o r r e l a t i o n f u n c t i o n o f the e l e c t r o n d e n s i t y , ( r e f . 5) S (»p,Kp)=F(Cn(A,T)) r rT/2 - - -Cn (A,T) = l i m i t (1/V) drx{1/T) dtNefr,t) He (r+4,t*T) If we assume that we have a maxwellian plasma t h i s gives: (see ref. 5) *3* S (Wp,Kp)-27TNe/|Kp|x(Fe| 1-Gij2+ZFi|Ge J 2) / j 1-Gi-GeJ* where e r e f e r s t o the e l e c t r o n s where i r e f e r s t o the io n s Z i s the number o f elementary charges per i o n F= (M/2TTKT)-5exp(-X2) X=(M/2KT)-SHp/|Kp| G=-oC2 (-2Xexp(-X 2) <Jexp(-t2) dt-iTl V2)} o 0(.2=(aTtNZQ2/KT)/|Kp|2 Q i s the e l e c t r o n i c charge Thus we can see t h a t , given the temperature and e l e c t r o n d e n s i t y o f t h e plasma, i t i s p o s s i b l e t o p r e d i c t the d i s t r i b u t i o n of energy i n the plasma. , (see f i g . 2 c ) Conversely, given a n e a r l y maxwellian plasma, we co u l d expect t o be able t o determine i t s d e n s i t y and temperature T-»oo v -V2 * * * g * * * from the shape of the s c a t t e r e d p r o f i l e . , CALCULATION OF THE SCATTEJRING SIONAL If we wish t o e x t r a c t t h i s i n f o r m a t i o n from the l i g h t s c a t t e r e d from our plasma, we must measure i t s frequency spectrum - t h a t i s , we must pass i t through a monochromator. with the monochromator s e t at Wl the power sent i n t o the d e t e c t o r Pd(Wi,Kl) i s then given by: * 4 * Pd(Wi,K1)= I - ( I H l ) Ps(Wi,Ks)dWdfl_ CO =aVPiJf(W1+W)S <w1+s-Wi,Kp) dWd/l/A o where T(W1+W) i s the monochromator t r a n s m i s s i o n f u n c t i o n . The shape of T(W1+W) i s determined by the s i z e of the entrance and e x i t s l i t s and by the d i s p e r s i o n of the monochromator. I f we wish t o maximize our s i g n a l we must make the entrance s l i t cover the l a s e r spot s i z e (400 fx i s t y p i c a l ) . T h i s width, m u l t i p l i e d by the d i s p e r s i o n o f the monochromator, i s then the minimum frequency window we can r e s o l v e with our e x i t s l i t , a narrow l i n e source has been used to measure T(W1 + W) both f o r the 400 }i minimum freguency window and f o r a 12 A window, (see f i g . 2d) T h i s c a l i b r a t i o n i s o n l y r e l a t i v e but the no r m a l i z a t i o n c o n s t a n t may be deduced by observing that the A window e 1.8 A nimum window -10 -8 -6 -4 -2 0 2 4 6 8 10 A A = A l V ^ W I in A FIG 2d THE MONOCHROMATOR TRANSMISSION FUNCTION VERSUS SLIT WIDTH whole image of a monochromatic source, freguency R1, w i l l be passed unchanged through the s l i t s so the only l o s s e s are due t o the o p t i c a l s u r f a c e s . y T h e s e are summarized below: U l e n s s u r f a c e s 2 m i r r o r s 1 g r a t i n g l i g h t passed . 96 . 9 .6 Thus T(W1)=.1H t o t a l .85 .81 .6 1*** Having ev a l u a t e d T(W1 + W), i t now remains t o e v a l u a t e S (W1 *8-l3i rKp) , ( r e f . e q u a t i o n 4), by Beans of equation 3. I t was evaluated n u m e r i c a l l y and i n t e g r a t e d with T{W1 + W) for0C=2.0 by means of a l i b r a r y computor program Generate 6. ( f i g . 2e) The r e q u i r e d values of Te (1.90x10* °K) and Ne (2.07x10**) were o b t a i n e d from experiments done with ruby l i g h t on our plasma j e t . ( r e f * 13) ot was chosen to make the spectrum s e n s i t i v e t o changes i n Ne and Te as w e l l as t o o b t a i n l a r g e t o t a l s c a t t e r i n g from the e l e c t r o n f e a t u r e . Our monochromator has f-number 6 so, assuming t h a t we match the F number of the t e l e s c o p e to t h a t of the monochromator, dO_=2x10-2 Sr. With t h i s i n f o r m a t i o n we can now e v a l u a t e Pd/Pi from equation 4. From f i g u r e 2e we can see t h a t we should use the minimum window of about 1.8 A to o b t a i n both s p e c t r a l d e t a i l and a s t r o n g s i g n a l . For t h i s window P d i a x - I . e x l O - 1 * ? ! . Our photomultiplier(BCA#7265) i s capable of d e t e c t i n g a s i n g l e photon with an e f f i c i e n c y of about 12% at 5300 A, so f o r a s i g n a l with shot n o i s e of 5% we r e q u i r e 400 p h o t o e l e c t r o n s or 3.3x10 3 photons. For t h i s we r e q u i r e 2.1x10* 7 frequency doubled photons or 8.0x10~ 2 j o u l e s i n c i d e n t on the plasma. I f our freguency doubling i s 25% e f f i c i e n t , t h i s i m p l i e s an i n c i d e n t energy requirement at 1.06 ji of .32 j o u l e s . *««12*** " »» 17 18 is A A s X i l W i - W D / W ; in A FIG. 2e THE CONVOLUTION OF S(Wp,Kp) WITH T(WUW) BftCKGROOND NOISE The s c a t t e r e d s i g n a l w i l l be superimposed on a background of l i g h t emitted from e i t h e r f r e e - f r e e (bremstrahlung) or free-bound { r a d i a t i v e recombination) t r a n s i t i o n s i n the plasma. The f r e e - f r e e r a d i a t i o n {both p o l a r i z a t i o n s ) i s g i v e n by: {ref. 7, p87) Pr=2x2. 39x10-s3NeNiTrG?d^dH/3«Te*s watts where: irG/3SjvexpC-1»H/KT)/{7lKT/hH)-s=. 355 Thus: Pr=7.26x10s photons per second =.726 photons per nanosecond Thus the detection time must exceed 270 nanoseconds before this signal exceeds the shot noise (20 photoelectrons). In 20 nanoseconds i t contributes only 1.7 photoelectrons. The r a t i o of the free-free t r a n s i t i o n s to the free-bound t r a n s i t i o n s i s given (ref.8 p272) approximately by: (F-B)/(F-P)=exp(hW/KT)-1 « 3 . 1 This equation i s v a l i d for hydrogen l i k e ions i n thermodynamic equilibrium when the degree of i o n i z a t i o n i s not large and hW«the i o n i z a t i o n energy. Thus, the t o t a l background i n t e n s i t y w i l l be about 7.1 photoelectrons i n 20 nanoseconds or about .36 photoelectrons per nanosecond. , This s i g n a l w i l l only be s i g n i f i c a n t when our detection time i s greater than 55 nanoseconds. In summary, i f the doubling e f f i c i e n c y reaches 25%, we w i l l reguire .32 joules of l i g h t from the neodymium laser incident in a maximum of 55 nanoseconds. At <x=2 t h i s w i l l produce a s c a t t e r i n g spectrum from which we may calculate He and Te. It i s averaged over a 1.8 A window and w i l l have a minimum expected flu c t u a t i o n on of 5%.. „. CHAPTER 3 THE NEODYHIUM GLASS LASER INTRODUCTION The theory o f the production o f high i n t e n s i t y or Q - s p o i l e d b u r s t s o f l a s e r r a d i a t i o n i s w e l l understood and i s , f o r i n s t a n c e , summarized i n d e t a i l by L e v i n e 9 . B a s i c a l l y , t h e a c t i v e medium of our l a s e r c o n s i s t s of 3% doped neodymium g l a s s (Owens I l l i n o i s ED-2) which i s e x c i t e d by a b u r s t of r a d i a t i o n from a xenon f l a s h t u b e . The r a d i a t i o n i s absorbed i n broad pumping bands and almost a l l (ref.10) -of t i e e x c i t e d i o n s then decay v i a phonon and r a d i a t i o n processes ( r e f . ? p198) to a long l i f e t i m e - o r metastable- l e v e l (QF3/-T=300 juseconds f o r t h i s glass) where they accumulate, when the number i n t h i s l e v e l exceeds that i n the lower l e v e l (41,,) a photon emitted spontaneously at the t r a n s i t i o n frequency (7\=1.06 ^i) w i l l be a m p l i f i e d through s t i m u l a t e d emission as i t passes through the g l a s s . S i n c e the lower l e v e l i s w e l l above the ground s t a t e , the thermal popu l a t i o n i n i t a t room temperature i s small and t h i s c o n d i t i o n i s r e l a t i v e l y e a s i l y achieved. I f m i r r o r s are placed at e i t h e r end of the c a v i t y and, i f the gain per pass exceeds the l o s s per pass ( t h r e s h o l d c o n d i t i o n ) the medium w i l l emit long time coherent r a d i a t i o n or l a s e . I f the l o s s e s are now suddenly reduced, the l i g h t i n t e n s i t y i n the c a v i t y w i l l grow r a p i d l y and the energy ##*15*** st o r e d i n the i n v e r s i o n necessary t o overcoae those l o s s e s w i l l be r e l e a s e d i n a sh o r t Q - s p o i l e d p u l s e . T h i s energy can be removed from the c a v i t y i f we make one of the m i r r o r s p a r t i a l l y t r a n s m i t t i n g . ***16*** LASER COBSTRUCTION LAYOUT The l a t e s t design (on which most of the r e p o r t e d experimental work was done) i s shown i n f i g u r e 3a. end mirror quartz plate polarizer cavity mirror dyecell partially forced air t r i q q e r transformer transmitting cooling a a front mirror pyrex sheath trigger ' wire. FIG 3a THE NEODYMIUM GLASS OSCILLATOR S e v e r a l m o d i f i c a t i o n s have been made from e a r l i e r models and the s p e c i f i c changes a r e r e f e r r e d to when r e s u l t s from *** -J7*** experiments on these are quoted. LASING IEDIDH The l a s e r employs e i t h e r one or two 7.6 cm by 1 cm c y l i n d r i c a l rods o f 3% neodymium doped barium crown g l a s s . One of the rods we used was Owens I l l i n o i s ED-2 while the other was a l s o 3% doped but of u n c e r t a i n o r i g i n . , L i t t l e d i f f e r e n c e i n t h r e s h o l d or Q - s p o i l e d power was n o t i c e d between the rods when they were used s i n g l y , so the numbers c h a r a c t e r i s t i c f o r t h e ED-2 g l a s s were assumed true f o r both rods. , (see r e f . 10) The g l a s s has t h e energy l e v e l diagram shown i n f i g u r e 3b. Ions i n the 41 l e v e l s are e x c i t e d by the flashlamp pulse i n t o the pumping bands from whence they decay (T< 10 yusec.) i n t o t h e metastable 4F l e v e l s . The lower of these ( l e v e l 2) i s r e s p o n s i b l e f o r the l a s i n g . ILH2BESCENCE LIFETIME The e f f i c i e n c y o f pumping and energy s t o r a g e i s determined, i n p a r t by t h e spontaneous decay time. T h i s has been measured (ref.11) f o r the ED-2 g l a s s as being about 300 yuseconds. .This l i f e t i m e i s q u i t e v a r i a b l e among g l a s s e s and i s s l i g h t l y s h o r t e r than has been r e p o r t e d f o r most. (ref.12 p1488) T h i s i s due, i n p a r t , to changes i n the p r o b a b i l i t y of r a d i a t i v e t r a n s i t i o n (43% decay t h a t way) due t o * **18*** energy in 10 cm photons a b o v e here p roduce co l o r c e n t e r s (exc i ted state absorpt ion) —L- in the g lass pump bands decay v i a phonon interact ion in about 1 jusecond 4Il5/ 2" -j t l eoz to l e v e l 2 leve l 1 1.15 4 v e l 2 1.139 g2=2 T2=300 psec. ^ g r o u n d s t a t e g=6 l e ve l s at .o4 9;»oi4, .ooo l e v e l 3 .226 e v e l 4 .195 94=2 T4-60 nsec . FIG 3b STATES OF THE NEODYMIUM ION IN GLASS d i f f e r e n t i o n environments (glasses are g u i t e random i n s t r u c t u r e ) and, i n p a r t , t o changes i n the r a t e of n o n r a d i a t i v e energy t r a n s f e r to the matrix, (ref.9) In f a c t , the inhomogeneity o f the g l a s s causes each ion to e x p e r i e n c e a d i f f e r e n t spontaneous decay time. (20 t o 1000 ^usec. Ref. 13) Thus, Ts j u s t r e p r e s e n t s a mean f o r purposes o f • c a l c u l a t i o n f o r times between .3Ts to 1.5Ts ( r e f . 9 p202-4). The spontaneous decay time i s a l s o a f f e c t e d by both the c o n c e n t r a t i o n of neodymium i o n s and the temperature. The l a t t e r produces both quenching through the simultaneous t r a n s i t i o n of two neighbouring i o n s to the 41 l e v e l (4F +41 =2x41,') and c r o s s r e l a x a t i o n (4F+4I =4I 0 / + 4F„ ) * 3/a is/4 %X 9/2 9/2 3/2' of energy t o the neighbouring i o n . However, both c o n c e n t r a t i o n e f f e c t s are s m a l l a t 331 doping. ( r e f . 9 ) They deplete a constant f r a c t i o n of the pumped io n s per second and hence appear i n the measured Ts. An i n c r e a s e i n temperature can however a f f e c t the measured l i f e t i m e . For our g l a s s an i n c r e a s e i n temperature from 0°C to 200°C i n c r e a s e s the l i f e t i m e by about 20% (ref.13) presumably because of an i n c r e a s e i n t h e thermal p o p u l a t i o n o f l e v e l 1. ( r e f . 9 p204) At the same time the m u l t i - e x p o n e n t i a l behavior becomes more marked and more of the i o n s decay v i a n o n r a d i a t i v e processes. (n=.43 at 20°C vs.34 at 2200C) (ref.13,14) **«20*** LOWER LASING LEVEL The l a s e r i s a l s o s t r o n g l y a f f e c t e d by the l i f e t i m e o f the lower l e v e l { l e v e l 4 ) . , T h i s a r i s e s because the p r o b a b i l i t y of a s t i m u l a t e d t r a n s i t i o n i s equal i n both d i r e c t i o n s so t h a t the pop u l a t i o n i n the lower l e v e l determines, i n l a r g e p a r t , ( p a s s i v e l o s s e s reported a s . 1% t o ,5%/cm) {ref s. 9-13) the abso r p t i o n of the: g l a s s . T h i s p o p u l a t i o n i s c o n t r o l l e d , both by the Boltzman e g u i l i b r i u m p o p u l a t i o n , and by the e q u i l i b r a t i o n time., The former {NoGexp {- E/KT)/ZGjexp{-AEj/KT) = 1.5 3x10 1* i o n s / c c versus J 8.89x10* 8 i o n s i n v e r t e d / c c / j o u l e / c c ) i s n e g l i g i b l e at room temperatures. The l a t t e r i s not w e l l known because the 5 /x r a d i a t i o n from t h a t l e v e l i s absorbed by the g l a s s . However, i n d i r e c t measurements have y i e l d e d times between 60 nanosec. {ref. 15) and 400 nanosec. ( r e f . 16) T h i s i s long enough t o s e r i o u s l y impede the Q-spoiled performance (pulse time 25 nsec.) but should not e f f e c t normal mode l a s i n g (pulse time 300 / i s e c . ) . CSOSSECTION AND LINEWIDTH The c r o s s e c t i o n , d e f i n e d as the f r a c t i o n a l a m p l i f i c a t i o n per e x c i t e d i o n per cc, does not e f f e c t the energy storage c a p a c i t y of the g l a s s d i r e c t l y but i t does e f f e c t the e f f i c i e n c y of energy recovery, the l a s i n g t h r e s h o l d and superluminescence g a i n s a t u r a t i o n e f f e c t s . For ***21*** our g l a s s t h i s c r o s s e c t i o n has been measured as 3 .G3x10 _ 2 2cm 2 a t t h e c e n t r e of the f l u o r e s c e n c e l i n e , ( r e f . 14,17) T h i s i s o n l y 336 . o f t h e c r o s s e c t i o n seen by neodymium i o n s i n s a p h i r e , p r i n c i p a l l y because t h e f l u o r e s c e n c e l i n e i n g l a s s i s c o n s i d e r a b l y widened (260 A f u l l w i d t h h a l f maximium) by t h e amorphous s t r u c t u r e of the g l a s s . Both l e v e l s are inhomogeneously broadened and t h e r e i s l i g a n d f i e l d s p l i t t i n g o f t h e l o w e r Kramers d o u b l e t s . S i n c e t h e dye Q - s p o i l e d l i n e w i d t h has been r e p o r t e d t o be as s m a l l as .005 A { r e f . 18) and s i n c e t h e r m a l b r o a d e n i n g amounts t o o n l y 20 A a t room temperature ( r e f . 9 p218), we might e x p e c t t h a t such a broad l i n e would l e a d t o s t r o n g "hole b u r n i n g " e f f e c t s and l e a v e much o f the i n v e r s i o n u n a v a i l a b l e f o r l a s i n g - a t l e a s t i n t h e Q - s p o i l e d mode* Hole b u r n i n g has been o b s e r v e d { r e f . 9) but i n g e n e r a l the c r o s s r e l a x a t i o n r a t e s between t h e s p l i t l e v e l s {>100 p i c o s e c o n d s compared w i t h 25 nanoseconds f o r t h e c omplete pulse) a r e f a s t enough and the wings of t h e homogeneous l i n e a re h i g h enough so t h a t e s s e n t i a l l y a l l t h e energy s t o r e d i n l e v e l 2 i s a v a i l a b l e , i n our e x p e r i m e n t , f o r l a s i n g . , JICITED STATE ABSORPTION The l a s i n g a c t i o n c o u l d be s e r i o u s l y impeded i f the e x c i t e d i o n s were a b l e t o absorb t h e l a s e r r a d i a t i o n a t 1.06 ju and make a t r a n s i t i o n upward i n t o t h e 4G l e v e l s . T h i s l o s s mechanism appears t o be v e r y s t r o n g a t 500°C and •**22*** the c r o s s e c t i o n has been measured a s 1/3 t h e normal downward c r o s s - s e c t i o n t h e r e . ( r e f . 20) I f however, t h i s mechanism were i m p o r t a n t a t room t e m p e r a t u r e , i t would reduce t h e g a i n by 5051 (one upward t r a n s i t i o n f o r e v e r y 3 downward) and reduce t h e e f f i c i e n c y i n Q - s p o i l e d mode by a t l e a s t 2/3. S i n c e t h e o b s e r v e d c r o s s - s e c t i o n a g r e e s w e l l w i t h c a l c u l a t i o n s based on t h e l i n e w i d t h ( r e f . 1 9 ) , we can o n l y c o n c l u d e t h a t t h i s l o s s mechanism i s not i m p o r t a n t . , POMPING TH1NSITIONS The l a s t i m p o r t a n t f l u o r e s c e n c e p r o p e r t y of t h e i o n s i s t h e i r a b i l i t y t o abs o r b energy by making t r a n s i t i o n s from the g r o u n d s t a t e i n t o t h e pump bands. E s s e n t i a l l y a l l th e s e t r a n s i t i o n s decay i n t o t h e m e t a s t a b l e l e v e l s ( l e v e l s 1&2 ) ( r e f . 9 ) i n a t i m e s h o r t i n comparison t o t h e pumping time (T=1 p s e c . ) . However, t h e s e t r a n s i t i o n s r e q u i r e photons whose energy l i e s w i t h i n t h e s e bands { a d d i t i o n a l bands a r e p r o v i d e d by t h e s p l i t t i n g o f t h e ground s t a t e HI l e v e l s a t room temperature ( r e f . 9 p220) ) and o t h e r photons a r e e s s e n t i a l l y wasted. Thus t h e c o n v e r s i o n e f f i c i e n c y i s dependent on the match between t h e s p e c t r a l o u t p u t o f the l i g h t s o u r c e , which i n our case i s a f u n c t i o n o f c u r r e n t , and t h e a b s o r p t i o n spectrum o f t h e g l a s s , {see f i - g . 3 c , refs.10&20) T h i s e f f i c i e n c y would a l s o be a f f e c t e d i f t h e p o p u l a t i o n o f neodymium i o n s i n t h e g r o u n d s t a t e were t o be ***23*** F=—r a. •3 o > >.« 8 .'> .6 CL O .4 (0 o W -1 1 1 1 1 1 r SPECTRAL OUTPUT OF THE XENON FLASHLAMP low cu rrent output high \ current \ t\/ output \ 1 1 r - n d 1 1 1 1 r 1 ABSORPTIVITY W f n r TUT — LAJ OF THE Nd. GLASS 1 I I I I L .2 .3 .4 .5 .6 .7 .8 .9 I.O l . l wavelength in /i F I G 3c THE OUTPUT OF THE F L A S H L A M P VERSUS THE ABSORPTIVITY OF THE NEODYMIUM GLASS s u b s t a n t i a l l y d e p l e t e d . However, s i n c e c o n c e n t r a t i o n e f f e c t s a r e s m a l l ( r e f . 9 ) most o f t h e i o n s a r e a v a i l a b l e f o r i n v e r s i o n and even an i n v e r s i o n o f one j o u l e p e r c c *«*24*** (8.89x10 1 8 ions) only changes the ground s t a t e p o p u l a t i o n by 3.1%. Thus, f o r p r a c t i c a l purposes, the pump c o n v e r s i o n e f f i c i e n c y i s independant o f the i n v e r s i o n . THE FL&SHLAMP For our l a s e r we have used {see f i g . 3a) a s i n g l e EG&G#FX-47C-6.5 f l a s h t u b e . (see ref.21) I t i s f i l l e d t o 400 t o r r with xenon and i s d r i v e n by a f l a t - t o p p e d c u r r e n t p u l s e of 3.6 kiloamps/cm 2 a t maximum power., (2.?kV) (see fig.3d) The f l a s h l a m p e f f i c i e n c y i n terms of l i g h t per j o u l e e l e c t r i c a l , i n c r e a s e s to a maximum a t about 2.5 kiloamps/cm 2 or about 1.7kV. (ref.22) T h i s has been observed by monitoring t h e l i g h t p u l s e with both a p h o t o m u l t i p l i e r {most s e n s i t i v e i n t h e v i s i b l e region) (see " D i a g n o s t i c s " ) and a photodiode (most s e n s i t i v e to the i n f a r r e d pump bands) (see figs.3d-3g) These s i g n a l s a r e not n e c e s s a r i l y p r o p o r t i o n a l to the number of pump photons but, s i n c e the time - F I G 3d THE PUMPING PULSE co C o o W 340 330 320 310 ; 300 2 9 0 THE FLASHLAMP LIGHTPULSE: width at half height 0 .5 l.O 1.5 2J0 e lec t r i ca l ene rgy in k J 0 .5 1.0 1*5 2.0 e l e c t r i c a l energy in k J FIG 3e FIG 3f d obtained with the photomultiplier A obtained with the photodiode FIG 3g photomultiplier signal agrees so well with the pin diode and, since they are nearly l i n e a r anyway, i t was decided to use them as such. Measurements of normal mode l a s i n g power versus the r e a l pumping power predicted from graph 3g have subsequently shown this to be correct over the range 1.4 kV to 2.7 k?. However, below about 1.4kV (2 . 1 kiloamps/cm2) we would not expect t h i s to hold as the pump e f f i c i e n c y r i s e s substantially there., (ref.22) I f we assume that the conversion e f f i c i e n c y (power absorbed per joule e l e c t r i c a l ) i s 3.6% at 2.4 kiloamps/cm 2 (1.6 kT) (ref.20) then from figure 3f we would predict an ef f i c i e n c y of 3.0% at 2.5 kV. If we now include the difference in energy between the pump photons and the laser photons, we would expect about 2% of the e l e c t r i c a l energy to be recoverable as inversion energy at t h i s voltage. WSSES IN THE l A S | i GLASS The glass matrix i t s e l f may also a f f e c t the absorbtion of pump l i g h t . Radiation with a wavelength shorter than 4500 A (ref.23) w i l l produce saturable color centres in the glass. I t i s the presence of these that produces the e r r a t i c spiking ( p a r t i a l Q-spoiling) i n normal mode. , (ref.9) However, since lasing goes on more or less continuously in normal mode, we would expect the losses due to these centres to be maximal i n t h i s mode and much smaller in the Q-spoiled mode. Thus, i f these centres are a **«27*** s i g n i f i c a n t l o s s mechanism they should produce an improvement i n Q - s p o i l e d performance r e l a t i v e t o the normal mode. The g l a s s matrix a l s o absorbs some l i g h t p a s s i v e l y through i m p e r f e c t i o n s and i m p u r i t i e s . However, i t i s r e l a t i v e l y easy t o keep the p u r i t y of these g l a s s e s high and the ED-2 g l a s s i s quoted as l o o s i n g between .1% and .3% per cm. For s i x i n c h e s of g l a s s t h i s amounts t o to between 1.5% and 5% per pass. Since Q - s p o i l e d i n v e r s i o n s a re t y p i c a l l y 7%/cm, these l o s s e s should not be l i m i t i n g but should be i n c l u d e d i n the o v e r a l l l a s i n g eguation. DIELECTRIC COATINGS There i s a second source of passive l o s s a s s o c i a t e d with the g l a s s i n r e f l e c t i o n from the ends o f the rods. s i n c e the ends are never g u i t e p e r p e n d i c u l a r to each other or t o the end m i r r o r s (we observed .2° which i m p l i e s a l o s s time f o r a photon s c a t t e r e d from the end t o s c a t t e r i n g t o the s i d e of 1.3 complete passes versus the normal end l o s s time of 2.4 passes) t h i s l i g h t i s e i t h e r l o s t or degrades both the temporal and s p a t i a l coherence o f the beam., Si n c e normally t h i s r e f l e c t i o n amounts t o 4% a t each of the 8 s u r f a c e s seen per complete pass i t i s necessary t o have the s u r f a c e s a n t i r e f l e c t i n g coated. Our rods were coated with A d o l f K e l l e r a i r hard d i e l e c t r i c c o a t i n g s . Though they are e s s e n t i a l l y completely «**28*** e f f e c t i v e when new, they d e t e r i o r a t e d q u i c k l y , r a p i d l y p i t t i n g and burning under repeated use. Since the average energy f l u x through each s u r f a c e i s about 1.7 J/shot (Q-s p o i l e d at maximum power) i t i s c o n c e i v a b l e that the damage could r e s u l t from s p a t i a l and temporal n o n u n i f o r m i t i e s i n the beam. ( r e f . 25) Dust might a l s o have been r e s p o n s i b l e even though great c a r e was taken to i n s u r e that the s u r f a c e s were dust f r e e when the rods were p l a c e d i n the holder..Once t h e r e , the holder overshadows the rod ends so t h a t they are not exposed to c i r c u l a t i n g a i r I t i s thus probably necessary t o use the harder beam d e p o s i t e d f i l m s . we might a l s o reduce the number of s u r f a c e s to 4 by r e p l a c i n g the two three i n c h rods by one s i x i n c h rod. The l a t t e r arrangement i s e n t i r e l y e q u i v a l e n t to our system b a r i n g the lower l o s s e s , ( r e f . 26) THE £0111 SUPPLY The energy f o r the flashlamp i s provided by a 600 J Q F c a p a c i t o r bank {see fig.3h) charged to a maximum of 2.7 kV by a Sorensen (#1020-30) high v o l t a g e power su p p l y . The bank c o n s i s t s of f i v e 120 ji¥ c a p a c i t o r s and a p p r o p r i a t e i n d u c t o r s (4^ uH) , so t h a t the output impedance of each c a p a c i t o r i n d u c t o r p a i r matches the r e a l impedance of the f lashlamp. , 3SI) The bank thus approximates a charged c a b l e . When the f l a s h t u b e i s t r i g g e r e d , the v o l t a g e drop propogates backwards through the bank and i s terminated ***2 9*** mm mm 4 Ll H + —< t 0 flashlamp [ 120>jF Sorensen 1020-30 power supply FIG 3h CAPACITOR B A N K e s s e n t i a l l y w i t h o u t r e f l e c t i o n s . (The bank i s a c t u a l l y s l i g h t l y overdamped t o p r e v e n t any c u r r e n t r e v e r s a l which would s e v e r e l y damage t h e f l a s h l a m p . ) (see f i g . 3d) THH C&YITY MIRRORS In o r d e r t o produce l a r g e i n v e r s i o n s , the l i g h t must be t r a n s f e r r e d from the f l a s h l a m p t o t h e g l a s s e f f i c i e n t l y . In the c u r r e n t model, (see f i g . 3a) t h i s i s done by means of a h i g h l y p o l i s h e d (about 85% r e f l e c t i v i t y ) e l l i p t i c a l (e=.64) m i r r o r . The f l a s h l a m p i s p l a c e d a t one fo c u s and t h e g l a s s r o d s a r e p l a c e d a t t h e o t h e r s o t h a t the a c t i v e xenon plasma i s imaged i n t o t h e g l a s s . The i n s i d e diameter of t h e f l a s h l a m p i s 1.3 cm v e r s u s the g l a s s r o d diameter o f 1.0 cm ( p l u s 0.2 cm pyrex c l a d d i n g ) so the e x a c t alignment i s not c r i t i c a l , though i t does a f f e c t t h e spot s i z e and shape near t h r e s h o l d . The m i r r o r s a r e s l i g h t l y ***30*** lon g e r than the f lashlamp so as to trap as much of the l i g h t as p o s s i b l e . , J2zS£QILING I f we wish to ob t a i n high l a s e r l i g h t power we must s t o r e c o n s i d e r a b l e energy i n the g l a s s and be abl e t o r e l e a s e i t i n a s h o r t p u l s e . S i n c e the gain through the rod i s p r o p o r t i o n a l t o the s t o r e d energy, then i n normal mode, we w i l l s t o r e energy u n t i l the gain equals the l o s s e s due t o mirr o r t r a n s m i s s i o n , s u r f a c e s c a t t e r i n g e t c . A l l f u r t h e r i n v e r s i o n energy w i l l be emitted as l a s e r r a d i a t i o n . Thus, i n normal mode, we are l i m i t e d i n t h e average l a s e r power t o the maximum flashlamp power times the pumping e f f i c i e n c y times the c a v i t y t r a n s f e r c o e f f i c i e n t , {about 96 k i l o w a t t s ) However, i f we now i n c l u d e an e x t r a s w i t c h a b l e l o s s i n the c a v i t y , {Q-switch) the s t o r e d energy i s no longer l i m i t e d by l a s i n g and w i l l r i s e u n t i l ! i t i s l i m i t e d e i t h e r by spontaneous decay, t e r m i n a t i o n o f the pump pulse or de p l e t i o n of the lower l e v e l s . When the l o s s i s switched out, the gain w i l l exceed the l o s s by a l a r g e f r a c t i o n so that the power i n s i d e the c a v i t y w i l l r i s e e x p o n e n t i a l l y and q u i c k l y deplete the i n v e r s i o n . III BLERCHABLE DYE In our l a s e r t h i s s w i t c h i n g i s provided by a s a t u r a b l e dye -Eastman Kodak #14015-4-dimethylaminodithiobenzel n i c k e l d i s s o l v e d i n 1*2 d i c h l o r o e t h e n e , molar e x t i n c t i o n c o e f f i c i e n t 2.5x10*/cm/raole/liter. T h i s dye i s used t o r a i s e t h e normal mode t h r e s h o l d j u s t enough, so t h a t l a s i n g does not occur u n t i l the end of the f l a s h l a m p pulse. Thus the i n v e r s i o n i s maximized and, t o ensure t h i s , the dye c o n c e n t r a t i o n must be adjusted f o r each new s e t t i n g of the c a p a c i t o r bank v o l t a g e . Once l a s i n g s t a r t s however, a b s o r p t i o n of the 1.06 jx l i g h t b l eaches the dye and t h e switch opens. The spontaneous decay time of the e x c i t e d dye molecules i s about 30 nanoseconds so, i f t h e l i g h t energy i n the c a v i t y r i s e s f a s t enough t o d e p l e t e the i n v e r s i o n i n t h a t time, we w i l l l o s e only the energy necessary t o bleach the dye once. I n f a c t , we can probably not q u i t e achieve t h i s because t h e r e i s a s m a l l component of the dye with a picosecond r e l a x a t i o n time and t h i s w i l l produce an e s s e n t i a l l y steady though i n s i g n i f i c a n t l o s s over a 20 nanosecond p u l s e . T h i s has been deduced from the f a c t t h a t at very low c o n c e n t r a t i o n s (very near normal mode thr e s h o l d ) picosecond modelocked p u l s e s have been observed, (ref.27) T h i s can o n l y occur i f , when the switch i s opened by a f l u c t u a t i o n s h o r t i n comparison t o the c a v i t y t r a n s i t time, i t can c l o s e b e f o r e the pulse r e t u r n s . That the average r e l a x a t i o n time i s as great as 30 **«32*** nanoseconds and, t h a t t h e e f f e c t i s onl y achieved a t low c o n c e n t r a t i o n s , i s good evidence t h a t the component re p r e s e n t s a very s m a l l f r a c t i o n of the dye and hence cannot make a s u b s t a n t i a l c o n t r i b u t i o n t o the l o s s e s . THE DYE-CELL The s o l u t i o n o f the dye i s con t a i n e d i n the c e l l shown i n f i g u r e 3a. I t has 1/8 inch guartz windows placed at the brewster angle (56.4°) t o minimize a b s o r p t i o n and r e f l e c t i o n r e s p e c t i v e l y . The c e l l i s made as t h i n a s p o s s i b l e {.31 cm) so as t o reduce t o a minimum the amount of s o l v e n t the beam passes through (.37 cm) and hence the s o l v e n t l o s s e s . The inner s u r f a c e s are e i t h e r g u a r t z or t e f l o n so as t o prevent l o s s of the dye through e i t h e r a b s o r p t i o n on, or r e a c t i o n with, metal s u r f a c e s . T h i s was observed t o occur i n the f i r s t d y e - c e l l which was co n s t r u c t e d o f aluminium., TH_E P O L M I U S The e f f i c i e n c y o f up co n v e r s i o n of neodymium l i g h t i n our c r y s t a l i s dependent on the d i r e c t i o n of p o l a r i z a t i o n of the i n c i d e n t beam.. When i t was not c o n t r o l l e d we observed c o n s i d e r a b l e f l u c t u a t i o n from shot t o shot i n the doubled power { 50%) so t h a t the power was not always optimal and the c r y s t a l c o u l d not be p r o p e r l y ***33*** a l i g n e d . I t was thus found necessary t o i n c l u d e a p o l a r i z e r i n the c a v i t y , (see f i g . 3a) The p o l a r i z e r c o n s i s t s of e i g h t g u a r t z p l a t e s 1/16 " t h i c k a l i g n e d at t h e brewster angle by means of a helium neon alignment l a s e r . Since the index of r e f r a c t i o n of fused guartz at the helium neon wavelength (.6328 ja) i s 1.457024 versus 1.449683 a t the neodymium wavelength (1.06 fi) , (ref.28) the e r r o r i n t r o d u c e d by a l i g n i n g a t the .6328 ji wavelength i s only .13°. Si n c e an e r r o r of 2.5° produces a t o l e r a b l e l o s s of o n l y 1.3% per pass, the l o s s from t h i s i n a c c u r a c y may be ne g l e c t e d . Since the p l a t e s are at the brewster a n g l e , each s u r f a c e r e j e c t s 12.4% of the energy i n c i d e n t i n the h o r i z o n t a l p o l a r i s a t i o n . There are 16 s u r f a c e s so we r e j e c t a t o t a l of 88.1% of the h o r i z o n t a l p o l a r i z a t i o n per complete pass. 1DDITIOHAL LOSSES PRODUCED BY THE- POIjiRIgER Once i n s i d e the c a v i t y , the p o l a r i z e r was a l i g n e d through o b s e r v a t i o n s of the l i g h t s c a t t e r e d from our v e r t i c a l l y p o l a r i z e d helium-neon alignment beam as i n d i c a t e d i n f i g u r e 3 i . In the course of t h i s alignment, we observed that the d y e c e l l produced some d e p o l a r i z a t i o n and r o t a t i o n of our i n c i d e n t beam. The d e p o l a r i z a t i o n was observed by simply pas s i n g the beam emerging from the d y e c e l l through a piece of p o l a r o i d and n o t i n g the i n t e n s i t y of the ***34*** t r a n s m i t t e d spot. The r o t a t i o n was observed by r o t a t i n g the p o l a r i z e r about the c e n t r a l (or 2) a x i s , {see f i g . 3 i ) With the d y e - c e l l i n p l a c e , the minima i n the upwards and downwards r e f l e c t e d spots was s h i f t e d away from the plane normal t o the Y a x i s by about .3«>. (see f i g . 3 i ) T h i s central (Z) axis upward reflected spots Y ax is quartz plates dyecel l -* downward _ reflected spots J. (X axis) '{ adjusted to be paral lel to the incident beam F I G 3i ALIGNMENT OF THE P O L A R I Z E R i m p l i e s t h a t the d i r e c t i o n of p o l a r i z a t i o n was r o t a t e d by about the same amount (. 3°) and though t h i s i s - q u i t e s m a l l , the energy put i n t o the h o r i z o n t a l p o l a r i z a t i o n can o n l y be removed by the p o l a r i z e r . Thus the e q u i l i b r i u m output p o l a r i z a t i o n i s g i v e n by: 9 .« e» {2-B)/RS.4° ( v a l i d f o r small & and 6 ') where: ei=rbtation produced i n one pass, H=fraction of horizontally polarized l i g h t rejected. Thus, i f the rotation at 1.06 ju i s of the same order as t h i s observed rotation at .6328 ju, the losses i n the polarizer produced by the tendency of the pola r i z a t i o n of the beam to rotate should be small. The p o l a r i z a t i o n of the beam may also a f f e c t the lasing action i n the neodymium glass. The ligand f i e l d s around an ion give i t a fixed prefered d i r e c t i o n of polarization for the emission of l i g h t . However, the amorphous structure of the glass causes t h i s d i r e c t i o n to fee randomly oriented for each , i n d i v i d u a l ion. Thus, f o r any s p e c i f i c p o l a r i z a t i o n , some ions exhibit a reduced crossection so that the o v e r a l l gain i s reduced. One author (iref.29) has offered t h i s as a possible explanation for a reduced e f f i c i e n c y with the polarizer included but other experiments (ref.30,31,32) indicate that the losses are due to s t r a i n induced birefringence. The l a t t e r r e s u l t s from nonuniform pumping and heating effects as the beam passes through the rod. In any case, the loss i n nonsymmetrical systems such as ours has been reported as n e g l i g i b l e i n normal mode (ref. 30) and as high as 2055 of the unpolarized energy i n Q-spoiled mode. THERHAL EFFECTS Thermal d i s t o r t i o n o f the g l a s s r e p r e s e n t s a s e r i o u s problem, (refs.#9 p228,#32,#33,34) Though at uniform temperature v a r i a t i o n s i n the index of r e f r a c t i o n are n e g l i g i b l e {.8x10—6 a c r o s s a 1inch d i s c ( r e f . 9 p192)), the low thermal c o n d u c t i v i t y (1.35 B/m/°C ref.10,13) and high c o e f f i c i e n t of thermal expansion (10.3x10 -*/°C) combine t o produce c o n s i d e r a b l e d e f o r m i t y ( l e n s i n g , bending) under p r a c t i c a l flashlamp pumping. (ref.32,33,35) These e f f e c t s have been found t o become severe f o r pump energies i n excess of 330 J / c c . (ref.33) Since our bank i s only capable o f d e l i v e r i n g 170 J / c c , we are w e l l w i t h i n t h i s l i m i t . However, we would s t i l l expect t o see some misalignment as w e l l as the b i r e f r i n g e n c e e f f e c t s mentioned above. In a d d i t i o n , the index of r e f r a c t i o n i s s u b s t a n t i a l l y changed by t h e number of i o n s i n the e x c i t e d 4F 3^ 2 s t a t e (changes of the order o f 5x10~ s r e f . 9 p228) so t h a t the pathlength can vary s u b s t a n t i a l l y a c r o s s the rods. As a r e s u l t > we have gone to c o n s i d e r a b l e e f f o r t to i n s u r e uniform h e a t i n g and c o o l i n g of the rods. They are held i n a uniform pyrex tube which i s f o r c e d a i r cooled.(The same a i r c o o l s the rods and the flashlamp.) The a i r i s water c o o l e d and can be s u p p l i e d at a more or l e s s constant r a t e . The flashlamp i s focused on the rods by the e l l i p t i c a l m i r r o r , but the rods subtend about 35<* of t h e flashlamp's l i g h t , so t h a t , the lower s i d e of the rods *«*37*** r e c e i v e more l i g h t than the upper. T h i s has been compensated f o r by r e p o s i t i o n i n g the m i r r o r s u n t i l l we obtained a n e a r l y uniform spot near t h r e s h o l d . T h i s r e s u l t s i n a c o n s i d e r a b l e improvement i n performance. Se have a l s o observed, as have others (ref s. 32, 33, 34), t h a t we can o b t a i n c o n s i d e r a b l e improvement by f i r i n g the l a s e r a t f i x e d i n t e r v a l s so t h a t a s t a b l e thermal g r a d i e n t i s e s t a b l i s h e d i n the rods. The s i t u a t i o n i s f u r t h e r improved i f the end m i r r o r s a r e r e a d j u s t e d d u r i n g t h i s procedure. THE CAVITY I II II1121S The final-components e s s e n t i a l to the o p e r a t i o n of the l a s e r are the m i r r o r s at the ends of the c a v i t y . The m i r r o r nearest the rods i s a 99% r e f l e c t i n g d i a l e c t r i c m i r r o r from Laser O p t i c s . The other m i r r o r i s p a r t i a l l y t r a n s m i t t i n g so t h a t the l i g h t may be recovered from the c a v i t y . Two d i e l e c t r i c f r o n t m i r r o r s were t r i e d -one 45% and the other 65% r e f l e c t i n g - -both from Laser O p t i c s - . The theory f o r , and r e s u l t s with, these are d i s c u s s e d i n t h e next s e c t i o n . QUANTITATIVE TH.E0.H3f INTRODDCTION I f we wish to understand and g u a n t a t i v e l y p r e d i c t the performance o f t h i s l a s e r system, i t i s necessary t h a t we develop a mathematical d e s c r i p t i o n of the l a s i n g process. The theory g i v e n below i s b a s i c a l l y t h a t presented by most authors. ( r e f s . 16,36, 37,38, 39) However, they have, i n g e n e r a l , s o l v e d f o r the Q - s p o i l e d performance i n terms of the r a t e equations, so t h a t i t has been necessary t o use c a l c u l a t i o n s done by computor i n terms o f reduced v a r i a b l e s . T h i s l i m i t s the u s e f u l n e s s of t h e i r r e s u l t s and obscures the u n d e r l y i n g mechanisms so I have w r i t t e n the equations i n terras of more measurable q u a n t i t i e s . As has already been noted, a l a s e r operates through s t i m u l a t e d r a t h e r than normal, f l u o r e s c e n c e emission. T h i s can occur because a photon, at the t r a n s i t i o n frequency, passing an i o n per c e n t i m e t e r squared i n e i t h e r the upper or lower s t a t e w i l l induce a t r a n s i t i o n with some p r o b a b i l i t y P. Thus: the gain=B= (dEi/dX) /AEi= (-dEs/dx) / A E i = (PN2G4-PN4G2) = 0^2/62-^4/04) *«*39*** where: the numbers r e f e r t o the l e v e l s as shown i n f i g . 3 b Es i s the energy s t o r e d i n the g l a s s per cc = N2-ftw= 1.87x10-1 j o u l e s / c c E i i s the energy i n c i d e n t on the g l a s s per cm 2 Nj i s t h e t o t a l number of i o n s i n l e v e l 1 Gj i s the degeneracy of l e v e l j (X i s the c r o s s e c t i o n guoted p r e v i o u s l y as 3. 03x10~ 2Ocm 2=PG2G4 Thus, as we f o l l o w a photon down a rod: dEi/Ei=BdX so: E i (X)=Ei (0)exp (*BX) I f H2 i s g r e a t e r than N4 then B i s p o s i t i v e and the photon w i l l be a m p l i f i e d . The medium w i l l l a s e i f the gain per pass exceeds the l o s s per pass ( t h r e s h o l d c o n d i t i o n ) , t h a t i s i f : BX>-ln (E) where 8 i s the f r a c t i o n of l i g h t r e t u r n e d to the rod. ***ttO*** NORMAL MODE LASING In normal mode, l e v e l 4 has time t o depopulate, so t h a t N4/N2?*0 and thus: B « N2/G2=tfEs/2-nW=.081Es . Me may show t h a t N4/N2 i s i n f a c t n e a r l y z e r o as f o l l o w s : A f r o n t mirror r e f l e c t i v i t y of 65% i m p l i e s a minimum t h r e s h o l d o f 1.4% gain/cm ( f o r a s i x i n c h rod) o r e g u i v a l e n t l y , 1.5x10 1 8 l e v e l 2 i o n s / c c compared to the thermal p o p u l a t i o n of l e v e l 4 of-1.5x10** i o n s . Thus the thermal c o n t r i b u t i o n to N4 may be neglected., The p o p u l a t i o n i n l e v e l 4 produced by decay from l e v e l 2 i s N2T4/T2<.1%N2 (assume g u a s i steady s t a t e ) and so i s a l s o n e g l i g i b l e . Thus, the only a p p r e c i a b l e c o n t r i b u t i o n t o N4 comes from the depopulation o f l e v e l 2 through l a s i n g . S i n c e , i n normal mode, the l a s i n g l a s t s through most of the flashlamp pulse (about 300 jusec.) t h e mean p o p u l a t i o n of l e v e l 4 can o n l y be of the order of .1% of the t o t a l number o f i o n s undergoing t r a n s i t i o n . 2zSP0ILED MODE LASING On t h e other hand, f o r s h o r t Q - s p o i l e d p u l s e s (25 nanoseconds) l e v e l 4 does not have time t o depopulate, (T4>60 nanosec.) so f o r t h i s case we may assume t h a t T4 i s 1*** e s s e n t i a l l y i n f i n i t y . Thus: dN4=-dN2 I f we n e g l e c t pumping of i o n s i n t o l e v e l 2 during the l a s e r p u l s e (.01% of t o t a l i n M2 are pumped i n 25 nanosec.) we have: N4 (t) = N2 (0)-N2 (t) thus: B=c/{»2/G2-N4/G4) = (2N2 (t)-N2 (0))/2 = tf(2Es(t)-Es(0) )/26»=-dEs/dEi and so *5* Es(t)=Es(0) (1+exp(-OEi(t)/nW) )/2 T h i s t e l l s us t h a t our energy recovery per u n i t energy f l u x i n c i d e n t on the g l a s s drops as exp(-. 162Ei) and, as we would expect, i s l i m i t e d to 50% of the t o t a l s t o r e d energy. We would thus expect t o see a p p r e c i a b l e s a t u r a t i o n e f f e c t s (gain down by 50%) a f t e r 4.3 J/cm 2 have passed through the g l a s s . T h i s compares t o a reported value of 13 J/cm* (ref.40) + or the more reasonable a m p l i f i e r e f f i c i e n c y e x p e c t a t i o n s {~3.5 J/cm 2) reported i n r e f e r e n c e 41. I t now remains t o c a l c u l a t e E i i n terms of the energy escaping through the p a r t i a l l y t r a n s m i t t i n g end mirror (Eex) . T h i s may be done q u i t e simply i f we f i r s t note that every photon c r e a t e d i n the c a v i t y decays as i f i t were alone without g a i n , so t h a t : *6* Ei=<fEc=(j>Eex/<p A where: d\ i s the mean number of passes a photon makes through the g l a s s Ec i s the l i g h t energy c r e a t e d di' i s t h e f r a c t i o n o f t h e energy c r e a t e d t h a t i s recovered through the p a r t i a l l y t r a n s m i t t i n g m i r r o r . Thus, t o s o l v e f o r E i , i t i s simply necessary t o f o l l o w a s i n g l e photon through i t s c r e a t i o n and e v e n t u a l l o s s t o the c a v i t y , (see f i g . 3 j ) For a photon a t A heading r i g h t , we have a t o t a l number of passes: d)o=<|>ij'22R {1-Syo 8|iy22exp(-4B»L) )•-» where i i s t h e mean number of passes through a s i n g l e rod f o r a double pass of one photon. Thus: J(i= tfo ( 1-exp <-B» L) ) Rr/2B*L Hr=H-tfo*exp<-BM.) • ^ o* V1exp(-2B ,L)+yo* JfTexp (-3B* L) I f we now s o l v e f o r the mean number o f passes a photon experiances during t h e c r e a t i o n process, assuming a constant gain B, we f i n d : end mirror ref lecttvity=y, glass rods^  bulk loss = B'/cm, polarizer & dyecell loss = 1-JTa front mirror reflectivity=R \ l end loss=1-Jf0 FIG 3j THE PASSIVE DECAY OF A PHOTON CREATED INSIDE THE CAVITY Vc»1/4x{ 1 + 3yo2 + 5Yo»y1+7yo*^1)x (1+YO* + YO* yl+Y o* The amplitude of t h a t photon at ft i s approximately; yo^y* 5(T-4B*L) Hence, the t o t a l mean number o f passes per photon c r e a t e d i s : w i t h i n 20% f o r B<8%/cm (one j o u l e s t o r e d per c c ) . I n a d d i t i o n , the equations are s t a b l e i n the sense t h a t , an excess of f l u x through some area along the rod w i l l lower the r e l a t i v e gain there so t h a t more photons w i l l be c r e a t e d elsewhere. T h i s w i l l tend to keep B constant on average and * 7 a * The approximations used above are v a l i d t o ***44*** f o r c e the t o t a l f l u x towards the l i n e a r l i m i t . The output per photon c r e a t e d i s gi v e n by; *7b* <j>,cyo»y15j'2C1-4B»Ll { 1-B) (1-Y o 8 )f 1 }f2 2Bexp(- f lB* L) )•-» Thus, r e w r i t i n g e g uation 6 i n terms of the t o t a l output energy, we get; *8* Eex=(J),,VEs (1-exp <-crfEex/hH^» A) )/2 where: V i s the t o t a l volume of g l a s s & i s i t s c r o s s e c t i o n a l area . LASING AT THBESBOLD I f we take t h e l i m i t as Eex~0, we f i n d the above equation reduces t o the normal t h r e s h o l d c o n d i t i o n . That i s : 1=2L(fc0'Es (0) /2fif= 2L(j>B (0) where B(0) i s the t h r e s h o l d gain In a l o s s l e s s system <}> reduces t o (1+R)-/(1-.R) so t h a t : B<0)= (1-B) /2L{1+R) The usual e x p r e s s i o n , d e r i v e d by equating the l o s s per pass t o t h e g a i n per pass y i e l d s : B ( 0 ) - ~ l n { R ) / 4 L T h i s d i f f e r s from our e x p r e s s i o n by l e s s than 41 f o r R>. 5 Thus, we have been a b l e t o d e r i v e an e x p r e s s i o n r e l a t i n g t he t o t a l o u t p u t energy t o t h e s t o r e d energy, m i r r o r r e f l e c t i v i t y and c a v i t y l o s s e s w i t h o u t c o n s i d e r i n g t h e d e t a i l e d time e v o l u t i o n of the p u l s e . , BLEACHABLE BYE LOSSES T h i s e x p r e s s i o n i s , however, o n l y v a l i d f o r c o n s t a n t p a s s i v e l o s s and does not i n c l u d e t h e Q-switch dye l o s s e s which are a n y t h i n g b u t p a s s i v e . S u p r i s i n g l y , t h i s a p p r o x i m a t i o n i s g u i t e good s i n c e , even a t maximum c o n c e n t r a t i o n ( c o r r e s p o n d i n g t o a bank v o l t a g e of 2.6kV) t h e d y e c e l l t r a n s m i s s i o n i s 43%. T h i s , c o u p l e d w i t h a molar e x t i n c t i o n c o e f f i c i e n t o f 2.5x10* L/cm.mole (see r e f . 2 7 ) y i e l d s a b l e a c h i n g energy o f 1.3x10- 3 J. S i n c e t h e p u l s e r i s e i s e x p o n e n t i a l , we may e s t i m a t e t h e energy l o s t i n t h e dye t o be: El*2EbTp/Td where: El= t o t a l energy l o s t i n t h e dye Eb=energy r e g u i r e d t o b l e a c h t h e dye T p = f u l l w i d t h a t h a l f h e i g h t o f t h e p u l s e Td=fluorescence l i f e t i m e of the dye (30 nsec.J, E x p e r i m e n t a l l y , t h i s {Eb=1.3x10 - 3 J maximum was obtained through measurements of the t r a n s m i s s i o n a t 1.06 of t h e dye at maximum c o n c e n t r a t i o n f o r l a s i n g combined with the molar e x t i n c t i o n c o e f f i c i e n t } has y i e l d e d about 5x10- 3 J f o r a l l Q-s p o i l e d pulses between 2.6 kV and 1.7 kV even though Tp and Eb change by a f a c t o r of t h r e e i n t h i s range. Since t h i s energy r e p r e s e n t s only between 1.5% and 4% of the t o t a l output energy i t may be s a f e l y n e g l e c t e d . OVEHftLL EFFICIENCY We must now c a l c u l a t e Es (0) -the t o t a l energy s t o r e d i n the rod - . Since the n a t u r a l l i f e t i m e and pumping e f f i c i e n c y are e s s e n t i a l l y independent of the i n v e r s i o n i n the rod, i n the absence o f l a s i n g we have: dEs/dt=- Es/Ts+/>W where: p = o v e r a l l conversion e f f i c i e n c y of e l e c t r i c a l energy t o s t o r e d energy W = e l e c t r i c a l power s u p p l i e d t o the flashlamp Ts=spontaneous l i f e t i m e of the neodymium i o n s (300 usee.) For our "square" l i g h t pulse t h i s y i e l d s : *9* Es{0) = EpTs (1-exp (-t/Ts))/Tp 0<t<Tp where Ep=the t o t a l e l e c t r i c a l energy s t o r e d i n the c a p a c i t o r bank THE CAVITY THIISFIS COEFFICIENT Alpha may be deduced from the b a s i c flashlamp pumping e f f i c i e n c y ( 2 % at 2.5kV -see "flashlamp"-) and the c a v i t y t r a n s f e r c o e f i c i e n t . For a c y l i n d r i c a l m i r r o r the mean l i g h t i n t e n s i t y at the r o d i s given by; {ref.20) Ir=2RcIo{ ( L 2 / i | - a 2 ) - s - a ) /L where: Io=the l i g h t i n t e n s i t y at the flashlamp s u r f a c e Rc=the r e f l e c t i v i t y o f the c a v i t y m irror ( 80%) L=the f l a s h t u b e l e n g t h (16.5 cm) a= the c a v i t y r a d i u s {1.8 cm) Since t h e r e i s o n l y a few percent d i f f e r e n c e between the e f f i c i e n c i e s of c y l i n d r i c a l and e l l i p t i c a l m i r r o r s , ( r e f . 4 2 ) , we assumed t h i s formula t o be v a l i d f o r our c a v i t y and thus p r e d i c t t h a t I r . 64Io. Since the f l a s h l a m p diameter i s 1.3 cm versus the r o d diameter o f 1.0 cm and, s i n c e each rod only occupies 7.6 cm of the c a v i t y , the e f f i c i e n c y o f t r a n s f e r of l i g h t from the flashlamp to the rod s u r f a c e should be 22.9%. Si n c e the rods are contained i n a pyrex sheath and, s i n c e the s u r f a c e of the rods i s sandb l a s t e d , we can expect a d d i t i o n a l l o s s e s due to r e f l e c t i o n of about 1555., Th i s i n c l u d e s 6% f o r the rough s u r f a c e ( r e f l e c t i o n averages that f o r angles up to 40°) and 4.5% f o r each of the pyrex s u r f a c e s . We can thus p r e d i c t an o v e r a l l e f f i c i e n c y f o r conversion o f e l e c t r i c a l energy t o energy store d i n the g l a s s of .4% per rod at a bank voltage of 2.5 kV. & s i n g l e rod might be expected t o d i s p l a y a s l i g h t l y higher e f f i c i e n c y because some o f the l i g h t focused o u t s i d e the ends of the rod w i l l be r e f l e c t e d i n t o i t . We would, however, expect t h i s e f f e c t t o be s m a l l . NDMERIC&L IVAiaSlIOfi We are now i n a p o s i t i o n t o p r e d i c t the major parameters of our l a s e r . I f we use the f o l l o w i n g values estimated from t h e m a t e r i a l s s p e c i f i c a t i o n s and data a l r e a d y presented, bulk l o s s i n the glass=B ,~.3%/cm the l o s s e s at the rod ends=1~yo»T% ( p r i m a r i l y due t o c o a t i n g damage) the l o s s at the back mirror=1-K 1«i1% -the l o s s i n the d y e c e l l and polariser=1-)(2K6% ( p r i m a r i l y due t o d e p o l a r i z a t i o n i n the s o l v e n t and l a s e r g l a s s o f the l a s e r beam) the f r o n t m i r r o r r e f l e c t i v i t y = R = 6 5 % we f i n d f o r o p e r a t i o n with a s i n g l e rod (1) and f o r two rods (2) r e s p e c t i v e l y : 1 2 f =3. 1 <f> =2.7 cf ' =.64 d>» = .55 B(0)=4.2%/cm B (0) =2.4%/cm Es(0)=.52 J/cc Es(0) = .30 J/cc = 3.1 J t o t a l =3.6 J t o t a l To check these estimates, we measured the peak l a s e r output power i n normal mode (by means of the i n t e g r a t e d s i g n a l from a pin diode) as a f u n c t i o n o f the power a v a i l a b l e f o r i n v e r s i o n i n the rods. ( r e f . Fig.31) The l a t t e r was determined r e l a t i v e l y as a f u n c t i o n of bank voltage from f i g u r e 3g and the s c a l i n g f a c t o r was determined by assuming that our c a l c u l a t e d o v e r a l l e f f i c i e n c y a t 2.5kV of .39% per rod was c o r r e c t . In normal mode we would expect t h a t , once l a s i n g has s t a r t e d , the power out should be given by: Pex=4>' (/>P-Es(0) /Ts) where pP i s the power a v a i l a b l e f o r i n v e r s i o n We would a l s o not expect t o see any l a s i n g at a l l u n t i l l 1.6 times t h r e s h o l d s i n c e the i n v e r s i o n i s expected t o r i s e as (1-exp (-t/Ts) ) < (1.6)-» which i s l e s s than (1.6)-* f o r 20 SI CD 15 =1 o (/) rd o 10 experimental points A one rod o two rods / 8 2.0 — 3.0 •A 1 1 1 4.0 5.0 6.0 joules inversion pumped into each rod in 300 jjseconds 7.0 FIG 3k NORMAL MODE LASING 0<t<300 useconds. Thus, f o r a s h o r t p u l s e , the r e a l pumping t h r e s h o l d power i s given by P=Es (o)/Ts (1-exp (-Tp/Ts) ). COMPARISON TO EXPERIMENT z£S£fiAL iQDE-Our experimental o b s e r v a t i o n s are p l o t t e d i n f i g u r e 3k.„ The p o i n t s f a l l on s t r a i g h t , l i n e s above about 4.5 J i n v e r s i o n but do not drop o f f as g u i c k l y as expected near 1.6 times t h r e s h o l d . The l i n e a r p o r t i o n i s good evidence that graph 3e does i n f a c t r e p r e s e n t the i n v e r s i o n power i n that r e g i o n . The d e v i a t i o n below 4.5 3 i s probably p a r t l y due to the i n c r e a s e i n the s p e c t r a l pumping e f f i c i e n c y of the flashlamp at lower c u r r e n t s , (ref.20,22) T h i s i n d i c a t e s t h a t graph 3e i s low i n t h i s r e g i o n . , S i n c e t h i s does not a f f e c t the r e s u l t s at h i g h e r c u r r e n t s and, s i n c e we are not i n t e r e s t e d i n o p e r a t i n g i n t h i s region, anyway, i t i s of only academic i n t e r e s t . The low power l a s i n g (which occurs below the expected t h r e s h o l d power o f 1.6Es(0)/Ts) i s a l s o p a r t l y e x p l a i n e d by s p a t i a l d i f f e r e n c e s i n damage l o s s e s , alignment and pumping a c r o s s the rods. The l a s e r f o o t p r i n t i s very nonuniform i n t h i s r e g i o n , (see f i g . 3 1 ) S i n c e the l o s s and gain parameters were c a l c u l a t e d as averages, th e s e l o c a l areas of high e f f i c i e n c y are n a t u r a l l y going t o d i s p l a y a t h r e s h o l d below the average. The power generated i n these r e g i o n s i s n a t u r a l l y l e s s than the power produced when the whole rod i s c o n t r i b u t i n g so, as se observed, we would expect a nonzero power around 1.6Es(0)/Ts which i s below the l i n e r e p r e s e n t i n g the c o n v e r s i o n e f f i c i e n c y of the whole rod. ***52*** footprints near threshold: changes as the front mirror is adjusted same alignment, 2o5 kV, q-spoi led 4* much better ali g ned -same power-but sti l l not optimal same alignment, more pumping, normal mode nick in the side of the spot is du to a spal l split from the side of the rod FIG 31 L A S E R FOOTPRINTS ON POLAROID FILM Above 4 j o u l e s the r e s u l t s f o r two r o d s d i s p l a y an e x c e l l e n t f i t t o theory. The r e s u l t s with one rod i n d i c a t e a s l i g h t l y s m a l l e r s l o p e r e l a t i v e to the s l o p e f o r two rods than p r e d i c t e d by theory. The observed r a t i o (obtained from the two s o l i d l i n e s ) was 1.9 versus the t h e o r e t i c a l r a t i o given by: The d i f f e r e n c e s are n e a r l y w i t h i n the l i m i t s of experimental e r r o r and can c e r t a i n l y be accounted f o r by changes i n alignment or s l i g h t d i f f e r e n c e s between rods i n the n a t u r a l l i f e t i m e of l e v e l 2. (see f i g . 3 k ) The experiment **#53*** was not repeated t o see i f the l a t t e r was, i n f a c t , the case. The s c a l i n g f a c t o r was checked by measuring the t o t a l output energy at 2.5 k?. T h e o r e t i c a l l y , we would expect t h a t d u r i n g l a s i n g : Eex=^» (f>P-Es{0)/Ts)Tp where Tp i s the l e n g t h of time during which l a s i n g o c c u r s . For two rods Tpcr200 juseconds so t h a t Ex=4.0 J , while f o r one rod Tpft150 ^seconds so t h a t Eex=1.1 3. These values both agree with t h e energy measured by the t h e r m o p i l e . (~3.5, ~ 1 . 1 j o u l e s r e s p e c t i v e l y ) T h i s i n d i c a t e s t h a t p i s e s s e n t i a l l y c o r r e c t , and a l s o through <J>* v e r i f i e s t h a t our estimate of the i n t e r n a l l o s s e s are s u b s t a n t i a l l y c o r r e c t . The r a t i o o f these e n e r g i e s corresponds to the r a t i o of the s i g n a l s from the p i n diode i n t e g r a t e d over the whole pu l s e . T h i s checks t h a t the i n t e g r a t e d p i n diode s i g n a l i s i n f a c t p r o p o r t i o n a l t o the t o t a l energy. F i n a l l y we checked t h a t the i n v e r s i o n does, i n f a c t , r i s e as (1-exp (-t/Ts)) without l a s i n g by measuring the observed time t i l l normal mode l a s i n g s t a r t s at 2 . 5 kV. From the pumping power and t h r e s h o l d energy, we p r e d i c t 1 7 5 useconds and 9 5 ^seconds, f o r one (assuming T s = 3 7 0 usee.) and two rods r e s p e c t i v e l y . We measured Ti-=90±15 useconds f o r the two rods but the s i n g l e r o d took only 130+15 useconds t o l a s e . again* t h i s i n d i c a t e s that we may have overestimated the t h r e s h o l d or underestimated the l i f e t i m e i n the case o f the s i n g l e rod. In s h o r t we have obtained an adequate d e s c r i p t i o n o f t h i s l a s e r s o p e r a t i o n i n normal mode. The values f o r the i n v e r s i o n energy and e x t r a c t i o n e f f i c i e n c y (cj)'} are a t l e a s t a c c u r a t e t o 20%. In the case of a s i n g l e rod t h e r e i s some doubt concerning the l i f e t i m e , t h r e s h o l d and e f f i c i e n c y c o e f f i c i e n t s but even i n t h i s case we would expect t h a t a l l the t r u e values are w i t h i n 20% of those used i n our model., COWPARISON TO EXPERIMENT -Q-SPOILED J5QDE-We are now i n a p o s i t i o n t o p r e d i c t the output i n the Q - s p o i l e d mode and to compare i t with experiment. Equation #9 enables us t o p r e d i c t the i n v e r s i o n f o r one and two rods r e s p e c t i v e l y . We estimated the time t o l a s i n g (the pump power was minimal f o r a given dye c o n c e n t r a t i o n so t h a t l a s i n g o c c u r r e d at t h e end of the l i g h t pulse) from the l i g h t pulse f a l l t i m e and f u l l width a t h a l f h e i g h t , (see f i g . 3e) The i n v e r s i o n power was o btained from f i g u r e 3g s c a l e d to P=.39% at 2.5 kV. We assumed that Ts f o r the s i n g l e rod was 37 0 pseconds and t h a t the p o l a r i z e r reduced •**55*** the a v a i l a b l e i n v e r s i o n by 20%. T h i s l a t t e r assumption i s p e s s i m i s t i c and w i l l break down f o r long pulse times, (r e f . 29, 30, 31) T h i s i n v e r s i o n combined with the v a l u e s of d\ and (j)1 used f o r the normal mode c a l c u l a t i o n s may be s u b s t i t u t e d i n t o equation #8 t o y i e l d the t h e o r e t i c a l curves i n f i g u r e s 3m,3n. •5 1.0 1.5 a.o electrical energy in kj" FIG 3m i These graphs a l s o i n c l u d e the output t h a t was observed e x p e r i m e n t a l l y . I t s departure from theory i s obvious. *#*56*** 1.01-Q-SPOILED PERFORMANCE ONE ROD >-c •Oh Z3 O theoretical output: polarizer no polarizer observed output 1.0 1'5 electrical energy in kJ 2-0 FIG 3n LOW ENERGY PULSES As i n normal mode, we can e x p l a i n the low energy output below t h r e s h o l d as being p r i m a r i l y due to s p a t i a l d i f f e r e n c e s across the l a s e r , (see fig.3d) A l s o , as the l a s e r drops below .1 j t o t a l output the pulse h a l f w i d t h r i s e s t o more than 200 nanoseconds. Pulses t h i s long allow time f o r the lower l a s e r l e v e l to depopulate so t h a t a f r a c t i o n of the i n v e r s i o n that was discounted i n eguation #8 i s slowly made a v a i l a b l e . A l s o , the e f f e c t of the p o l a r i z e r i s reported t o disappear i n normal mode, so we could expect that as the power drops and the l a s i n g time i n c r e a s e s t h i s f r a c t i o n of the i n v e r s i o n (20%) should a l s o become a v a i l a b l e . We have i n d i c a t e d (see fig,3m,3n) the i n i t i a l *#*57*** t h e o r e t i c a l o u t p u t w i t h o u t t h e 20% from t h e p o l a r i z e r and i t appears t h a t t h i s c o u l d account almost c o m p l e t e l y f o r the d e v i a t i o n s . , I t i s a l s o of i n t e r e s t t h a t t h e p u l s e w i d t h i s 150 nanoseconds a t .15 J f o r a s i n g l e r o d w h i l e f o r two t h e p u l s e w i d t h i s a l r e a d y down t o 50 nanoseconds. Thus, i t i s not s u p r i s i n g t o f i n d t h a t t h e f a s t r i s i n g p a r t o f t h e c u r v e f o r a s i n g l e r o d c o r r e s p o n d s almost e x a c t l y t o the e x p e c t e d o u t p u t w i t h o u t t h e p o l a r i s e r w h i l e t h e f a s t r i s i n g p a r t of the c u r v e f o r two r o d s i s s h i f t e d towards the e x p e c t e d o u t p u t i n c l u d i n g t h e l o s s . Thus, f o r low pump powers, we have good agreement w i t h t h e o r y . T h i s l a s t s u n t i l s u d d e n l y t h e e x p e r i m e n t a l l y observed o u t p u t s a t u r a t e s a t about .28 J f o r both one and two r o d s . , I n t h e case o f t h e two r o d s we a r e a b l e t o i n c r e a s e t h e pump power by more t h a n a f a c t o r of two above t h r e s h o l d and over t h i s whole range t h e o u t p u t i n c r e a s e s by o n l y .8 J . T h i s compares q u i t e u n f a v o u r a b l y w i t h our p r e d i c t i o n of 1.3 «J. HIGH POHER LASIIG S i n c e the l a s e r s a t u r a t e s a t t h e same o u t p u t energy f o r both one and two r o d s , we might have p o s t u l a t e d t h a t t h e l o s s e s p r o d u c i n g t h i s s a t u r a t i o n a r e dependent on the net energy f l u x through t h e g l a s s . T h i s would be t h e case f o r such mechanisms as i m p u r i t y e x c i t a t i o n i n t h e g l a s s or t h e r m a l l y i n d u c e d d i s t o r t i o n , b i r e f r i n g e n c e and d i s a l i g a m e n t . However, we found t h a t the dye c o n c e n t r a t i o n p l o t t e d as a f u n c t i o n o f pump energy a l s o s a t u r a t e s , (see fig.3m) Since we can expect the dye to bleach when the l o s s through the dye i s approximately equal to t h e gai n above t h r e s h o l d , we would expect the dye c o n c e n t r a t i o n t o be p r o p o r t i o n a l to the energy s t o r e d above t h r e s h o l d . The s a t u r a t i o n i n the c o n c e n t r a t i o n of the dye i n d i c a t e s then, that the i n v e r s i o n i s j u s t not being produced. Since the pump energy i s d e f i n i t e l y a v a i l a b l e (see normal mode r e s u l t s ) and s i n c e i n v e r s i o n s over a j b u l e / c c (we a n t i c i p a t e only .81 J / c c a t 2 kJ pump) have been r e a d i l y o b t a i n e d by other authors we can only conclude t h a t the i n v e r s i o n i s being a c t i v e l y d e p l e t e d . SjgPJBJPLDORESCENGI EMISSION The mechanism I b e l i e v e i s r e s p o n s i b l e i s p a r a s i t i c o s c i l l a t i o n ( e f f e c t i v e l y superf luorescence) s e t up between the c a v i t y m i r r o r s and the neodymium g l a s s . The s u r f a c e o f the r o d i s sandblasted so there i s a l o t of s c a t t e r i n g from any p a r t i c u l a r mode and the t h r e s h o l d f o r an i n d i v i d u a l mode i s high. However, the c a v i t y i s l a r g e and we would expect much of the l i g h t s c a t t e r e d from one mode to be refocused elsewhere on t h e r o d . I t i s not necessary that a c t u a l l a s i n g occur s i n c e the energy l o s t through spontaneous emission i s about 70% o f the pumping i n v e r s i o n energy f o r one rod a t s a t u r a t i o n . Thus, we r e g u i r e t h a t a spontaneously emitted photon gain only HH% on average from s t i m u l a t e d emission b e f o r e i t i s l o s t . I f we c o n s i d e r a s i n g l e rod a t s a t u r a t i o n , we f i n d a gain of 6? / c a , I f we assume t h a t the spontaneously emitted photons are emitted p e r p e n d i c u l a r t o the rod and are r e f o c u s e d by the c a v i t y m i r r o r s on the rod an i n f i n i t e number o f times and are l o s t through a m i r r o r r e f l e c t i v i t y of only 80%> we o b t a i n a t o t a l s t i m u l a t e d e m i s s i o n of 40%. T h i s i s by no means a complete c a l c u l a t i o n s i n c e i t i g n o r e s both the i n t e n s e s c a t t e r i n g that occurs a t the rod s u r f a c e as w e l l as the much l a r g e r c o n t r i b u t i o n to the s t i m u l a t e d emission made by the photons emitted d i a g o n a l l y . However, i t y i e l d s r e s u l t s t h a t are o f the r i g h t o r d e r and i s at l e a s t s t r o n g l y s u g g e s t i v e . At higher pumping powers, the amount of energy gained per spontaneously emitted photon has t o i n c r e a s e but t h i s f r a c t i o n i s a very s t r o n g f u n c t i o n of the gain (an average gain of 40% means t h a t many modes are e x p o n e n t i a l with r e s p e c t to t h e gain) and hence we would not expect much of an i n c r e a s e i n the i n v e r s i o n . Thus, we would expect only the marginal improvement i n l a s i n g t h a t was, i n f a c t , observed. (see fig.3a) In t h e case of two rods the gain i s down by 43% but presumably t h i s i s compensated f o r by the lower c a v i t y end l o s s e s due to the g r e a t e r l e n g t h . An exact numerical c a l c u l a t i o n c o u l d be performed t o v e r i f y t h i s completely but the evidence presented so f a r seems to me t o be c o n c l u s i v e enough. ADDITIONAL ABSORPTION AT 1^06 ^ On t h i s b a s i s , tubes of water were p l a c e d between the l a s e r rod and the c a v i t y m i r r o r t o i n c r e a s e the a b s o r p t i o n of t h e 1.06 ju r a d i a t i o n . However, water does not absorb w e l l and i t a l s o c u t s down on the f l a s h l a m p pumping e f f i c i e n c y so we were unable t o untangle the two e f f e c t s . C e r t a i n l y t h e r e was no dramatic improvement, so presumably to reach the t h e o r e t i c a l performance we must o b t a i n c l a d rods. In c o n c l u s i o n , I am convinced t h a t , as has been repor t e d f o r neodymium g l a s s d i s k a m p l i f i e r s 7 cm a c r o s s (ref.41) and elsewhere (ref.9,40,43) the g a i n i n my l a s e r i s being l i m i t e d to only s l i g h t l y above t h r e s h o l d by s u p e r f l u o r e s c e n c e . When t h i s problem has been c o r r e c t e d by the use of an a p p r o p r i a t e c l a d d i n g m a t e r i a l , I c o n f i d e n t l y expect to see my l a s e r reach i t s t h e o r e t i c a l energy with two rods of 1.6 J Q - s p o i l e d a t 2.6 kV. REVIEW OF THE LITERATURE IHILISHED THEORY At t h i s p o i n t i t i s a p p r o p r i a t e t o q u i c k l y sample the l i t e r a t u r e p u b l i s h e d on o v e r a l l neodymium l a s e r performance. ,As f a r as I can determine, the theory f o r l a s e r a c t i o n has always been approached through the time dependent r a t e equations and i n v o l v e s determining the power i n s i d e the c a v i t y , (ref.37,38) T h i s i s perhaps a p p r o p r i a t e i n the case of normal mode c a l c u l a t i o n s (ref.16) but when a p p l i e d t o the s t r o n g l y n o n l i n e a r Q - s p o i l e d p u l s e becomes very complicated. S i m p l i f y i n g assumptions such as l i n e a r i t y and d i s t r i b u t e d gain and l o s s c o e f i c i e n t s (ref.16) must be used and, even then, the equations are onl y s o l u b l e by computer i n terms of reduced v a r i a b l e s , without the programs and e x p l i c i t e d eterminations of the s c a l i n g f a c t o r s the r e s u l t s are only of l i m i t e d u s e f u l n e s s . In c o n t r a s t , my c o n s e r v a t i o n equation i s e x a c t , i n t u i t i v e l y obvious and immediately a p p l i c a b l e t o measurable experimental parameters. I t does not i n c l u d e the e f f e c t s of r a d i a l nonuniformity and g i v e s no i n f o r m a t i o n about the r a t e at which the e q u i l i b r i u m i s reached. However, the method may be extended t o cover both these problems -the former through a c o n s i d e r a t i o n o f t h e f l u x as a f u n c t i o n o f r a d i a l p o s i t i o n and the l a t t e r through s o l v i n g the equation i n s t e p s o f the c a v i t y l i f e t i m e . But what i s more important, an e x p r e s s i o n f o r determining the optimum output mirror r e f l e c t i v i t y (R) may be d e r i v e d by simply d i f f e r e n t i a t i n g the eguation with r e s p e c t t o R and s e t t i n g the r e s u l t equal z e r o f o r the maximum, (see chapter IV) The e q u i v a l e n t s t o t h i s e x p r e s s i o n i n r e f e r e n c e s #37,38 are t h r e e dimensional computer drawn graphs some of which I s t i l l have d i f f i c u l t y t r a n s l a t i n g i n t o p r a c t i c a l terms. EXPERIMENTAL JESfLTS The complexity o f p u b l i s h e d theory has l e d to a c o n s i d e r a b l e v a r i e t y of experimental parameters being re p o r t e d or not r e p o r t e d f o r experimental work, (refs.9,39,40,45,46) In g e n e r a l though, when the necessary i n f o r m a t i o n i s a v a i l a b l e i t i s c o n s i s t e n t with my p r e d i c t i o n s . Reference #39 obtained .48 J from a 3.25" rod at a 100 J/cc pumping versus my p r e d i c t i o n of .55 J f o r a 3" rod at 170 J / c c pumping but h i s l o s s e s were somewhat lower than mine.(21 J / c c t h r e s h o l d pumping versus 50 J / c c f o r my rod) Others though, (ref.20) do r e p o r t c a v i t y l o s s e s more s i m i l a r t o mine. (69 J / c c t h r e s h o l d ) Reference #40 r e p o r t s an i n v e r s i o n of 1.46 J/cc a t a pumping energy of 243 J/cc versus my p r e d i c t i o n o f .85 J / c c f o r 170 J/cc pumping. These r e s u l t s are c o n s i s t e n t when one c o n s i d e r s t h a t my c a v i t y t r a n s f e r c o e f f i c i e n t i s low because of the d i f f e r e n c e i n s i z e between t h e rods and the flashlamp. My t h e o r e t i c a l output from two rods compares well with the output from a 13 cm dye 'Q-switched rod o f 1.2 J r e p o r t e d i n r e f e r e n c e #18. One g l a r i n g e x c e p t i o n to t h i s g eneral agreement i s found i n r e f e r e n c e #44 which r e p o r t e d a t h r e s h o l d o f 3400 J/ c c pumping (presumably i n a l o n g pulse?) with a two inch rod. I can only conclude t h a t someone e l s e has unknowingly run i n t o t r o u b l e with s u p e r f l u o r e s c e n c e . Indeed, s i n c e almost a l l the papers do not i n d i c a t e t h a t they used c l a d rods, my experiance would l e a d me t o be h i g h l y s c e p t i c a l of t h e i r high output power r e s u l t s . At any r a t e , i n g e n e r a l , a l l t h e u s e f u l i n f o r m a t i o n on performance t h a t I have found tends to c o l l a b o r a t e my p r e d i c t i o n s . QUALITATIVE PEBFOBMANCE INTBODUCTIQN ¥e have now f a i r l y e x h a u s t i v e l y reviewed the major f e a t u r e s of t h i s l a s e r s performance. I t i s a p p r o p r i a t e then, at t h i s p o i n t , t o present a b r i e f summary of some of our h i s t o r i c a l and q u a l i t a t i v e r e s u l t s . HISTOBICAL Our f i r s t l a s e r c o n s i s t e d of a three i n c h neodymium doped rod i n a c y l i n d r i c a l c a v i t y pumped by a small diameter (.5 cm) xenon flashlamp. The power supply was capable of d e l i v e r i n g 900 j o u l e s i n 1000 useconds which, when we i n c l u d e t h e i n c r e a s e d c a v i t y t r a n s f e r c o e f f i c i e n t , i s e q u i v a l e n t to about 1.6 kV with our present system. Since the l o s s e s were lower (no d y e - c e l l and p o l a r i z e r ) we were able to o b t a i n approximately one j o u l e normal mode i n 1000 useconds. Attempts to Q - s p o i l the l a s e r with a r o t a t i n g prism were, however, u n s u c c e s s f u l probably because of v i b r a t i o n i n the m i r r o r . S i n c e p u l s e s Q-switched by r o t a t i n g prisms tend to be q u i t e long {about 70 jaseconds f o r our prism a t one j o u l e output {ref.40)) and s i n c e we r e q u i r e a narrow l i n e {about 2 A o r l e s s from s c a t t e r i n g theory v e r s u s the 3 A or more observed with prisms (ref.4 7)) we decided to ***65*** abandon the prism and t o s u b s t i t u t e a bleachable dye Q-switch. ?e were then a b l e to obt a i n about .2 j o u l e s Q-s p o i l e d e s s e n t i a l l y independent of power above the 700 J t h r e s h o l d . T h i s t h r e s h o l d i s lower than we would at f i r s t expect from the r e s u l t s from our present system, but when we i n c l u d e the lower c a v i t y l o s s e s and l o n g e r pumping time i t i s understandable. However, as was observed f o r one rod i n . EsC-0) -J (one rod) 3.1 J b—3.6 J 0 .1 .2 .3 .4 .5 .6 time i n JJ s e c. 6.0 J F I G 3o THE^ Q-SPOILED NEODYMIUM LIGHT PULSE (SHAPE^_AS'. A" FUNCTION OF THE INITIAL STORED ENERGY: CEs(O)) the present system, the p u l s e was s t i l l of the order o f 150 nanoseconds l o n g {see F i g . 3o-a) and the peak power was consequently much too low. By r e d e s i g n i n g the ca p a c i t o r • b a n k to reduce the pumping pu l s e time to 500 ^seconds, we were abl e t o n e a r l y double the peak pumping power. . T h i s enabled us, with c a r e f u l alignment, to o b t a i n p u l s e s of about 50 nanoseconds h a l f width with t o t a l energy of about .3 j o u l e s , {see f i g . 3 o - c ) However, these narrower pulses were not r e p r o d u c i b l e and tended to break i n t o two p u l s e s separated by about 5 juseconds. Presumably, t h i s time i s some m u l t i p l e of the time necessary t o depopulate the lower l a s e r l e v e l (#4). In any event, the performance was s t i l l u n s a t i s f a c t o r y and a f t e r one more i n t e r i m design, we a r r i v e d a t the c u r r e n t arrangement. T h i s i s capable, with two rods, of producing pulses r e p r o d u c i b l e t o 10% i n peak power and, with a h a l f width of about 20 nanoseconds, {see fig.3o-d) However, i t i s s t i l l l i m i t e d t o a t o t a l output of only about .35 J i n Q-s p o i l e d mode. , SPECIAL TECHIipjJES During a l l t h i s development we were c o n s t a n t l y faced with near t h r e s h o l d i n v e r s i o n s and consequent marginal performance. Thus, as w e l l as i n c r e a s i n g the pump power t o i n c r e a s e the i n v e r s i o n * we attempted to i n c r e a s e i t s e f f e c t i v e n e s s by lowering the t h r e s h o l d by minimizing the l o s s e s . FRONT MIRIOR ALIGNMENT I n i t i a l l y , the f r o n t m i r r o r s were a l i g n e d through the i n t e r f e r e n c e f r i n g e s from a helium-neon alignment l a s e r . However, we soon found t h a t we c o u l d reduce the t h r e s h o l d s u b s t a n t i a l l y by r e a d j u s t i n g the m i r r o r and o p t i m i z i n g the output near t h r e s h o l d . The l a s e r output was monitored by o b s e r v i n g the l a s e r " f o o t p r i n t " l e f t on a piece of black p o l a r o i d f i l m . The f o o t p r i n t s near t h r e s h o l d show c o n s i d e r a b l e s p a t i a l n o n u n i f o r m i t y though the rod i s depleted q u i t e u n i f o r m l y a t high pump powers i n normal mode and shows o n l y a uniform i n c r e a s e i n beam divergence i n Q-s p o i l e d mode. (see f i g . 3 1 ) The t h r e s h o l d spots were optimized with r e s p e c t to both spot u n i f o r m i t y and t o t a l energy. The alignment procedure i s q u i t e tedious s i n c e the maximum i s s t r o n g l y r i d g e shaped and maximizing i n each d i r e c t i o n of t i l t produces only a slow convergence t o the true optimum. However, i t i s worthwhile s i n c e t h i s can produce a decrease i n the t h r e s h o l d by as much as 40%, presumably because of the d i f f e r e n c e i n the index o f r e f r a c t i o n of g l a s s between .6328 p and 1.06 p as w e l l as both thermal and pumping d i f f e r e n c e s a c r o s s the rods. CAVITY MIRROR ALIGNMENT We a l s o found t h a t the p o s i t i o n of the c a v i t y r e f l e c t o r was q u i t e important, p a r t i c u l a r l y when we were using the s m a l l bore flash-tubes. Again, the p o s i t i o n was s y s t e m a t i c a l l y v a r i e d while the l a s e r performance near t h r e s h o l d was monitored. U n f o r t u n a t e l y , i t i s even more d i f f i c u l t to o b t a i n the optimum p o s i t i o n i n g f o r the c a v i t y m i r r o r than i t i s f o r the f r o n t m i r r o r because the f r o n t m i rror optimium alignment compensates f o r the nonuniform pumping produced by c a v i t y misalignment. During s e v e r a l attempts at b u i l d i n g l a s e r s we t r i e d s i x d i f f e r e n t c a v i t y m i r r o r s with e x c e n t r i c i t i e s v a r y i n g between 1.0 and .64. The o n l y d i f f e r e n c e s between them seemed to be i n the p o s i t i o n necessary to o b t a i n uniform pumping and the s e n s i t i v i t y of the l a s i n g to t h i s p o s i t i o n i n g . i s has been r e p o r t e d i n r e f e r e n c e #42, there appeared to be l i t t l e e f f e c t on the t o t a l maximum l a s e r power, s u p r i s i n g l y , the more e l l i p t i c a l m i r r o r s turned out t o be the l e a s t s e n s i t i v e to alignment. S i n c e we are c u r r e n t l y u sing an e l l i p s e of e x c e n t r i c i t y .64 and, s i n c e the f l a s h t u b e i s l a r g e r than the l a s e r rod, we have managed to reduce the s e n s i t i v i t y of our present l a s e r to c a v i t y alignment to a minimum. LASER ROD ALIGNMENT I t was a l s o found important t o keep the rod ends p e r p e n d i c u l a r t o the l a s e r beam. As has already been noted, even a s m a l l e r r o r w i l l d e f l e c t the l i g h t r e f l e c t e d from the ends out of the c a v i t y . Though the a n t i r e f l e c t a n c e c o a t i n g s are supposed t o keep l i g h t frost being r e f l e c t e d , they q u i c k l y d e t e r i o r a t e with use. Thus, we are a b l e t o observe a s u b s t a n t i a l improvement when the rods were c o r r e c t l y a l i g n e d . The thermal s t r a i n s produced when the rods are pumped {see "thermal e f f e c t s " 3.1) a f f e c t s t h i s alignment. I n our most s e n s i t i v e c o n f i g u r a t i o n s , i t was found necessary t o both a l i g n the end m i r r o r and operate with the flashlamp being f i r e d at r e g u l a r i n t e r v a l s (1 to 2 minutes per shot) with c o n s t a n t c o o l i n g . T h i s i n t e r v a l has been found by o t h e r authors (ref.32,33,34,35) t o be a p p r o p r i a t e f o r r e l a x i n g the thermal g r a d i e n t s and d i s t o r t i o n s i n the g l a s s . In our c u r r e n t system, because we have s l i g h t l y more gain than f o r m e r l y , we have not found t h i s pulse t i m i n g t o be necessary. HATERIALS DAMAGE The c a v i t y l o s s e s are o b v i o u s l y s t r o n g l y dependent on the c o n d i t i o n o f the t r a n s m i t t i n g s u r f a c e s i n s i d e the c a v i t y . Since we use a i r c o o l i n g , there i s always some dust being d e p o s i t e d even though we p r o t e c t most of the s u r f a c e s with dead a i r spaces. Thus, most of the s u r f a c e s ( e s p e c i a l l y the d y e c e l l windows and top p l a t e s of the p o l a r i z e r ) must be p e r i o d i c a l l y c l e a n e d . The a i r hard Adolf M e l l e r a n t i r e f l e c t a n c e c o a t i n g s on the ends of the l a s e r rods w i l l - not r e s i s t s o l v e n t s and are best cleaned with n i t r o g e n or by very g e n t l e wiping with c o t t o n . The d i e l e c t r i c m i r r o r s and q u a r t z windows stand up much b e t t e r but, to completely remove a l l f i l m s , i t was found best t o complete the c l e a n i n g by r u b b i n g with dry c o t t o n . F i n e paper tends t o s c r a t c h and c o l l o d i n l e a v e s an o r g a n i c f i l m . Even with c a r e f u l c l e a n i n g we s t i l l found some p i t t i n g produced i n the guartz s u r f a c e s when the a n t i r e f l e c t a n c e c o a t i n g s were new. T h i s i s probably p a r t l y due to p o l i s h i n g i n c l u s i o n s l e f t i n the s u r f a c e of the quartz and p a r t l y t o high power modelocked f i l a m e n t s . The l a t t e r has been observed i n dye Q - s p o i l e d neodymium l a s e r s a t powers as low as 100 HS/cm 2. (ref.25) Since the power i n s i d e our c a v i t y i s g)/^» times t h a t o u t s i d e or 150 MW with two rods, we c o u l d w e l l have obtained the s h o r t high power pulses reported i n r e f e r e n c e #25. As i n t h a t r e f e r e n c e , f u r t h e r damage ceased a f t e r some degradation of the c a v i t y s u r f a c e s . They a t t r i b u t e t h i s to a decrease i n the c a v i t y gain but i t seems more l i k e l y t h a t , s i n c e the l a s i n g processes are i n t r i n s i c a l l y n o n l i n e a r , t h a t i t i s r e l a t e d t o the s p a t i a l and temporal coherence of the beam.,At any r a t e , the t o t a l energy f l u x through the s u r f a c e s i n our c a v i t y i s only about 2.2 J/cm 2 i n 15 nanoseconds maximum and guartz s u r f a c e s are commonly r e p o r t e d to stand more than ten times that without damage, (ref.48) I t i s a l s o worth n o t i n g that most of the s u r f a c e s are at the brewster angle and so experience only about 1.1 J/cm 2. **«71*** IMPLICATIONS OF DAMAGE THRESHOLDS U n f o r t u n a t e l y i f we manage to achieve our p r e d i c t e d energy of 1.6 j o u l e s we w i l l expose the s u r f a c e s i n s i d e the c a v i t y t o much higher l e v e l s o f r a d i a t i o n . T h i s energy w i l l produce a t o t a l f l u x of 10 jo u l e s / c m 2 or about 670MW f o r the d u r a t i o n of the 15 nanosecond p u l s e . S i n c e these l o a d i n g s are approaching the t h r e s h o l d s f o r s e r i o u s damage i n a s m a l l number of s h o t s , we should probably keep the output energy below .65 j o u l e s or 4 J/cm 2 f l u x . T h i s i s , of cour s e , c o n t i n g e n t on the r e f l e c t i v i t y of the f r o n t m i r r o r . I f we reduce the r e f l e c t i v i t y then (jj/tj)1 approaches u n i t y and our output can approach the f u l l 4 J/cm 2. The exact dependence of the output and energy f l u x on m i r r o r r e f l e c t i v i t y i s d i s c u s s e d i n chapter f i v e . PULSE SHAPE The pulse h a l f w i d t h i s j u s t as important f o r meeting our requirements f o r l i g h t power as i s the t o t a l output energy. The change i n pul s e shape with i n c r e a s i n g t o t a l output energy i s i l l i s t r a t e d i n f i g u r e 3o. We can e x p l a i n t h i s behavior i n terms of eguation #8 as f o l l o w s : I n i t i a l l y the l i g h t energy i n s i d e the c a v i t y r i s e s as exp(St) where S i s p r o p o r t i o n a l t o t h e energy s t o r e d above t h r e s h o l d . Thus, when we a r e very near *»*72*** t h r e s h o l d the power w i l l r i s e g u i t e s l o w l y and much of the energy s t o r e d i n the rod w i l l be l o s t b e f o r e the power r i s e s very f a r . However, when the i n v e r s i o n gets t o even only .2 J / c c above t h r e s h o l d we are down t o an e - f o l d i n g time of only 10 nanoseconds with our c a v i t y . „ With t h i s s h o r t r i s e t i m e , the l o s s i n s t o r e d energy dur i n g the r i s e i s sma l l so the gain i s not much reduced and the power can climb much higher. Once the gain has dropped below t h r e s h o l d S becomes negative and the energy i n t h e c a v i t y s t a r t s t o decay. I f t h e r e i s a l o t of energy i n the c a v i t y when t h i s happens, i t w i l l p r o v i d e a s u b s t a n t i a l f l u x through the rods before i t i s f i n a l l y l o s t (2.7 complete passes or about 15 nanoseconds) and so d r i v e E s ( t ) w e l l below t h r e s h o l d . Thus S becomes l a r g e and negative and the l a s i n g g u i c k i y s t o p s . Conversely, i f the energy i n the c a v i t y i s s m a l l , then Es passes through t h r e s h o l d s l o w l y and S i s c l o s e t o z e r o so that the f a l l time f o r the energy i n the c a v i t y i s l a r g e . We could expect t h a t , s i n c e the s t o r e d energy drops as 1-exp(-B E i ) , the energy stor e d i n the c a v i t y at the end of the pulse w i l l drop Es more s l o w l y than t h e energy present when Es i s above t h r e s h o l d . Thus, as observed, we c o u l d expect the r i s e t i m e t o be c o n s i d e r a b l y l a r g e r than the f a l l time and more so f o r l a r g e r i n v e r s i o n s . •**73*** DIAGNOSTICS LASER FOOTPRINTS Having completed the d i s c u s s i o n o f the c h a r a c t e r i s t i c s o f t h e l a s e r i t o n l y remains to i n d i c a t e how these r e s u l t s were obtained. A crude measure of the l a s e r performance was provided by the l a s e r f o o t p r i n t s produced by i t oh black p o l a r o i d f i l m . T h i s was a u s e f u l d i a g n o s t i c f o r alignment near l a s e r t h r e s h o l d and was our only check on beam s p a t i a l u n i f o r m i t y . However, f o r higher power Q - s p o i l e d o p e r a t i o n we r e q u i r e d a more q u a n t i t a t i v e monitor. DETECTION OF LIGHT AT 1.06 JJ THE PIN DIODE This was p r o v i d e d by a f r a c t i o n of the beam which was s p l i t o f f and fed through a ground g l a s s screen (to average i t ) and then through n e u t r a l d e n s i t y f i l t e r s i n t o a MD2 Monsanto s i l i c o n p i n diode, (see fig.3p) The beam s p l i t t e r c o n s i s t e d of a g l a s s p l a t e s e t n e a r l y a t the brewster angle so t h a t only a t i n y f r a c t i o n of the beam was removed. That t h i s f r a c t i o n was r e p r e s e n t a t i v e of the whole was checked by passing the whole beam through f i l t e r s and i n t o the d e t e c t o r . , glass plate beam splitter filters pin diode glass plate beam splitter neodymium oscillator doubling chrystal filters IP21 photomultiplier a 50-O. terminator at the oscilloscope a delay line terminated, in 50 _n at the oscilloscope F I G 3p LASER LIGHT MONITORS S i n c e the r i s e - t i a e of the l i g h t p ulse i s only a few nanoseconds, our d e t e c t o r and accoapanyinq e l e c t r o n i c s must be at l e a s t that f a s t . The s i g n a l was monitored by a T e k t r o n i c s 454A o s c i l l o s c o p e which has a r i s e t i m e of about one nanosecond. The r i s e - t i m e o f the re v e r s e b i a s e d p i n diode i s s p e c i f i e d by the coapany as about .5 nanoseconds. The f a l l time i s not s p e c i f i e d and may be as much as f i v e times l a r g e r . T h i s would s t i l l be adeguate t o f o l l o w the average power o f t h e l i g h t pulse though one would probably not be able t o see the i n d i v i d u a l modelocked p u l s e s (normally 100 picoseconds, maximum 5 nseconds) which may have been r e s p o n s i b l e f o r the e a r l y damage to our guartz windows and a n t i r e f l e c t a n c e c o a t i n g s , {see ref.25) The diode*s b i a s v o l t a g e was maintained by a .1 uF ceramic c a p a c i t o r connected d i r e c t l y t o i t . T h i s i s t o avoid the long c u r r e n t response times a s s o c i a t e d with remote powersupplies. Since the c u r r e n t i s fed d i r e c t l y i n t o a 50/v ca b l e {also terminated i n a 50J2. to prevent back r e f l e c t i o n ) a l l o w i n g f o r a maximum s i g n a l of 250 m i l l i v o l t s (1% of the bias voltage) f o r a maximum time of 500 nanoseconds s t i l l o n l y produces a drop i n t h e v o l t a g e a c r o s s the c a p a c i t o r of .1%. Thus, unless the photoconversion e f f i c i e n c y o f the diode d e c l i n e s with c u r r e n t (the diode i s r a t e d f o r a peak c u r r e n t 240 times the c u r r e n t a t 250 mV) the response s h o u l d be l i n e a r . T h i s was checked by p l a c i n g f i l t e r s of measured de n s i t y at 1.06 fx i n f r o n t of the photodiode. (see f i g . 3g) In f i g u r e 3q each p o i n t r e p r e s e n t s a d i f f e r e n t l a s e r pulse. The peak power was maintained r e l a t i v e l y constant by using the same dye, bank v o l t a g e e t c e t e r a , but was a l s o monitored through the frequency doubled output. I t i s worth n o t i n g t h a t n o r m a l i z i n g t h e s i g n a l to the sguare root of the doubled power (see f i g . 3 q r second qraph) a p p r e c i a b l y reduces the s c a t t e r i n the data (standard d e v i a t i o n i s 6.2% versus the 10.6% i n the raw data) while n o r m a l i z i n g t o the doubled power i t s e l f does not. (standard d e v i a t i o n i s 13.1%) This i n d i c a t e s t h a t the c o n v e r s i o n e f f i c i e n c y i s s t i l l r i s i n g as the i n p u t power squared. ***76*** 2 0 -.2 -.4 -.6 -.8 -1.0 Log10Cf Taction of the light at 1*06 JJ t r a n s m i t t e d by t h e f i l t e r ) FIG 3q **#77*** However, which ever graph we use, we can see t h a t the s i g n a l from the potodiode i s e s s e n t i a l l y l i n e a r with r e s p e c t t o the input l a s e r l i g h t . 121-BALLISTIC THERMOPILE To c a l i b r a t e the s i g n a l so that i t can be converted i n t o watts, we measured the t o t a l energy d e l i v e r e d i n the p u l s e by absorbing the whole beam i n a TRG 109 b a l l i s t i c t h e r m o p i l e . T h i s u n i t employes two i d e n t i c a l carbon cones each monitored by i t s own i d e n t i c a l t h e r m o p i l e . One cone a c t s as the absorber while the other i s used f o r a r e f e r e n c e . I t i s necessary to employ acute angled cones t o i n s u r e t h a t the l i g h t r e f l e c t e d from the cone s u r f a c e i s not b a c k s c a t t e r e d but penetrates deeper i n t o the cone u n t i l l i t i s absorbed. The t h e r m o p i l e s are connected v i a a b r i d g e network and the output i s c a l i b r a t e d d i r e c t l y i n j o u l e s . The c a l i b r a t i o n was checked and found t o be o f f by about 20% but t h i s was c o r r e c t e d f o r . DETECTION OP LIGHT AT _j_53 THE IP21 PHOTQMHLTIPLIES Once a s m a l l p a r t of the beam has been used t o monitor the neodymium l a s e r l i g h t power, the r e s t of the beam i s passed through a rubidium dihydrogen phosphate c r y s t a l to freguency double i t . {see f i g . 3 p ) The output from **#78*** t h i s i s again monitored by s p l i t t i n g o f f a' s m a l l p o r t i o n of the beam with a g l a s s p l a t e s e t n e a r l y at the brewster angle and feeding i t through a ground g l a s s s c r e e n and n e u t r a l d e n s i t y f i l t e r , t h i s time, to an RCA IP21 p h o t o m u l t i p l i e r . 0 -.2 CM -.4 > fd C C CD cn '(/> '</> -.6 0> CN TJ Q_ O i — i X3 -.8 W | o CD O 1.0 -1.2 0 -.2 -.4 -.6 -.8 -1.0 -1.2 loq (fract ion of the light; at o53p 310 transmitted by the f i l ter) FIG 3 r THE PHOTOMULTIPLIER SIGNAL NORMALIZED TO THE S Q U A R E OF THE 1o06 p LIGHT POWER V E R S U S FILTER DENSITY This tube does not respond to the unused neodymium l i g h t ( t h i s was checked) and so can provide a r e l i a b l e measure of **#79*** the frequency doubled l i g h t power. As with the photodiode, the v o l t a g e s a c r o s s the l a s t a m p l i f y i n g stages are maintained by c a p a c i t o r s chosen so t h a t , with a t h r e e v o l t s i g n a l l a s t i n g f o r 500 nanoseconds, we c o u l d only expect a .6% drop i n v o l t a g e . Thus, we can expect the tube response to be l i n e a r with i n p u t l i g h t f o r s i g n a l s l e s s than .5 v o l t s . As was done i n the case of the p i n di o d e , the l i n e a r i t y was checked with c a l i b r a t e d f i l t e r s , (see f i g . 3 r ) Since each p o i n t r e f e r s t o a d i f f e r e n t shot, we have normalized the s i g n a l s t o the sguare of the pin diode s i g n a l , se were a b l e t o measure both s i g n a l s on the same o s c i l l o s c o p e t r a c e by sending the p h o t o m u l t i p l i e r s i g n a l through a 100 nanosecond delay l i n e . SOMA BY In c o n c l u s i o n , I am q u i t e c o n f i d e n t t h a t we are able t o measure both the r e l a t i v e fundamental and freguency doubled l i g h t powers as a f u n c t i o n of time with a d i s c r i m i n a t i o n ( r i s e t i m e or f a l l t i m e ) o f about two nanoseconds. I am a l s o c o n f i d e n t t h a t our c a l i b r a t i o n i n watts, a t l e a s t of our photodiode s i g n a l , i s ac c u r a t e t o wit h i n 10%. CHAPTER H FREQUENCY DOUBLING THEORY Once we had ob t a i n e d some output a t 1.06 p we then freguency doubled some of i t t o r a d i a t i o n at .53 p. In theory, t h i s may be done by p a s s i n g the l i g h t a t 1.06 ji through a t r a n s p a r e n t n o n l i n e a r d i e l e c t r i c medium. S i n c e t h e d i p o l e s i n the medium w i l l o s c i l l a t e a t the fundamental freguency (w) we may f o u r i e r decompose t h e i r motion i n t o a l i n e a r sum o f harmonic o s c i l l a t i o n s a t i n t e g e r m u l t i p l e s of W. I f we now arrange t h a t the component of the d i p o l e f i e l d at 2W should s t a y i n phase with the component at W, then we would expect t h a t the c o n t r i b u t i o n s t o the e l e c t r i c f i e l d at 2W from each s u c c e s s i v e d i p o l e would add. Thus, we would expect the e l e c t r i c f i e l d t o grow, a t l e a s t i n i t i a l l y , as the p a t h l e n g t h through t h e medium, so t h a t the power should grow as the le n g t h squared. Since the f i r s t n o n l i n e a r term i n the p o l a r i z a b i l i t y i s p r o p o r t i o n a l to the i n c i d e n t f i e l d squared, the amplitude o f each d i p o l e a t 28 should a l s o be p r o p o r t i o n a l t o the i n c i d e n t f i e l d squared. Thus, we c o u l d expect t h a t , the power a t 2W should qrow i n i t i a l l y as the i n p u t power squared times the pathlength sguared. pHANTTTSTIVE THEORY A more complete d e s c r i p t i o n o f t h i s process i s given i n r e f e r e n c e #4 9 p177-222 among ot h e r s . . In p r a c t i c e , the c o n d i t i o n t h a t the l i g h t at W and the l i g h t a t 2W stay i n phase i s met by using a c r y s t a l turned so that the o r d i n a r y wavelength at w j u s t matches the e x t r a o r d i n a r y wavelength at 2W. In such a system we f i n d ; *10* 'T| =Pt2«)/P{W) =2{Do/S) ^ 2»?D2L2sine2 (&KL/2) P {«) /[M* (&KL/2) 2) where: Do i s t h e magnetic p e r m i t t i v i t y of f r e e space, S i s the e l e c t r i c p e r m i t t i v i t y of f r e e space, N i s the o r d i n a r y index of r e f r a c t i o n , KL i s the d i f f e r e n c e i n phase between the o r d i n a r y and e x t r a o r d i n a r y waves, over the path l e n g t h through the c r y s t a l , P(»)/A i s the power at the fundamental freguency W per u n i t a r e a , T) i s the e f f i c i e n c y of c o n v e r s i o n of power at H t o power at 2W, and D i s the n o n l i n e a r o p t i c a l c o e f f i c i e n t =5.0x10-2*F/V. As TJ r i s e s the power l e f t a t » f a l l s and the f i e l d a t 2W s t a r t s t o p e r t u r b the o s c i l l a t i o n of the d i p o l e s . Thus, we *##82*** begin to feed energy back i n t o the fundamental f i e l d and the gain s a t u r a t e s . For our c r y s t a l (rubidium dihydrogen phosphate 1.5 cm long) t h i s s a t u r a t i o n occurs f o r 25%. (see ref.50) Thus, even assuming t h a t i s given by equation #10 a l l the way up to the maximum o f 25%, we would s t i l l r e g u i r e .46 j o u l e s i n 15 nanoseconds (44 MW/cm2) from our l a s e r t o achieve i t . Bore reasonably, we w i l l probably r e q u i r e a t l e a s t t hree times t h a t much power ( 150 HW) t o o b t a i n the 25% c o n v e r s i o n and t h i s assumes optimum alignment. With our present .35 J i n 15 nanoseconds we c o u l d r e a s o n a b l y expect to achieve only h a l f the t h e o r e t i c a l e f f i c i e n c y of 13% or about 7% or .025 J . T h i s i s only 31% of our requirement of .08 J . The doubling e f f i c i e n c y c o u l d be improved t o meet our requirements i f we were t o reduce the beam diameter with a t e l e s c o p e but, s i n c e the l a s e r was expected t o be a b l e to d e l i v e r 140 Ml/cm 2, we d i d not c o n s i d e r i t necessary., APPARATUS I f we wish t o o b t a i n these r e l a t i v e l y high e f f i c i e n c i e s , we must be able to reduce the AKL i n equation #10 to z e r o . For our c r y s t a l t h i s i s done by r o t a t i n g the o p t i c a l a x i s r e l a t i v e to the incomming beam. These c r y s t a l s are i n g e n e r a l temperature and pressure s e n s i t i v e but i n RDP these e f f e c t s are r e l a t i v e l y s m a l l . 5 0 Thus, i f the h o l d e r i s accurate enough, we may a d j u s t the angle and expect t o ###83*** remain permanently on the doubling maximum. microyrneter rotates cel l and is accurate to atleast rads. RDP chrystal polarization of the incident beam -loOcf A / laser , light allowing rotation orthogonal axis ce l l filled wi th — ^ index matching^ fluid ( F 0 7 ^ ) FIG 4a THE FREQUENCY D O U B L E R : CELL AND HOLDER With t h i s i n mind, we s e t the c r y s t a l i n a holder which was l i g h t l y sprung t o keep the c r y s t a l f i r m l y i n place. The h o l d e r was contained i n a c e l l (see f i g . 4 a ) which was f i l l e d w i t h index matching f l u i d { 3 H Co. F l u o r o c h e m i c a l FC-77) both to minimize l o s s e s from r e f l e c t i o n and to prevent the c r y s t a l from absorbing water from the a i r . The c e l l was he l d i n a mount a l l o w i n g n e a r l y independant r o t a t i o n about t h r e e orthogonal a x i s . S i n c e the h a l f width of the d o u b l i n g peak may be as s m a l l as 9x10 -* rads i n the most c r i t i c a l d i r e c t i o n , we c o n s t r u c t e d the mount to be a d j u s t a b l e t o w i t h i n 5 x 1 0 _ s r a d i a n s i n i t s l e a s t s e n s i t i v e d i r e c t i o n . EXPERIMENTAL RESDLTS Once we had mounted the c r y s t a l and a l i g n e d i t s f r o n t f a c e p e r p e n d i c u l a r t o the neodymium beam we immediately o b t a i n e d a s m a l l amount of doubled output. However, when we attempted to tune the c r y s t a l by o p t i m i z i n g the power i n the doubled l i g h t with r e s p e c t t o the i n p u t neodymium power sguared as i s d e s c r i b e d under " d i a g n o s t i c s " , we found t h a t t h e r e s u l t s were too i r r e p r o d u c i b l e from shot to shot. That i s , a t constant angle we observed f l u c t u a t i o n s as l a r g e as 50%. We assumed t h a t t h i s was due t o f l u c t u a t i o n s i n the i n p u t beams p o l a r i z a t i o n and so i n c l u d e d a p o l a r i z e r i n t h e c a v i t y . With t h i s accomplished, the f l u c t u a t i o n s dropped t o below 10%. We were now a b l e t o o p t i m i z e the tuning f o r t u r n i n g about the d i r e c t i o n of p o l a r i z a t i o n <z a x i s ) . (see f i g . 4b) The h a l f width of the peak f o r tuning i n t h i s d i r e c t i o n proved to be about 7x10~ 3 r a d i a n s (.4°) while the ) different runs 8x10"* rads. angle in radians F I G 4b -THE DOUBLING MAXIMUM FOR TURNING ABOUT THE DIRECTION OF THE INCIDENT LIGHT'S POirARIZ ATION (about the z axis) • ( f ^ / optimum proved to be about 4x1O - 3 r a d i a n s wide. The e f f i c i e n c y at t h e peak tended t o f l u c t u a t e r a t h e r more as a percentage from shot t o shot ( 10%) than i t d i d elsewhere. We next t r i e d t o o p t i m i z e the tuning f o r t u r n i n g about the x a x i s , we found t h a t r o t a t i o n i n t h i s d i r e c t i o n (around the beam) produced a s l i g h t detuning i n the f i r s t d i r e c t i o n (z axis) so t h a t each t u r n had to be fol l o w e d by a r e t u r n to t h e z a x i s maximum. , When t h i s was done we found no a p p r e c i a b l e change over a t o t a l range of 12° (see f i g . 4 c f o r some of the r e s u l t s ) I f the SDP c r y s t a l i s t r u e l y u n i a x i a l we c o u l d expect the doubled output to go 10 8 6 CO o rt Q_* 0 0 angle in radians _D_ I O X 1 0 " 2 rads. F I G 4c THE DOUBLING EFF IC IENCY FOR TURNING ABOUT THE INCIDENT B E A M (about the x ax is) as the square of the enerqy i n the c o r r e c t d i r e c t i o n t h at i s as c o s * ( S ) . This would imply a h a l f width o f 66° which i s con s i d e r a b l y l a r g e r than that observed f o r the d o u b l i n g of ruby l i q h t with KDP as we l l as beinq much l a r q e r than the range we explored. A l t e r n a t e l y , we may -just not have c r o s s e d the peak. Tuning i n the t h i r d d i r e c t i o n a l s o seemed to produce no a p p r e c i a b l e e f f e c t over the whole of our range o f about 30°. Si n c e t h i s was c o n s i s t e n t with the r e s u l t s f o r doubling ruby l i g h t we made no f u r t h e r attempt t o l o c a t e a maxima i n t h i s d i r e c t i o n . #**87*** DOOBLED EHE8GY Once we had tuned t o the maximum f o r t u r n i n g about the d i r e c t i o n of the i n p u t beam p o l a r i z a t i o n , we made an attempt to measure the a b s o l u t e freguency doubled energy. To do t h i s we passed t h e beam through a copper s u l f a t e s o l u t i o n to remove the neodymium l i g h t and then i n t o the thermopile c a l o r i m e t e r . S i n c e the l o g a b s o r p t i v i t y of the f i l t e r c e l l i s 2 . 3 a t 1 .06 u, the neodymium l i g h t ( . 35 J) can c o n t r i b u t e only 1.8 mJ to our r e a d i n g . S i n c e the l i g h t at .53 fa i s a l s o a ttenuated by the f i l t e r (log a b s o r p t i v i t y ~ i 1 6 ) our r e a d i n g of 15 mJ t r a n s l a t e s i n t o a doubled energy of 19 mj or approximately the 25 mJ we p r e d i c t e d from theory. The accuracy of t h i s value i s i n doubt because t h i s energy i s near the l i m i t of s e n s i t i v i t y of the t h e r m o p i i l e but i t i s c e r t a i n l y c o n s i s t e n t with the o b s e r v a t i o n t h a t the doubled power i s s t i l l growing as the sguare o f the i n p u t power. T h i s o b s e r v a t i o n (see " d i a g n o s t i c s " ) i n d i c a t e s t h a t the e f f i c i e n c y i s s t i l l w e l l below the s a t u r a t i o n and so may well be the 5% our energy measurement e n t a i l s . CONGLDSIjOfiS In c o n c l u s i o n then, we have been a b l e t o produce doubled neodymium l i g h t with somewhere near 5% ef f iciency.., We have been a b l e t o tune to the maximum i n one d i r e c t i o n but have not been a b l e to i d e n t i f y any c l e a r #••88*** maximum f o r the p r e f e r r e d d i r e c t i o n of p o l a r i z a t i o n . Even with t h i s alignment though, with our p r e d i c t e d peak power o f 140 ME/cm2 we c o n f i d e n t l y expect t o reach e f f i c i e n c i e s near s a t u r a t i o n (25%). As t h i s would produce a doubled output o f about .4 j compared to our requirement of .08 J t h i s should be more than adequate f o r our l a s e r s c a t t e r i n g experiment. CHAPTER 5 CONCLUSIONS AND DESIGN MODIFICATIONS I t i s cle a r from the previous discussion that a l l that i s necessary to make t h i s experiment work i s to stop the depletion of the energy stored i n the neodymium through superfluorescence. Once we have done t h i s , we can expect to have about 1.6 J at 1.06 u -more than f i v e times the energy at 1.06 JA necessary (assuming 25?5conversion to .53 ja light) to observe the electron s a t e l l i t e - . Unfortunately, we are li m i t e d by surface damage problems to about 40% of our best output (.65 J) but even t h i s should produce about 80 mJ at .53 u (1/2 the th e o r e t i c a l conversion efficiency) and should be more than adeguate. PREREQUISITE MODIFICATIONS Thus, to complete the experiment, we are only required to stop the losses from superfluorescence -that i s to replace the pyrex holder by one that absorbs strongly at 1.06 u, for example, with one made of samarium doped qlass. Alternately, we could order rods already cladded i n the samarium doped qlass. Either way we w i l l stop the neodymium fluorescence l i g h t from being reflected o f f the mirrors and back through the rods to produce the extra stimulated # • • 9 0 * * * emission. T h i s w i l l produce a neodymium g l a s s l a s e r whose frequency doubled output w i l l be adequate f o r our s c a t t e r i n g experiment. However, s i n c e we are l i m i t e d t o on l y 40% of i t s p o t e n t i a l power by damage requirements, we can probably f i n d a more o p t i m a l f r o n t mirror r e f l e c t i v i t y . , OPTIMIZATION OF FRONT MIRROR REFLECTIVITY F i r s t o f a l l , i f we 'ignore damage, the o p t i m a l m i r r o r r e f l e c t i v i t y may be obtained by d i f f e r e n t i a t i n g equation #8 with r e s p e c t to R. Assuming, f o r s i m p l i c i t y , a d i s t r i b u t e d c a v i t y l o s s given by then: Thus: Eex=-A<b*ln ( (1-f)/.081LEs<0) }/.162 d> T h i s eguation when combined with equation #8 y i e l d s a unique s o l u t i o n f o r R as a f u n c t i o n of t h e i n v e r s i o n Es{0). For our c a v i t y with the two rods t h i s y i e l d s R=.595 a t 2.2 kJ pumping power. T h i s i s g u i t e c l o s e to the R=.65 which we a c t u a l l y used and should give only 1% more output. I f we were t o decrease t h e l o s s e s by u s i n g a s i n g l e s i x i n c h rod we would o b t a i n a 18% i n c r e a s e at the new optimum r e f l e c t i v i t y o f 0.605. OPTIHOU I l l f i I II INTEEN1L FLUX FIXED BX 1 & I 1 G E B E 2 2 I S I I 1 I T S Thus we can see that i n order to avoid damage we must reduce the r e f l e c t i v i t y c o n s i d e r a b l y below the optimum v a l u e f o r maximum output energy. I f we r e q u i r e t h a t the f l u x through the c a v i t y be 4 J/cra 2 t h e n equation #8 becomes: Eex=2.85cj>»Es(0)-3. 14c£Vcf S o l v i n g f o r R g i v e s us B=.35 at 2.2 kJ e l e c t r i c a l pump energy. T h i s w i l l y i e l d a t o t a l output energy o f 1.34 -joules which i s 29% l e s s than the o p t i m a l . I f we reduce the f l u x s t i l l f u r t h e r t o 2 J/cm 2 then at 2.2 kJ pump energy B=.26 and Eex=.82 J . T h i s r e p r e s e n t s a more s u b s t a n t i a l drop i n e f f i c i e n c y {56%) but i t i s s t i l l more output than we would get with a 65% m i r r o r l i m i t e d to 4 J/cm 2 f l u x . (.65 J) In s h o r t , t o ob t a i n a t h r e e f o l d i n c r e a s e i n the output power of our l a s e r without r i s k i n g s e r i o u s i n t e r n a l damage, a l l we need t o do i s t o o b t a i n s u i t a b l e c l a d d i n g f o r the neodymium rods and t o r e p l a c e t he f r o n t m i r r o r by one of about 30% r e f l e c t i v i t y . H i t h these two changes we c o u l d expect an output o f 1.1 j o u l e s f o r an i n t e r n a l f l u x of about 2.9 J/cm 2. 21111 IMPBOVEMEHfS We c o u l d improve the l a s e r J s performance i n other ways but, f o r most of these, the g a i n i s marginal and the e f f o r t l a r g e . I f we were to i n c r e a s e pumping, say by adding another f l a s h l a m p , we would s t i l l be l i m i t e d t o a maximum output o f 2 j o u l e s f o r an i n t e r n a l f l u x of about 3J/cm 2. .. The same problem occurs when we t r y t o i n c r e a s e t h e output by d e c r e a s i n g the c a v i t y l o s s e s , say by r e p l a c i n g the two t h r e e inch r o d s by one s i x inch r od. I f we were t o t i l t the rods to the brewster angle the s u r f a c e area of the rod exposed t o the beam would be n e a r l y doubled bat we would s t i l l have to worry about the power d e n s i t i e s on the back mirror. However, i f the i n v e r s i o n were high enough, these d e n s i t i e s c o u l d be l e s s than h a l f the output f l u x so we could c o n c e i v a b l y reach the damage t h r e s h o l d f o r t h e output mirror of 3 J/cm 2 o r 2.3 j o u l e s . T h i s again r e p r e s e n t s only a f a c t o r of two improvement over the expected performance with j u s t the 30% m i r r o r . Thus we are l i m i t e d by m a t e r i a l s damage t o a t o t a l output energy o f about two j o u l e s . The o n l y way t o go beyond t h i s i s t o i n c r e a s e the beam diameter. T h i s can be done with rods up to about 6 cm. diameter (see ref.38) where thermal d i s t o r t i o n and nonuniform pumping l i m i t f u r t h e r s c a l i n g . For e n e r g i e s beyond t h i s one must t u r n to d i s c a m p l i f i e r s , (see ref.41) •##93*** FXHAL SOHMAHY In c o n c l u s i o n then, we are q u i t e c o n f i d e n t t h a t we have obtained the c o r r e c t e x p l a n a t i o n f o r our l a s e r * s f a i l u r e to meet design e x p e c t a t i o n s . With the a d d i t i o n o f samarium doped g l a s s c l a d d i n g to the rods and with a 30% r e f l e c t i v i t y output m i r r o r , we c o n f i d e n t l y expect to reach 1.1 j o u l e s output without i n c u r r i n g any damage t o the s u r f a c e s i n s i d e the l a s e r . 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