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`Cul-de-sac` microstrip resonators for high-speed integrated optical commutator switches. Jaeger, Nicolas A. F.; Chen, Mingche 1993

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"Cul-de-sac" microstrip resonators for high speed integrated optical commutator switchesNicolas A.F. Jaeger and Mingche ChenUniversity of British Columbia, Department of Electrical EngineeringVancouver, British Columbia, Canada V6T 1Z4ABSTRACTA novel microstrip resonator structure for use with integrated Y-branch optical modulatorsfabricated in Ti:LiNbO3 is proposed. The legs of the structure are intended to act as the electrodesof the modulator, with light being directed into each of the output waveguides of the Y-branch onalternate half-cycles of the standing wave excited in the resonator; forming an optical commutatorswitch. Such resonators having A1203 substrates were designed, fabricated, and tested.Measurements on one such resonator, operating at 7. 12 GHz and having an unloaded quality factorof 123, indicate that 50Vshould develop across the ends of its legs for 35mWdissipated power;the corresponding values, from the model used to design the resonator, were 179, 50V,and24 mW, respectively. Using the model it is shown that a similar resonator fabricated on LiNbO3should be able to develop about 50Vfor 100 mW dissipated power at 15 GHz.1 .INTRODUCTIONIn this paper we present some of design considerations, fabrication details, and test resultsfor a novel, half-wave, microstrip resonator, the "cul-de-sac" resonator, that is intended to be usedin conjunction with a Y-branch optical modulator' to form an optical commutator. The name ofthe resonator type reflects the similarity between the resonator structure and the well known streetsign; i.e. ,theresonator consists of two substantially parallel legs open on one end and connectedon the other end by an open ring, see figure 1 .Whilethe resonators fabricated to date, andreported on here, were made on Al203 substrates, the parallel legs are intended to act as theelectrodes of a Y-branch optical modulator fabricated using a Ti:LiNbO3 technology; directingpulses of light alternately into each of the output waveguides on successive half cycles of thestanding wave excited in the resonator.Although there has been consistent research into Y-branch type optical modulators inTi:LiNbO324, the devices studied tended to have relatively small branch angles, allowing for loweroperating voltages and insertion losses due to radiation, which led to long devices. Devices havinglarger branch angles are shorter and require higher voltages and they have higher losses due toradiation but have lower losses due to absorption and scattering; in fact, by using large voltages ondevices with larger branch angles some of the radiated light is recaptured and steered into theguiding branch improving the insertion loss, in some cases by more than 1 dB5.It is the general thrust of this work to explore the use of resonators in the design of highfrequency, low power consumption, electrooptic modulators. Due to the resonator's inherentlynarrow-band nature, such electrooptic modulators would probably find application as opticalcommutators in time division multiplexer/demultiplexer systems6'7.482/ SPIE Vol. 1794 Integrated Optical Circuits 11(1992) 0-81 94-0973-1/93/$4.O0Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use: '(-branchparallel legsFigure 1 .Acul-de-sac resonator acting as the electrodes of a Y-branch optical modulator.2. THE RESONATOR STRUCTURE AND MODELThe resonator is to be a half-wave (or odd multiple of a half-wave) resonator so that thepotential on each of the parallel legs will be of opposite polarity, establishing a voltage between thelegs across the gap. It is intended that the potential difference between the end of the resonator'slegs be much higher than that on the microstrip feed line; i.e. ,theresonator is to act as a voltagetransformer. In this way, the resonator electrode can apply a high voltage to the optical modulatorwhile requiring relatively little power from the source. It was our goal to limit the supplied powerto 100 mW while obtaining a modulating voltage of about 50Vacross the gap.Losses are a major factor when determining the structure of a resonator. There are two mainkinds of loss in microstrip resonators: ohmic skin loss and radiation loss. Since, for a fixedfrequency, the ohmic loss is proportional to the length of the line, a half-wave resonator (as opposedto higher order odd multiples of a half-wave) will have the least loss of this kind. Radiation lossis primarily due to discontinuities in the transmission line, i.e. ,itis mainly dependent on thegeometrical structure.The hairpin8 and the open ring9 structures were initially considered as candidates for theresonator electrodes. They were modelled to determine their suitability for the intended application."Current crowding"1° near the inner edges of the two closely spaced legs of the hairpin resonatorincreased the ohmic loss to unacceptable levels. In the open ring structure, if the radial length ofthe gap was to be sufficient for the microstrip constituting the resonator to serve as the opticalSPIEVol. 1794 Integrated Optical Circuits 11(1992) / 483InputI Ight output lightopen ringDownloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use:'s electrodes, the width of the microstrip would have been too wide; resulting in theenergy being stored primarily as a large current, rather than as a large voltage, i.e. ,reducingthedesired voltage transformation effect. The best design that we have studied to date, in that it willmeet our power/voltage goals, namely the cul-de-sac resonator, is a hybrid of the hairpin and theopen ring structures.As can be seen from figure 1 ,thecul-de-sac structure has two major discontinuities, one ateither end of the parallel legs. Still, since the interelectrode gap is narrow,10 m, the dipoles(in fact quadrupoles when the images in the ground plane are considered) formed at the ends areinefficient radiators. For our model the radiation loss was calculated using a formula for planar1usingthe method of images (see for example Ref. 12). On the other hand, the narrowgap causes current crowding so that the legs should be kept short. Since the legs are intended toact as the electrodes of Y-branch optical modulators with relatively large branch angles, 1-2°, theycan be relatively short, e.g. ,thelegs need only account for about one fourth of the total length ofa 15 GHz resonator on LiNbO3.Further down we will show that, in order to obtain a large voltage between the legs of ourresonator, we will want a large unloaded quality factor, Q.Itis well known thatQ=(2rdW)/P1; where is the resonant frequency of the resonator, W, is the stored energy, andP1 is the average power loss. Also, since the energy in a resonator is stored in the electric andmagnetic fields, i.e. ,inthe voltage and current distributions, if we wish to obtain a large voltagebetween the ends of the resonator's legs then the microstrip forming the resonator should have ahigh characteristic impedance.To determine structure parameters, such as the width of the strips, the radius of the ring,and the length of the parallel legs, it is important to know the voltage (or current) and impedancedistributions along the microstrip line forming the resonator. To do this it is convenient to modelthe resonator as a straight line resonator. Figure 2a is the straight microstrip line equivalent circuitwhere: section AB corresponds to the ring, CA and BD correspond to the parallel legs, EC and DFare the excess lengths caused by the open ends, and 0 is the midpoint of the resonator. The parallellegs, being virtually identical to coupled microstrips in their structure, have a characteristicimpedance Z1 that is smaller than that of the ring Zr,therefore,the corresponding equivalentmicrostrip is wider. The steps in the characteristic impedances have the effect of making thevoltage distribution along the microstrip piecewise sinusoidal; also, they cause the propagationconstant for the parallel legs k1 to be different from that for the ring section lç. Knowing Z1, Zr,k1, and lç the voltage distribution can be obtained. Furthermore, the attenuation constants for thetwo parts, a1 and ar, are different as well. Using a and ar the total ohmic loss can be calculated.For our model a1 was assumed to be the same as that for two coupled microstrip lines (see forexample Ref. 13) and ar was taken to be that for the microstrip constituting the ring.Although the characteristic impedance of the microstrip composing the resonator should belarge, the input impedance of the resonator is a function of the coupling position which can,theoretically, be any value between zero and infinity. However, in order to reduce the reflectionloss, the power should be coupled into the resonator at a point where the input impedance ismatched to that of the power source; this may require the use of a quarter-wave transformer. Here484/ SPIE Vol. 1794 Integrated Optical Circuits 11(1992)Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use: A 0 B DE1____________ ____________I(a)---e P7/Zr Zrk\\\\\\\\\\\\N\\\\\\\\\1Z9 (b)Figure 2. (a) The straight microstrip line equivalent circuit for the cul-de-sac resonator.(b) The equivalent circuit used to calculate the input impedance and the coupling.SPIEVol. 1794 Integrated Optical Circuits 11(1992) / 485Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use: have assumed that the entire source power may be delivered to our resonator and is dissipatedtherein.For the purpose of modelling the input impedance and the coupling between the source andthe resonator, the equivalent circuit in figure 2a can be further simplified, as shown in figure 2b,as two shunt, open-circuited, uniform transmission lines. Here 0 is the electrical length from thecoupling point P to the centre of the resonator and Z, is the source impedance. In this model thecharacteristic impedance of the transmission line forming the resonator is the same as that of themicrostrip constituting the ring. This circuit is equivalent to the cul-de-sac resonator if we areconcerned only with the input impedance looking into a point on the ring. Using basic transmissionline theory with this model it can be shown that the input impedance is2ZQ1= USfr2O (1)itThe relationship between the voltage across the gap at the open ends of the parallel legs V0 and thesource voltage V is41 (2)Zr (1+)2 Zwhere 13 is the coupling coefficient. In other words the source voltage can be transformed by afactor of {2B"I(1+J)}X(8QuZ/nZs)½. Clearly, 13 =1maximizes the factor 2JI(1+13).Also,zs is usually a fixed value. While a large Zr5desirable, the losses associated with its increase putlimits on its possible value. It is, therefore, desirable to design a resonator having a relatively largeQ.3.RESULTS AND DISCUSSIONTo verify our model, cul-de-sac resonators designed to operate at 7 GHz were fabricated onAl203 substrates and tested. The structure parameters wereoptimized, i.e. ,togive a maximum V0for the least amount of power dissipated, assuming Z =50 fl andB =1.Thethickness of thesubstrate was 0.89 mm. The microstrip forming the resonators was made of 6 j.m thick,electrolytically deposited Au; in order to obtain this thickness a double masking technique was usedin the patterning11. The gap between the parallel legs was 12 jim. Each of the legs was 1.3 mmlong and 0. 14 mm wide. The mean radius of the ring was 0.86 mm and the width was 0. 14 mm.The calculated Zrwas95fl andthe predicted Qwas179. This gave an expected V0 of 50Vfor24 mW input power. The devices were tested using a scalar network analyzer. A plot of thenormalized reflected power vs. frequency is shown in figure 3. The measured Qforthis devicewas 123 and f was 7. 12 GHz (since we are using a scalar network analyzer to take a reflectionmeasurement, the value for Qdiffersslightly from that obtained by simply using the ratiofO/Af3dB11). Using the model above and assuming that the resonator impedances would be nearlyequal to the design values, a V0 of 50Vwould require 35mWinput to this resonator.486/ SPIE Vol. 1794 Integrated Optical Circuits 11(1992)Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use:— —2.0--a)00 —4.0-0ci)÷J0_ci)ci)ck0 —8.0-ci)Na—10.0-0z—12.0 -—14.0 - —6.50 7.50Frequency in GHzFigure3. A plot of the normalized reflected power vs. frequency for a cul-de-sac resonator.Using our model a resonator was designed to operate at 15 GHz on a 0.3 mm thick z-cutplate of LiNbO3. The structure parameters were optimized assuming Z, =50 =1,agapwidth of 4 ;.m, and Au microstrip 6 m thick. The length of the each parallel leg would be0.35mmand the width would be 0.03 mm. The mean radius of the ring would be 0.79 mm andthe width would be 0.02 mm. The calculated Zr was 62 nandthe predicted Qwas71. This gavean expected V0 of 59Vfor 100mWinput power. Assuming a similar reduction of 30% betweenthe Q's of the fabricated resonator and the model, we have calculated that a V0 of 49 V wouldresult for 100 mW input power. In other words such a resonator should meet our power/voltagerequirements.SPIEVol. 1794 Integrated Optical Circuits 11(1992)14873dBI 3dB55.4 MHztf0=7.12 GHzI I I I I I I I I I I I I I I6.75 7.00 7.25Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use: SUMMARYA novel microstrip resonator, the cul-de-sac resonator, that is intended to be use with Y-branch optical modulators has been proposed. Some of the considerations taken into account whenmodelling and designing these devices were described. Resonators of this type were fabricated onA1203 substrates and were tested to verify the model. Measurements indicate that resonators of thistype fabricated on LiNbO3 should develop about 50 V between the ends of their legs whiledissipating 100 mW of power at 15 GHz.5. ACKNOWLEDGEMENTThis work was supported by an operating grant from the Natural Sciences and EngineeringResearch Council of Canada. 6. REFERENCES1 .N.A.F.Jaeger and W. C .Lai,"Y-BranchOptical Modulator,8 SPIE Vol. 1583 IntegratedOptical Circuits, pp. 202-209, 1991.2. W. K. Burns, A.B. Lee, and A.F. Milton, "Active Branching Waveguide Modulator, "Appl.Phys. Lett. ,vol.29, no. 12, pp. 790-792, 1976.3 .Y.Silberberg, P. Perimutter, and J.E. Baran, "Digital Optical Switch, "Appl.Phys. Lett. ,vol.51, no. 16, pp. 1230-1232, 1987.4. P. Granestrand, B. LagerstrOm, P. Svensson, L. Thylén, B. Stoltz, K. Bergvall, J.E. Falk, andH. Olofsson, "Integrated Optics 4 X 4 Switch Matrix with Digital Optical Switches, "Electron.Lett.,vol. 26, no. 1, pp. 4-5, 1990.5. W.C. Lai, "LiNbO3 Y-Branch Optical Modulator," M.A.Sc. Thesis, Univ. ofBritish Columbia,1991.6. A. Djupsjöbacka, "Time Division Multiplexing Using Optical Switches," IEEE J. Select. AreasCommun.,vol. 6, no. 7, pp. 1227-1231, 1988.7.N.A.F. Jaeger, "High Speed Integrated Optical Modulators in Lithium Niobate and CompoundSemiconductors, "CCTATechnical Papers, pp. 1 17-122 ,1992.8. R.J. Roberts and B. Easter, "Microstrip Resonators having Reduced Radiation Loss, "Electron.Lett.,vol.7, no. 8, pp. 365-368, 1971.9.I. Wolff and V.K. Tripathi, "The Microstrip Open-Ring Resonator," iEEE Trans. MicrowaveTheory Tech. ,vol.MTT-32, no. 1 ,pp.102-107, 1984.10. S.E. Schwarz, M.D. Prouty, and K.K. Mei, "Radiation from Planar Resonators," IEEETrans. Microwave Theory Tech. ,vol.MTT-39, no. 3, pp. 521-525, 1991.1 1 .M.Chen, "Microstrip Resonators for High Speed Optical Commutator Switches, "M.A.Sc.Thesis, Univ. of British Columbia, 1992.12.R.F. Harrington,Time-HarmonicElectromagnetic Fields, chapter 3, McGraw-Hill, NewYork, 1961.13. K.C. Gupta, R. Garg, and I.J. Bahi, Microstrip lines and Slotlines, pp. 153-197, ArtechHouse, Norwood, 1979.488/ SPIE Vol. 1794 Integrated Optical Circuits 11(1992)Downloaded from SPIE Digital Library on 07 Jun 2011 to Terms of Use:


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