Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 425
Pulsed excitation of nonlinear distributed coupling intozinc oxide optical guides
R. M. Fortenberry,* G. Assanto, t R. Moshrefzadeh,t C. T. Seaton, and G. I. Stegeman
Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
Received July 23, 1987; accepted September 25, 1987
Prism and grating coupling of high-energy laser pulses into thin-film ZnO waveguides has been investigatedexperimentally by using nanosecond and picosecond pulses. Large decreases in the coupling efficiency, angularshifts in the optimum coupling angle, and pulse distortion have all been observed with increasing pulse energy,primarily at 532 nm but also at 572 and 750 nm. Pulse-probe experiments indicated an intensity-dependentrefractive index with a nonlinearity turn-off time of 1 usec, in good agreement with calculations based on a thermalnonlinearity. The experimental observations were interpreted successfully in terms of a traveling-wave interactionbetween the incident and generated guided-wave fields for incident pulses of duration much shorter than thenonlinearity recovery time.
1. INTRODUCTION
Third-order nonlinear interactions in waveguide configura-tions have been the object of intense studies because of theirpossible application to all-optical signal processing.1 One ofthe simplest nonlinear guided-wave phenomena is the effectof a nonlinear refractive index on the distributed couplingprocess by which a prism or a grating is used to couple anexternally incident radiation field into waveguide modes.In fact, many useful optical operations such as optical limit-ing,23 optical bistability,4 5 and optical switching36 -9 havealready been achieved experimentally through nonlineardistributed coupling characterized by a power-dependentguided-wave wave vector. We previously reported in letterform3 a summary of our experiments on optical limiting andoptical switching in both prism and grating coupling to ZnOwaveguides that exhibit a thermal nonlinearity. In anotherpaper' 0 in this issue we have outlined the theory of nonlineardistributed coupling as it relates to pulsed laser excitation.In this paper we describe our experiments in detail.
In a distributed input coupler, such as a prism or a diffrac-tion grating, efficient coupling is obtained only when thecomponents of the wave vectors of the incident field and ofthe guided field match along the direction of guided-wavepropagation. 11"2 However, as the guided-wave power growsunder the coupler, the guided-wave wave vector changes ifone of the guiding media exhibits an intensity-dependentrefractive index, usually written as n = no + n2I, where I isthe local intensity. This loss of wave-vector synchronismleads to a cumulative mismatch in phase for the growingguided wave and results in a decrease in coupling efficien-cy,2'3 an angular shift in the optimum coupling angle, anddistortion in the pulse envelope in the case of pulse excita-tion. Various aspects of this phenomenon were observedpreviously during the excitation of surface plasmons andthin-film guided waves. Previous work in this area hasshown how a nonlinear distributed coupler may be employedto determine the sign and size of a nonlinearity.3,
9 13-15 Re-cently experimental results3 8 have indicated that multipleswitching within a single pulse can occur for a nonlinear
distributed coupler involving an absorptive nonlinearity.Such a nonlinearity occurs whenever the turn-off or relax-ation time of the nonlinearity is longer than the width of thepulse being used to excite the nonlinear medium. As dis-cussed in Ref. 10, this technique of observing the temporalpulse shape of a guided wave provides a method for deter-mining the relative amounts of each type of nonlinearitypresent, including, in simple cases, the effects of relaxationtime.
In this paper we present experimental evidence that con-firms the salient features of nonlinear distributed couplinginvolving an integrating nonlinearity, that is, a nonlinearitywhose relaxation time is long compared with the pulsewidth. First, we briefly review the salient features predict-ed in the paper of Assanto et al.10 Next we discuss thefabrication and waveguiding characteristics of the ZnO filmsused in this study. Finally, we present the experimentalresults obtained on prism and grating coupling into thesewaveguides.
2. REVIEW OF THEORY
Here we only summarize the salient features of the theory ofnonlinear distributed coupling detailed in the paper of As-santo et al.10 Writing the field incident onto the base of acoupling prism (refractive index np) at an angle 0 to thesurface normal as
426 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
U-
o wZnJ
oM
INPUT ENERGY
Fig. 1. The coupling efficiency versus pulse energy for a nonlinearsubstrate with n2(thermal) = 10-14 m2/W and At = 10-2T.
Pout AN=O
50
Fig. 2. Variation in pulse profile with incident pulse energy, whichvaries logarithmically from 10-7 (Em) to 10-4 (E,:) J/mm for anintegrating nonlinearity with n2 (thermal) = 10-14 m2 /W.
Here the incident light has a field distribution given by ain(x, t)along the base of the prism and ko = w/c. The time depen-dence contained in the field amplitudes describes the pulsenature of the excitation. For the guided-wave field, a is theattenuation (intensity) coefficient, I is the distance overwhich a guided-wave-field amplitude falls to lie of its initialvalue (because of reradiation back into the prism alone), andag,(x, t) is the guided-wave-field amplitude normalized sothat lagw(x, t)12 is the guided-wave power in watts per squaremeter. In the absence of diffusion effects and for incidentpulses much shorter than the nonlinearity relaxation time,T >> At, the evolution of the guided-wave phase 0(x, t) isgiven by
a k d (x, t) =0 n k sin0+A-J dt'iagw(x, t')I, (4)
dzn2 (z)lf(z)4
A- (5)
E dzlf(z)I4
where n2 (z) is the intensity-dependent refractive index forthe slow (termed integrating) nonlinearity. From Eq. (4) itis useful to define, for an integrating nonlinearity,
A~tn2eff n2 At (6)
T
which hows that the effective nonlinearity for pulses ofwidth At is reduced by the ratio of the pulse width to therelaxation time.
These equations can be interpreted as follows. The valueof the instantaneous phase shift 0(x, t) relative to the phaseof the guided wave [contained in aw(x, t)] determineswhether the guided wave grows with propagation distance.Assuming for simplicity that the guided-wave phase is aconstant (which it is not), for 0(x, t) = mr, the guided wavegrows for even values of m and decays for odd values of m.Defining the coupling efficiency as
J dtlagw(x > Xs, t)12
(7)
where Ec is the incident pulse energy and the couplingprism is terminated at x, the coupling efficiency can de-crease with increasing pulse energy. An example is shown inFig. 1 for the variation in coupling efficiency with incidentpulse energy. Furthermore, the time envelope of the guid-ed-wave pulse becomes distorted relative to the incidentpulse; for example, see the pulse evolution in Fig. 2. It isprimarily these two aspects of nonlinear coupling that areinvestigated experimentally in this paper.
3. EXPERIMENT
A. Waveguide Fabrication and CharacterizationNonlinear coupling was investigated through prism andgrating coupling into ZnO thin-film waveguides. The filmswere made by magnetron rf sputtering by using a modifiedDenton system equipped with a partial-pressure controller.Following the guidelines outlined by Hickernell,16 high sub-strate temperatures (350-400'C) and high deposition rates(20 A/sec) were used with 20-50% oxygen in the chamber toproduce high-optical-quality, dense films.
A number of techniques were used to characterize thefilms. X-ray analysis was used to verify that the c axis of thecrystallites in the polycrystalline film coincides with thenormal to the substrate surface. Also determined were theaverage crystallite size of approximately 300 A and a latticespacing along the c axis of 5.190 A, in good agreement withthe bulk value of 5.206 A.17 This last measurement indi-cates that the films are relatively strain free. Rutherfordbackscattering showed the Zn-to-O ratio to be 1:1 to within1%. Absorption measurements indicated a band edge at 384nm, the same as in bulk ZnO,' 8 and predicted an absorptioncoefficient ranging from 0.01 to 0.001 cm-l at 532 nm. Adamage threshold in excess of 2-4 GW/cm2 was measured at532 nm using 10-usec pulses.
The film index and thicknesses were determined by cou-pling into multiple transverse-electric (TE)-polarized (Efield in plane of film) modes with strontium titanate cou-pling prisms. At wavelengths of 532 and 572 nm, film indi-ces of 2.032 and 2.013, respectively, are in excellent agree-ment with the bulk ZnO values of 2.033 and 2.013, respec-tively. Propagation losses as low as 1 dB/cm were found forthe TEO mode.
All the above characterizations indicated that the ZnOfilms were of very high quality.
B. Pulsed Laser MeasurementsA number of different laser systems, operating in both thenanosecond and picosecond time domains, were used to
Fortenberry et al.
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 427
| YAG LASER |0 I |- OPTICS- stepperFig. 3. Apparatus used to__ measure tecuigeiin vesenr oreusndneal:bemotor
Fig. 3. Apparatus used to measure the coupling efficiency versus energy or versus incidence angle: bs, beam splitter; di, d2, detectors.
measure nonlinear coupling into the ZnO waveguides.Their characteristics will be discussed in Section 4. Fornanosecond pulse-coupling-efficiency measurements, whichrequire comparing the incident with the guided-wave pulseenergy, a calibrated energy meter (Laser Precision Rj-7200)was used. For picosecond pulses a silicon P-I-N photodi-ode (Motorola MRD-510) was used for detection, and theoutput was displayed on a Tektronix 7912AD transient digi-tizer. This system, which had a nanosecond response time,was also used for measuring pulse distortion, as was a 10-psec Hamamatsu streak camera.
Careful measurements were also made of the couplingefficiency as a function of the incidence angle. The appara-tus is shown in Fig. 3. The rotation stage is controlled to aresolution of 10-3 deg under computer control.
4. EXPERIMENTAL RESULTS
A. Coupling-Efficiency MeasurementsIn the first experiments we measured the prism-couplingefficiency as a function of pulse energy. A frequency-dou-bled Nd:YAG laser operating at 10 Hz with 10-nsec, multi-longitudinal-mode (passively Q-switched) pulses was usedas the source (Quantel 580) and was focused down to adiameter of _0.3 mm. The efficiency of coupling into theTEO mode of a 0.6-,4m ZnO film with SrTiO3 prisms wasmeasured over 4 orders of magnitude of pulse energy. Thecoupling efficiency versus incidence angle was first opti-mized at low powers, and then the pulse energy was in-creased, which produced the results shown in Fig. 4. Themost salient feature observed was the monotonic decrease incoupling efficiency-up to a factor of 20. Similar decreasesin coupling efficiency were obtained with other ZnO wave-guides as well as with Nb 2O5 waveguides provided by F.Hickernell of Motorola.
The experiments were repeated with a passively mode-locked, frequency-doubled (X = 532 nm) Quantel 501C laseroperating at 10 Hz with 25-psec pulses. Because the pico-
second pulses are a factor of 500 shorter in time than thenanosecond pulses, the peak intensity in the picosecondpulses is a factor of 500 larger for the same pulse energy.The close correspondence with the nanosecond data shownin Fig. 4 indicates that the limiting process is primarilyenergy rather than intensity dependent.
The coupling efficiency as a function of pulse energy wasalso measured at the wavelengths 572 and 750 nm. A dyelaser using Rhodamine 590 was used for the 572-nm wave-length, and a dye laser using LDS 760 was used for the 750-
25
20
I!
I0
X X X°X 4;
X1 x.
I I
10 00 000 10000AR Ce- I 10 100 1000
INPUT PULSE ENERGY (J/P)
Fig. 4. Measured coupling efficiency versus pulse energy at X = 532nm for prism coupling into the ZnO waveguides: X's identify 10-nsec pulse data; O's identify the 25-psec pulse data.
20
15
10
5
-X x o
I } | I X I10 100 1000
INPUT PULSE ENERGY (LJ/P)no~~~~~~~~~~~~00
Fig. 5. Coupling efficiency versus pulse energy for nominally10-nsec pulses at different excitation wavelengths: X's, X = 532 nm;O's, X = 572 nm; it's, X = 750 nm.
U'-
Fortenberry et al.
I X
X I
10000
10000
428 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
100
U)
:
80
60
40
20
00 100 200 300 400 500 600 700
CHANGE IN COUPLING ANGLE (10-3 deg)Fig. 6. In-coupling efficiency versus coupling angle at low and highpowers. The vertical scale of the higher-energy pulse (broadercurve) was adjusted to match the rising edge of the lower-energycurve.
nm wavelength. The dye laser was a Quantel TDL IIIpumped with the doubled output of the Quantel 481 laser.For 10-nsec pulses, the observed variation in coupling effi-ciency with pulse energy is shown in Fig. 5. These resultsindicate a weak dependence of the nonlinearity on wave-length, with a slow falloff with increasing wavelength.
As a final check on the energy-versus-intensity depen-dence of the coupling efficiency, 10-psec pulses at 150 kHzfrom a Coherent 700 dye laser, pumped by a frequency-doubled mode-locked Quantronix 416 laser, were used. Noloss in coupling efficiency was observed for a peak powerdensity of 20 MW/cm2, or the equivalent of 200 J for a 10-nsec pulse. Nanosecond measurements at the same powerdensity showed at least a factor of 2 drop-off in couplingefficiency. Hence the nonlinearity is only weakly wave-length dependent (i.e., nonresonant) and is energy depen-dent on both nanosecond and picosecond time scales.
Grating couplers were also used to verify that the nonlin-ear coupling process is common to distributed couplers.The coupling grating had a periodicity of 0.34 /Am and wasion milled into the ZnO film to a groove depth of 0.02 Am.The shape of the coupling efficiency versus pulse energywas qualitatively similar to that obtained with the prismcouplers.
We obtained the sign of the nonlinearity by measuring thevariation in coupling efficiency with incidence angle by us-ing the apparatus shown in Fig. 3. The typical dependenceof the output intensity, at two different pulse energies, isshown in Fig. 6. The salient features are that the angularwidth of the coupling curve increases monotonically withincreasing energy and that the peak shifts to larger angles.These results show that the guided-wave effective indexincreases with pulse energy and the nonlinearity has a posi-tive sign typical of thermal nonlinearities in ZnO.
The turn-off time of the nonlinearity was measured byprobing the coupling region before, during, and afterthe high-power nanosecond pulses. That is, a continuousHe-Ne laser operating at X = 632 nm was coupled into theZnO waveguide by using the same coupling region as the 532-nm, 10-nsec pulse. The He-Ne beam-coupling efficiencydrops dramatically when the pulse arrives and then recovers
exponentially in time, with a characteristic recovery time of_ 1,4sec.
B. Pulse-Distortion MeasurementsA separate set of experiments was performed on the tempo-ral profile of the in-coupled pulses. The typical profilesgenerated theoretically in the paper of Assanto et al.10 indi-cate that an initially symmetric pulse envelope becomesasymmetric at high pulse energies.
The experimental arrangement was essentially that shownin Fig. 3, with beam splitters added at the input and outputto monitor the pulse profiles. Most of the measurementswere taken with a 1-nsec rise-time photodiode; the remain-der were taken with a 10-psec streak camera.
For the first set of measurements the coupling angle wasfirst optimized at low powers, and subsequently the pulseenergy was increased. As the pulse energy is increased, thepulse becomes progressively more distorted; the results areshown in Fig. 7. Rapid switching, to both higher and lowerenergies, occurs within the pulse profile. At even higherenergies, multiple up-and-down switching is observed. Theswitching time (rate of change of power with time) was mea-sured with a 10-psec-resolution streak camera. In general,the higher the incident pulse energy, the faster the switchingtime. For example, a switching time of _1 nsec was ob-tained for the bottom part of Fig. 7.
This experiment was repeated with a frequency-doubledQuantronix 416 Nd:YAG laser, which was simultaneously Qswitched and mode locked. The laser output at 532 nmconsisted of a train of _50-psec pulses, separated by 13 nsecunder a Q-switched envelope of 300-nsec duration. Thedetection system basically integrated the energy in eachindividual pulse and produced a series of spikes whose enve-lope corresponded to the pulse energies. When the totalenergy in the pulse train was set to the value obtained for asingle 10-nsec single-longitudinal-mode pulse, the distortionin the output envelope exhibited the same shape as that of asingle 10-nsec pulse, with a corresponding change in the timescale. These results are consistent with an energy-depen-dent nonlinearity whose characteristic relaxation time islonger than 300 nsec.
Figure 8 shows the results obtained at fixed incident pulseenergy but with varying angles of incidence. Increasingpulse distortion, including pronounced multiple switching,is obtained as the incidence angle is decreased from approxi-mately its optimum coupling angle for the chosen pulseenergy, Fig. 8a in this case. The low-power optimum cou-pling angle corresponds to Fig. 8c, and the trends substanti-ate the results shown previously in Fig. 6.
5. DISCUSSION
With the possible exception of some details of the 25-psecresults in Fig. 4, all the results in this paper are consistentwith a thermal nonlinearity with a relaxation (turn-off) timeof 1,4sec. The coupling efficiency versus pulse energy andversus coupling angle was analyzed in terms of the theorysummarized in Section 2 (and discussed in detail in thepaper of Assanto et al.10). As predicted in Ref. 10, we foundit impossible to distinguish between a Kerr law and an ab-sorptive nonlinearity just by fitting to the coupling-efficien-
Fortenberry et al.
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 429Fortenberry et al.
PULSE + PULSE1O
100
80
Ln)zLUI-
60
40
20
0
TIME
PULSE1 + PULSE7
100
80
Li)
I-
60
40
20
0
PULSE1 PULSE5
100
80
I-
zLUI-z
60
40
20
0
TIME
Fig. 7. Comparison of experimental and theoretical temporal pulse profiles at three different energy levels. The first experimental trace ineach pair corresponds to the input pulse. Horizontal scale is 10 nsec/division.
cy versus input-pulse-energy curve. This inability to distin-guish also occurred when the coupling efficiency varied withincidence angle at high powers. However, the microsecondturn-off time of nonlinearity indicates an absorptive nonlin-earity on the time scale of the pulses used here. Assumingthe form n = no + n2I and a relaxation time r, a value of n2 /r
of 2 X 10-8 m2/J was obtained from both the coupling-
efficiency versus pulse-energy and the incidence-angle data.For the measured relaxation time of 1 psec, this result leadsdirectly to n2 _ 2 X 10-14 m2/W for the thermal nonlinearity.This value should be compared with thermal nonlinearitiesin other materials, for example, 3 X 10-k1 m2/W in ZnS.19
On the basis of the thermal heat capacity and density ofZnO, we estimated that the temperature rise in the film was
TIME
430 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
Fig. 8. Input (first trace) and output pulse shape at five different coupling angles at fixed pulse energy: c, the optimum low-power couplingangle, 0,opt. a and b, 12 and 5 min of angle, respectively, higher than 0opt; d and e, 5 and 12 min of angle, respectively, lower than 0opt. Horizontalscale is 10 nsec/division.
_60C for 100-yJ incident pulses of 10-nsec duration. For athermo-optic coefficient of 3 X 10-5 for ZnO, the corre-sponding index change was _ 1-2 X 10-4.
Most previous reports on reduction in coupling efficiencyand shifts in optimum coupling angle that use pulsed lasershave been interpreted in terms of instantaneously respond-ing Kerr-law nonlinearities. 9 ,13- 15 This identification, rela-tive to integrating thermal nonlinearities, cannot be madeuniquely without additional information, for example,pulse-distortion measurements as discussed later in thispaper.
The single 25-psec pulse experiments on coupling efficien-cy versus pulse energy (Fig. 4) do show a deviation fromtheory when only a single absorptive nonlinearity is as-sumed. The power densities are of the order of tens ofgigawatts per square centimeter, large enough for two-pho-ton effects to be important.2 0 Because the sign of the two-photon nonlinearity is opposite that of the thermal nonlin-earity, the two effects initially cancel, and the coupling effi-ciency remains larger than when the thermal nonlinearityalone contributes to the nonlinear coupling process. How-ever, because the two-photon nonlinearity increases qua-
Fortenberry et al.
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 431
dratically with intensity versus linearly for the thermal case,
the two-photon nonlinearity dominates for pulse energies in
excess of tens of microjoules, and the coupling efficiency
decreases faster than for the thermal case, as observed.
These results are all in qualitative agreement with the find-
ings in Ref. 10 for interference effects between a fast nega-
tive nonlinearity and a slow positive nonlinearity.The distortion in pulse shape on in-coupling provides the
most convincing evidence for the integrating nature of the
nonlinearity. Media whose nonlinear response, both turn-
on and turn-off, is instantaneous on the time scale of the
pulse width lead to pulse distortion symmetric about the
pulse maximum. On the other hand, asymmetric pulse dis-
tortion is the signature of integrating nonlinearities. Asym-
metric pulse distortion was obtained here, as evidenced in
Figs. 7 and 8. Excellent agreement was obtained between
experiment and theory, as shown in Fig. 8.The switching within the pulse envelope is of special inter-
est since it is of potential device relevance. Switchdown
occurs when the driving field falls approximately m7r (m =
1, 3, 5. .. ) out of phase with the guided-wave field, and
switchup corresponds to m = 0, 2, ... The larger the pulse
energy, the faster the nonlinear phase changes and hence the
faster the switching time. This fact was verified experimen-
tally. Although the switching can be fast-subnanosec-ond-the material does not relax for the order of one micro-
second. For this time period a spatial temperature and
hence a refractive-index distribution exist in the coupler
region. Thus reproducible switching characteristics will not
be obtained for pulses whose separation is less than the
characteristic relaxation time, making this phenomenon not
useful for switching high-repetition-rate serial data streams.A different interpretation of a similar switching phenome-
non has been published by Pardo et al.7 In their study
grating coupling into a sapphire-silicon waveguide was
investigated, and switching was also observed. In their
experiments only a single switch was observed, presumably
because higher power levels were not used because of
unavailability or material damage. Their switching was
interpreted in terms of interference between Kerr-like non-
linearities due to carrier creation in the silicon and thermal
effects. Their analysis treated the waveguide as a Fabry-Perot 6talon with incident power corresponding to the aver-
age pulse power. This approach neglects propagation
effects, and Pardo et al. concluded that their theory repro-
duced their experiment results. This conclusion is in con-
trast to our work in which agreement between experiment
and theory is obtained with only an integrating nonlinearity.
Our approach also predicts the switching observed in their
experiment. However, the multiple switching peaks that we
observe experimentally cannot be predicted from their pub-
lished theory.In summary, we have investigated experimentally the cou-
pling of high-power pulses into ZnO waveguides through
gratings and prisms. Measurements of the coupling effi-
ciency versus pulse energy, angular shifts in the optimum
coupling angle with pulse energy, and distortion and switch-
ing within the pulses were all interpreted successfully in
terms of a thermal nonlinearity with a relaxation time (1
psec) longer than the pulse width or pulse train envelope.
ACKNOWLEDGMENTS
This research was supported by the Joint Services Optics
Program of the U.S. Army Research Office and the U.S. Air
Force Office of Scientific Research.
* Permanent address, The Heath, P.O. Box No. 11, Run-
corn, Cheshire, WA7 4QF UK.t Permanent address, Dipartimento di Ingegneria Elet-
trica, Vialle delle Scienze, Universita degli Studi, 90128 Pa-
lermo, Sicilia, Italy.Permanent address, 3M Center, MS 201-2N-19, St. Paul,
Minnesota 55144.
REFERENCES
1. G. I. Stegeman and C. TL Seaton, J. Appl. Phys. 58, R57 (1985).2. J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X.
Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).3. R. M. Fortenberry, R. Moshrefzadeh, G. Assanto, X. Mai, E. M.
Wright, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49,687 (1986).
4. W. Lukosz, P. Pirani, and V. Briguet, in Optical Bistability III,H. M. Gibbs, P. Mandel, N. Peyghambarian, and S. D. Smith,eds. (Springer-Verlag, Berlin, 1986), p. 109.
5. G. Assanto, B. Svensson, D. Kuchibhatla,.U. J. Gibson, C. T.Seaton, and G. I. Stegeman, Opt. Lett. 11, 644 (1986).
6. F. Pardo, A. Koster, H. Chelli, N. Paraire, and S. Laval,in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Pey-ghambarian, and S. D. Smith, eds. (Springer-Verlag, Berlin,1986), p. 83.
7. F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J.Quantum Electron. QE-23, 545 (1987).
8. G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Iron-side, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
9. S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl.Phys. 60, 1591 (1986).
10. G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stege-man, J. Opt. Soc. Am. B 5, 432 (1988).
11. Y. J. Chen and G. M. Carter, Solid State Commun. 45, 277(1983).
12. C. Liao and G. I. Stegeman, Appl. Phys. Lett. 44, 164 (1984); C.Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D.Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
13. Y. J. Chen and G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).14. G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett.
43, 891 (1983).15. Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne,
Appl. Phys. Lett. 48, 272 (1986).16. F. S. Hickernell, in 1980 IEEE Ultrasonics Symposium Pro-
ceedings (Institute of Electrical and Electronics Engineers,New York, 1980), p. 792.
17. W. L. Bond, J. Appl. Phys. 36, 1674 (1965).18. W. Hirsachwald, P. Bonasewicz, L. Ernst, M. Grade, D. Hof-
mann, S. Krebs, R. Littbarski, G. Neumann, M. Grunze, D.Kolb, and H. J. Schulz, "Zinc oxide," in Current Topics inMaterials Science, E. Kaldis, ed. (North-Holland, Amsterdam,1981), Vol. 7, Chap. 3.
19. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Mac-Leod, and F. van Milligen, Appl. Phys. Lett. 45, 1031 (1984).
20. E. W. van Stryland, H. Vanherzeele, M. A. Woodall, M. J.Soileau, A. L. Smirl, S. Guha, and T. F. Boggess, Opt. Eng. 24,613 (1985).
