W. S. Goruk, P. J. Vella, R. Normandin, and G. 1. Stegeman
A simple inexpensive modulator based on a combination of the photorefractive and electrooptic effects inTi:in-diffused LiNbO 3 waveguides is demonstrated.
1. Introduction
The modulation of optical signals in planar integratedoptics can be achieved through spatial and/or temporalchanges in the effective refractive index of a waveguide.This has been demonstrated in experiments where ac-oustooptic,'-3 photorefractive,4' 5 electrooptic,6 strain-optic, 7 surface grating 8 phenomena (or a combinationof these effects) were utilized in modulating an incidentguided wave. In the present work we describe a novelmodulator based on a combination of the photorefrac-tive and electrooptic effects. It is essentially an inte-grated optics version of the electrooptic switch firstdemonstrated in bulk LiNbO3 by Kenan et al.9 Lightincident onto a photorefractive grating at and near theappropriate Bragg angle is first split into two beamswhose relative intensity varies with the exposure timeused in writing the grating. The electrooptic effect isthen used to modulate temporally these beams via aninput electrical signal. The resulting modulator is auseful low cost laboratory tool which does not requireelaborate fabrication. Furthermore, by using standardholographic techniques, various optical elements suchas lenses and couplers may be written into the wave-guide and switched on and off by this method.
II. Theory
The photorefractive method of writing grating ho-lograms in planar optical waveguides has been reported
W. S. Goruk is with Mohawk College of Applied Arts & Technology,Metallurgy Department, Hamilton, Ontario L8N 3T2; P. J. Vella iswith Bell Northern Research, Department 3K31, P.O. Box 3511,Station C, Ottawa, Ontario K1Y 4H7; R. Normandin is with StanfordUniversity, Ginzton Laboratories, Stanford, California 94303; andG. I. Stegeman is with University of Arizona, Optical Sciences Center,Tucson, Arizona 85721.
previously, 4 5 and only a brief description will be givenhere. Here we make use of the large photorefractiveeffect known to occur in LiNbO3 when light in theblue-green region of the spectrum is incident. Twoguided waves (writing beams at X = 0.5145 ,gm from anAr+ laser) with wave vectors fi and 132 interfere toproduce a grating with periodicity A = 2r/og (fig = ,- 2. The phase fronts are aligned along the directionnormal to g. For the case illustrated in Fig. 1(a), g= 2o sin0o, where fo = I I = 121, Oo is the angle be-tween fll (or 132) and the x axis, and g lies along the zaxis. The effective waveguide refractive index is givenby
n' = no + An sin(g r), (1)
and the depth of modulation An depends on numerousfactors such as the writing beam intensities and dura-tion, waveguide, and mode parameters.
Consider now a set of electrodes deposited onto thewaveguide surface as indicated in Fig. 1(c). When avoltage V is applied to the electrodes which are sepa-rated by a distance d, an effective index8 10 changeAN,
AN = 1/2 n(O)r 3 3 2Vird
(2)
is superimposed onto the photorefractive grating via theelectrooptic effect. (There is an additional effect dueto the material piezoelectricity, but this is believed tobe a secondary mechanism here.) The parameter r33is the appropriate electrooptic coefficient for the ge-ometry shown in Fig. 1(c). Hence the total refractiveindex is
n' = n + An sin(#g r) + AN. (3)
A similar phenomenon has been analyzed previouslyvia a coupled mode approach by Kotani et al.8 (In theircase a surface corrugation instead of a holographicgrating was used to obtain the initial division of theincident guided wave into two beams.) They showedthat the diffracted light intensity Id is given in terms of
Fig. 1. (a) Geometry used for writing a holographic grating into aTi:in-diffused LiNbO 3 waveguide with 0.5145-,um light; (b) beamsplitting of a guided wave ( = 0.6328 Am) by a holographic grating;(c) modulation of a guided beam by the application of an electric field
across a holographic grating (1.59-mm gap electrodes).
the incident guided wave light intensity Ii byd 2I = e sin2 (Lg vK7;+62). (4)I, K2 + 2
Here Lg is the length of the grating with periodicity A,and 3 is the phase mismatch term due to both the elec-trooptic effect and/or misalignment AO of the incidentbeam from the Bragg angle OB, i.e.,
= + -AO. (5)
The parameter Ke is given by
Ke = K cos(20
B), (6)
where K iS the coupling coefficient which appears in thecoupled wave equations. 8 Maximum diffraction occurswhen 3 = 0, which is usually obtained by ensuring thatthe guided wave is incident at the Bragg angle. It is alsouseful to note that a misalignment in the direction of theincident light can be compensated for by applying anappropriate voltage. Furthermore, the voltage AVwhich must be applied to go from the mth to the m +Ith minimum is given approximately (KeL < /2) by
AV + K2L2___d
27r2 m(m + 1) nr 3 3Lg
111. Experimental
The waveguides studied were y cut x-propagatingTi:in-diffused LiNbO 3 waveguides characterized ap-proximately 11 by exponential refractive-index profiles.Gratings were written into the waveguide as indicatedin Fig. 1 by coupling two cw laser beams from anargon-ion laser (X = 0.5145 Am) into TEo waveguidemodes via rutile prisms. Two separate gratings werestudied; the angles between the writing beams whichwere symmetric about the x axis were 3 (1.59-mmspacing between electrodes) and 40 (0.3-mm spacing).Typically the incident powers in each beam were 1
mW, and the gratings were written in 1-sec exposures.These parameters were adjusted to produce approxi-mately a 50:50 splitting ratio when He-Ne guided wavelight was incident at the appropriate Bragg angle. Thefirst set of electrodes consisted of two strips separatedby -1.6 mm painted on with silver paint. The secondhad a set of evaporated 1500-A thick aluminum elec-trodes with a 0.3-mm spacing.
The modulator characteristics were studied with 0.1mW of He-Ne laser light. Light was coupled into andout of the TEO mode via rutile prisms. The gratingswere studied within a few months of their fabrication,and it was verified six months later that the gratingswere still present. Modulation was obtained byapplying a time varying voltage across the electrodes,and the deflected and undeflected beam intensities weremeasured with a calibrated photodiode.
Some of the pertinent operating characteristics of themodulator are shown in Fig. 1(c) and Figs. 2-4. Whenthe incident and deflected beams were kept away fromthe electrode edges, the quality of both beams was goodas indicated in Fig. 1(c). The properties of the dif-fracted beam when a sinusoidal time varying voltage isapplied to the electrodes are shown in Fig. 2. For lightincident at the Bragg angle, the output signal is theharmonic of the fundamental. Away from the Braggangle, the output can be chosen to be either in phase orout of phase with the modulation signal.
The variation in the diffraction efficiency with ap-plied voltage is indicated in Figs. 3 and 4. The (sinx/x) 2
response function predicted by Eq. (4) is reproducedexperimentally in Fig. 3(a). It is shown in Fig. 3(b) thata relatively linear response region can be found on theslopes of the response curve of Fig. 3(a). This operatingregion can easily be accessed by applying a dc biasvoltage to the electrodes or by misaligning (AO 7 0) theincident beam appropriately (Fig. 2). Finally in Fig.3(c), the sidebands of the response function are clearlyevident. The voltage separation between the minima(200 V in this case) agrees to within 10% with that pre-dicted by Eq. (7). This indicates that the electroopticcoefficient r3 3 within the in-diffused waveguide with thesuperimposed holographic grating has changed verylittle from its original value in bulk LiNbO3.
Detailed measurements of the modulator responsefunction (modulator efficiency) are reproduced in Fig.4. (100% efficiency corresponds in this case to completeextinction of the diffracted beam.) As is evident fromFig. 4, the agreement between experiment and theoryis excellent. The best extinction ratio obtained was -20dB, and the applied voltage corresponded to an appliedelectric field of 0.22 X 106 V/m.
The beam quality displayed anomalous behaviorwhenever the incident and/or deflected beams werepropagated near the electrode edges. (Hence thesespurious effects were produced very easily with thenarrow gap electrodes.) In Fig. 5(a) the incident beamwas propagated near the electrode edge, and only areasonably small amount of spreading due to laserdamage was observed. When a large voltage (300 V)was applied in a direction to move the response farther
(a)Fig. 2. Modulation signals obtained with a sinusoidal electrodevoltage for different directions of the incident guided wave relative
to the grating Bragg angle.
from optimum than it originally was, the beam qualityof the undiffracted light deteriorated drastically asshown in Fig. 5(b). Apparently the application of theelectrode voltage alters the local refractive index dueto the applied electric field. We hypothesize that thefields at the electrode edges are sufficiently high to causethe waveguide to approach the cutoff condition, andhence the beam quality is much more susceptible tolaser damage. As indicated in Fig. 5(c), when a largevoltage is used to obtain approximately the maximumdiffraction condition and the beam is propagated nearthe electrode edges, both the diffracted and undif-fracted beams were diffused over a large range of angles.Based on these observations it was important to keepthe guided wave beams away from the electrodes tomaintain reasonable beam quality.
IV. Summary
We have demonstrated a simple efficient modulatorwhich relies on a combination of the electrooptic andphotorefractive effects in Ti:in-diffused LiNbO3waveguides. This device is relatively simple to fabri-cate. It requires a blue-green laser and conductivepaint for electrodes. An electric field of -0.2 X 106 V/mis needed to produce an extinction ratio of -20 dB forthe geometry used here. Furthermore, the grating maybe easily erased by putting the waveguide in an oven at4000C for a few hours to remove the photorefractivegrating.
This research was supported by the Canadian Nat-ural Science and Engineering Research Council.
(b)
(c)
Fig. 3. Intensity of the diffracted guided wave obtained when atriangular voltage waveform was applied to the electrodes (0.3-mmgap spacing). Vertical scale for waveform: 50 V/div. Horizontalscale: 5 msec/div. Vertical scale for modulation signal: arbitraryunits: (a) full modulator response function; (b) linear response region;
Fig. 4. Modulator efficiency (100% complete extinction) vs ap-plied voltage across the 1.59-mm electrode gap. Solid line corre-
sponds to theory [Eq. (4)].
(a) (b) (c)
Fig. 5. Beam quality when the guided wave was propagated near the electrode edge (narrow gap): (a) No applied voltage. The spot corresponds
to the undiffracted beam. (b) 300 V applied in a direction away from the Bragg condition. The spot corresponds to the undiffracted beam.(c) 300 V applied to produce a diffracted beam near the condition for maximum diffraction. Upper and lower beams correspond to the un-
diffracted and diffracted beams.
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