spie proceedings [spie 1984 cambridge symposium - cambridge (tuesday 23 october 1984)] integrated...

Linear Ti:LiNb03 Modulators at 1.3 pm for Electromagnetic Field Sensing

Catherine H. Bulmer and Suzanne C. Hiser*Naval Research Laboratory, Optical Sciences Division, Code 6570

Washington, DC 20375

Abstract

Theory and experiment at 1.3 pm are presented to describe and compare the behavior oftwo kinds of channel waveguide modulators in Ti- indiffused LiNb03: Mach - Zehnderinterferometers and directional couplers. Each device can be operated as a linearmodulator when biased to an appropriate point, either by passive geometrical means or byapplication of a DC voltage. However, the device voltage responses differ, beingsinusoidal for an interferometer and varying as sin2x /x2 for a directional coupler.There is good agreement between calculated and measured device responses. The lineardynamic range of each kind of modulator is reported. We have measured linearity over 76dB and voltage sensitivities of - 13 pV.

Introduction

Guided -wave devices in Ti:LiNb03, coupled with single -mode fibers, are of interestfor electromagnetic field detection where a non -metallic sensor is wanted which does notperturb the field to be measured. The radiation is detected at a dipole antenna connectedto electrodes on the LiNb03 modulator. For this purpose, a linear modulator is desired.One method of achieving linear modulation is to use an asymmetric channel waveguideMach- Zehnder interferometer, where one arm is extended by one quarter guide wavelengthwith respect to the other so that there is an intrinsic phase bias of w /2. We havepreviously described interferometric modulator operation at 0.83 pm.1 Another method isto use a channel waveguide directional coupler with appropriate coupling parameters. Yaoet a1 have described a sensor employing a directional coupler modulator.2 In this paperwe describe and compare the behavior of interferometer and directional coupler as afunction of voltage, and we give experimental results for each device for 1.3 pmwavelength operation.

Theory - Interferometer and Directional Coupler Modulator Operation

Waveguide intensity modulators have been described by several authors.3 Considerfirst a single -mode channel waveguide Mach - Zehnder interferometer with a total phasedifference 0t between the arms as indicated schematically in Fig. 1. The waveguidebranches are symmetrical and operate as 50:50 power dividers. Light modulation occurs dueto variation of t. If 0t = 0, the modes in the two arms are in phase at the outputbranch and couple to give the symmetric lowest order mode which propagates along theoutput channel, resulting in maximum output power. If 4t = x, the modes are out of phaseat the output branch and couple to give the first antisymmetric mode which is cut off inthe single -mode output channel and therefore radiates into the substrate, giving zerochannel output. For unity input power, the output power is given by:

Po = 2 (1 + cosh t) = cos 2(0 t/2) (1)

where 4t may be the sum of an intrinsic phase difference 00 between the interferometerarms and an electro- optically induced phase difference 40, which is proportional to thevoltage V applied to electrodes. Hence:

Po = 2 (1 + cos[0 + KV]) (2)

where K is a constant. In Fig. 2a we show Po as a function of t = [0o + KV]. For00= 0, Po varies cosinusoidally with V and so, for small voltages, Po variesquadratically with V. For o = w/2

Po = 2 (1 - sin KV)

*Sachs Freeman Associates, Bowie, MD

(3)

SPIE Vol. 517 Integrated Optical Circuit Engineering (1984) / 177

Linear Ti:LiNb03 Modulators at 1.3 >on for Electromagnetic Field Sensing

Catherine H. Bulmer and Suzanne C. Hiser*Naval Research Laboratory, Optical Sciences Division, Code 6570

Washington, DC 20375

Abstract

Theory and experiment at 1.3 jim are presented to describe and compare the behavior of two kinds of channel waveguide modulators in Ti-indiffused LiNb03i Mach-Zehnder interferometers and directional couplers. Each device can be operated as a linear modulator when biased to an appropriate point, either by passive geometrical means or by application of a DC voltage. However, the device voltage responses differ, being sinusoidal for an interferometer and varying as sin 2 x/x^ for a directional coupler. There is good agreement between calculated and measured device responses. The linear dynamic range of each kind of modulator is reported. We have measured linearity over 76 dB and voltage sensitivities of ~ 13 |iV.

Introduction

Guided-wave devices in Ti:LiNb03, coupled with single-mode fibers, are of interest for electromagnetic field detection where a non-metallic sensor is wanted which does not perturb the field to be measured. The radiation is detected at a dipole antenna connected to electrodes on the LiNb03 modulator. For this purpose, a linear modulator is desired. One method of achieving linear modulation is to use an asymmetric channel waveguide Mach-Zehnder interferometer, where one arm is extended by one quarter guide wavelength with respect to the other so that there is an intrinsic phase bias of */2. We have previously described interferometric modulator operation at 0.83 van. 1 Another method is to use a channel waveguide directional coupler with appropriate coupling parameters. Yao et al have described a sensor employing a directional coupler modulator.2 in this paper we describe and compare the behavior of interferometer and directional coupler as a function of voltage, and we give experimental results for each device for 1.3 ^m wavelength operation.

Theory - Interferometer and Directional Coupler Modulator Operation

Waveguide intensity modulators have been described by several authors.3 consider first a single-mode channel waveguide Mach-Zehnder interferometer with a total phase difference <f>t between the arms as indicated schematically in Fig. 1. The waveguide branches are symmetrical and operate as 50:50 power dividers. Light modulation occurs due to variation of <{>£. If <j>t = 0, the modes in the two arms are in phase at the output branch and couple to give the symmetric lowest order mode which propagates along the output channel, resulting in maximum output power. If <j>t = if, the modes are out of phase at the output branch and couple to give the first antisymmetric mode which is cut off in the single-mode output channel and therefore radiates into the substrate, giving zero channel output. For unity input power, the output power is given by:

PQ = | (1 + cos4» t) = cos 2(0^2) (1)

where <}>£ may be the sum of an intrinsic phase difference 4>o between the interferometer arms and an electro-optically induced phase difference A<j>, which is proportional to the voltage V applied to electrodes. Hence:

PQ = i (1 + cosU o + KV]) (2)

where K is a constant. In Fig. 2a we show P0 as a function of 4>t = [<!>o + KV]. For ^o^ °' po varies cosinusoidally with V and so, for small voltages, P0 varies quadratically with V. For <|>o = */2

PQ = i (1 - sin KV) (3)

*Sachs Freeman Associates, Bowie, MD


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Thus Po varies sinusoidally with voltage V, as shown in Fig. 2b. The ordinate axis isshifted by w/2 relative to Fig. 2a. For small voltages, sin KV Pe. KV, so the output powervaries linearly with the input voltage.

The intrinsic phase bias 00 may be achieved passively as in Fig. 3 by an opticalpath differential 4L, where one interferometer arm is extended by AL relative to theother. Then 00 is given by

o- kneff4L (4)

where k = 21r /X and neff is the mode effective index. For 00 = R /2, we requireAL = Xg /4 where Xq = i /neff is the guide wavelength. At X = 1.3 pm, for theextraordinary mode polarization, this corresponds to AL 2.1 152 nm. Also, in Fig. 3, weshow the vertical field electrode structure used with Z -cut, X- propagating LiNb03 toallow use of the r33 electro -optic coefficient with the TM (extraordinary) mode.

It is clear from Eqn. (2) and Fig. 2, that, independent of the value of 00, theinterferometer power output varies in some sinusoidal, or cosinusoidal, fashion withvoltage. The effect of a finite 00 is to shift the zero voltage point along the sinecurve. Best linearity is obtained if the zero voltage point corresponds to half- maximumtransmission, which is obtained for 00 = A /2, as shown in Fig. 2b.

Now consider a single mode channel waveguide directional coupler as shown in Fig. 4.The power transferred Pl is described by4

2

P1 = sin 2 pL

and the straight- through power P2 is

P2 = 1 - P1

where lossless propagation is assumed. The variable p is given by

p[r2 + (.)2+

(5)

(6)

(7)

where r is the coupling coefficient and 4ß is the phase mismatch, being the magnitude ofany difference of the mode propagation constants in the two coupler arms. L is the totalcoupler interaction length which equals the electrode length. As for the interferometer,a vertical field electrode is used, with Z -cut, X- propagating LiNb03.

For zero applied voltage, there is perfect phase -matching because the two couplerarms are identical. Thus, from Eqs. (7) and (5), p = r and Pl = sin2 rL. Whenvoltage is applied, a phase mismatch is induced by the electro -optic effect. The electricfield direction is opposite in the two arms, so the changes in the two mode propagationconstants are equal in magnitude but opposite in sign, resulting in a finite A. As thepropagation constants are changed, the coupling coefficient is also perturbed. However, atypical change Ar is very much smaller than 4ß and we shall regard r as constant, while 4ßvaries directly with the applied voltage or 4ß = CV where C is a constant. We write Eqns.(5) and (7) to indicate more clearly the dependence of Pl on voltage:

where

P = r 2L2 sin2 (pL)1 (pL)2

pL = 2 [4r2L+ (4ßL)

The exact form of the sin2x /x2 type variation depends on the magnitude of rL.

(8)

In Fig. 5 we show the power transferred P1 and the straight- through power P2 as afunction of 4ßL (which is directly proportional to voltage) for various rL values between0 and 2a. For rL = 0, there is no power transfer and for rL = w or 21r, Pl = 0 at zerovoltage (4ßL = 0). Generally, as rL increases, the magnitude of the sidelobes increases.For rL = ,r /2 or 31r/2, P1 varies between 0 and 1 in the main lobe and thus has a

178 / SPIE Vol 517 Integrated Optical Circuit Engineering (1984)

Thus P0 varies sinusoidally with voltage V, as shown in Fig. 2b. The ordinate axis is shifted by */2 relative to Fig. 2a. For small voltages, sin KV « KV, so the output power varies linearly with the input voltage.

The intrinsic phase bias <|> o may be achieved passively as in Fig. 3 by an optical path differential AL, where one interferometer arm is extended by AL relative to the other. Then <j>o is given by

V kneffAL (4)

where k = 2ir/X and n eff is the mode effective index. For <j> o = */2, we require AL = Xg/4 where Xg = X/ne ff is the guide wavelength. At X = 1 . 3 ^i / for the extraordinary mode polarization, this corresponds to AL « 152 nm. Also, in Fig. 3, we show the vertical field electrode structure used with Z-cut, X-propagating LiNb03 to allow use of the r33 electro-optic coefficient with the TM (extraordinary) mode.

It is clear from Eqn. (2) and Fig. 2, that, independent of the value of (j>o , the interferometer power output varies in some sinusoidal, or cosinusoidal , fashion with voltage. The effect of a finite $o is to shift the zero voltage point along the sine curve. Best linearity is obtained if the zero voltage point corresponds to half -maximum transmission, which is obtained for <}> o = */2, as shown in Fig. 2b.

Now consider a single mode channel waveguide directional coupler as shown in Fig. 4. The power transferred PI is described by 4

r 2 2P l = 2 sin pL (5) P

and the straight-through power P2 is

P 2 = 1 - (6)

where lossless propagation is assumed. The variable p is given by

(7)

where K- is the coupling coefficient and AB is the phase mismatch, being the magnitude of any difference of the mode propagation constants in the two coupler arms. L is the total coupler interaction length which equals the electrode length. As for the interferometer, a vertical field electrode is used, with Z-cut, X-propagating LiNb03-

For zero applied voltage, there is perfect phase-matching because the two coupler arms are identical. Thus, from Eqs. (7) and (5), p = * and PI = sin^ rL. When voltage is applied, a phase mismatch is induced by the electro-optic effect. The electric field direction is opposite in the two arms, so the changes in the two mode propagation constants are equal in magnitude but opposite in sign, resulting in a finite AB. As the propagation constants are changed, the coupling coefficient is also perturbed. However, a typical change Ar is very much smaller than A3 and we shall regard * as constant, while A3 varies directly with the applied voltage or AB = CV where C is a constant. We write Eqns. (5) and (7) to indicate more clearly the dependence of P^ on voltage:

p s r 2L 2 sin (pL) 1 (PL) 2 (8)

where

pL = i [4ir 2L 2 + (ABL)

The exact form of the type variation depends on the magnitude of *rL.

In Fig. 5 we show the power transferred P^ and the straight-through power ?2 as a function of ABL (which is directly proportional to voltage) for various rL values between 0 and 2w. For rL = 0, there is no power transfer and for tcL = TT or 2w, PI = 0 at zero voltage (ABL = 0). Generally, as rL increases, the magnitude of the sidelobes increases. For rL = w/2 or 3*/2, PI varies between 0 and 1 in the main lobe and thus has a

/ 78 / SPIE Vol. 517 Integrated Optical Circuit Engineering (1984)


greater modulation range than for any of the other rL values. If P1 were set to 0.5with a finite 4ßL, e.g., by applying a DC voltage, then P1 might be linearly modulatedabout 0.5 by applying small AC voltages. For rL = m/2 the main lobe is narrower than forrL = 3m/2, so a smaller DC bias would be required. However, for any finite rL value, a DCbias might be introduced to set the coupler to its maximum linearity point about which anAC voltage would then modulate the outputs.

Device Design, Fabrication and Characterization

The various devices were all designed to be single -mode at 1.3 prn. On onephotolithographic mask we designed interferometers with 00 = m/2 and also with other00 values between 0 and m. The mid -arm spacing at the point where the interferometerarms become asymmetric was 66 pm. The channel waveguide width, for straight channels andinterferometers, was 6 pm. On a second photolithographic mask we designed channelwaveguide directional couplers, with inner spacing d varying from 2 to 6 pm andinteraction length varying from 1 to 6 mm. The waveguide width was 7 pm.

We used Z -cut, X- propagating LiNb03 so the TM (extraordinary) mode would bemodulated through the r33 electro -optic coefficient and the TE (ordinary) mode would bemodulated through r13. Ti waveguides of thickness 350 -450 A were diffused for 6 -8 hr at1050 °C in flowing oxygen which was bubbled through water to suppress out- diffusion.5The substrate edges were optically polished to allow end -fire coupling. An insulatingbuffer layer of Si02 (- 300 nm thick) was formed by chemical vapor deposition over thesubstrate before the electrodes were defined in - 200 nm Al. The interferometerelectrodes were 10 mm long with a 7 pm gapwidth. On the couplers the electrode lengthvaried, being equal to the interaction length, and the gapwidth varied according to thespacing d.

Measurements were made using a 1.3 pm GaInAsP laser. Light was butt -coupled throughthe LiNb03 polished edge from a single -mode fiber along which a linear polarization wasmaintained. The polarization could be rotated using a half -wave plate between the laserand fiber so that either mode polarization could be excited in the LiNb03. The outputpower was measured using a x60 objective and a Ge or GalnAs /InP detector which wasscreened to avoid any substrate light.

Interferometers were characterized by measuring the intrinsic phase bias 00 and themodulation or half -wave voltage V,. 4)0 is determined by measuring the voltages requiredto drive the output to maximum and minimum, or by comparing the output at zero voltage tothe maximum output.' Vm is the voltage required to induce A4 = m and hence to drive theoutput from maximum to minimum. Directional couplers were characterized by measuring thepower transfer ratio at zero voltage. Then, in Eqns. (5) and (6) p = r, giving

rL = tan -1(P

1/P

2)

The coupling ratio parameter rL is thus determined (here rL includes small amounts ofcoupling which can occur in the bend regions before the coupler arms are wellseparated6). The dynamic range of various interferometers and couplers was measuredusing a spectrum analyzer and a lock -in amplifier. In order to investigate any possiblephotorefractive effects (optical damage), we measured straight channel, interferometer anddirectional coupler transmission as a function of optical power. Interferometer 00 anddirectional coupler rL were also measured at both low and high optical power levels.

Experimental Modulation as Function of Voltage

For the interferometric modulator we have seen that theoretically the output powervaries in a sinusoidal fashion with voltage. The position of the ordinate axis and theoutput at zero voltage depend on the intrinsic phase bias 00. In Fig. 6 we show Po,for both modes, measured experimentally as a function of the DC voltage applied toelectrodes as in Fig. 3. For the TM mode in Fig. 6a, (1)0 = 94° and Vm = 4.5 V. Forthe TE mode in Fig. 6b, 00 = 89.4° and Vm = 18.0 V. For these and otherinterferometers, we measured modulation depths, or extinction ratios (10 logPurin /Pmax),of at least -25 dB.

The outputs of a directional coupler modulator vary in a sin2x /x2 fashion withvoltage. However, from Eq. (8), the variation is determined by the magnitude of thecoupling ratio rL as well as by the voltage (which directly affects oß). In Fig. 7 weshow the power transferred Pl and straight -through power P2, measured for the TM mode, ontwo different couplers, as a function of DC applied voltage. For the rL value of eachcoupler, measured at zero voltage, we also show the corresponding theoretical curvecalculated as a function of 4ßL. There is generally good agreement between theory andexperiment, especially for P1 and with regard to the positions of the minima and maxima.

SP /E Vol. 517 Integrated Optical Circuit Engineering (1984) / 179

greater modulation range than for any of the other rL values. If P^ were set to 0.5 with a finite A&L, e.g., by applying a DC voltage, then PI might be linearly modulated about 0.5 by applying small AC voltages. For K-L = */2 the main lobe is narrower than for K-L = 3*/2, so a smaller DC bias would be required. However, for any finite rL value, a DC bias might be introduced to set the coupler to its maximum linearity point about which an AC voltage would then modulate the outputs.

Device Design, Fabrication and Characterization

The various devices were all designed to be single-mode at 1.3 }irn. On one photolithographic mask we designed interferometers with (j> 0 = ?r/2 and also with other <{> 0 values between 0 and TT. The mid-arm spacing at the point where the interferometer arms become asymmetric was 66 n^. The channel waveguide width, for straight channels and interferometers, was 6 jim. On a second photolithographic mask we designed channel waveguide directional couplers, with inner spacing d varying from 2 to 6 nm an<3 interaction length varying from 1 to 6 mm. The waveguide width was 7 >im.

We used Z~cut, X-propagating LiNb03 so the TM (extraordinary) mode would be modulated through the r33 electro-optic coefficient and the TE (ordinary) mode would be modulated through rj^. Ti waveguides of thickness 350-450 A were diffused for 6-8 hr at 1050°C in flowing oxygen which was bubbled through water to suppress out-diffusion.5 The substrate edges were optically polished to allow end-fire coupling. An insulating buffer layer of Si02 (~ 300 nm thick) was formed by chemical vapor deposition over the substrate before the electrodes were defined in ~ 200 nm Al. The interferometer electrodes were 10 mm long with a 7 jim gapwidth. On the couplers the electrode length varied, being equal to the interaction length, and the gapwidth varied according to the spacing d.

Measurements were made using a 1.3 ji GalnAsP laser. Light was butt-coupled through the LiNb03 polished edge from a single-mode fiber along which a linear polarization was maintained. The polarization could be rotated using a half-wave plate between the laser and fiber so that either mode polarization could be excited in the LiNb03. The output power was measured using a x60 objective and a Ge or GalnAs/InP detector which was screened to avoid any substrate light.

Interferometers were characterized by measuring the intrinsic phase bias <|> 0 and the modulation or half-wave voltage Vw . (j> 0 is determined by measuring the voltages required to drive the output to maximum and minimum, or by comparing the output at zero voltage to the maximum output. 1 V^ is the voltage required to induce A<j> = ?r and hence to drive the output from maximum to minimum. Directional couplers were characterized by measuring the power transfer ratio at zero voltage. Then, in Eqns. (5) and (6) p = r, giving

K-L = tan" 1 (P 1 /P 2 )*

The coupling ratio parameter rL is thus determined (here trL includes small amounts of coupling which can occur in the bend regions before the coupler arms are well separated^). The dynamic range of various interferometers and couplers was measured using a spectrum analyzer and a lock-in amplifier. In order to investigate any possible photorefractive effects (optical damage), we measured straight channel, interferometer and directional coupler transmission as a function of optical power. Interferometer <j> o and directional coupler rL were also measured at both low and high optical power levels.

Experimental Modulation as Function of Voltage

For the interferometric modulator we have seen that theoretically the output power varies in a sinusoidal fashion with voltage. The position of the ordinate axis and the output at zero voltage depend on the intrinsic phase bias <j> o . In Fig. 6 we show Po , for both modes, measured experimentally as a function of the DC voltage applied to electrodes as in Fig. 3. For the TM mode in Fig. 6a, <fr o = 94° and V^ = 4.5 V. For the TE mode in Fig. 6b, <j> 0 = 89.4° and Vv = 18.0 V. For these and other interferometers, we measured modulation depths, or extinction ratios (10 log pmin/ pmax)' of at least -25 dB.

The outputs of a directional coupler modulator vary in a sin 2 x/x 2 fashion with voltage. However, from Eq. (8), the variation is determined by the magnitude of the coupling ratio tcL as well as by the voltage (which directly affects A&). In Fig. 7 we show the power transferred PI and straight-through power P2, measured for the TM mode, on two different couplers, as a function of DC applied voltage. For the rL value of each coupler, measured at zero voltage, we also show the corresponding theoretical curve calculated as a function of A3L. There is generally good agreement between theory and experiment, especially for P^ and with regard to the positions of the minima and maxima.



At high voltages there is generally some decrease in total coupler throughput. For eithervoltage polarity, the mode effective index is reduced in one arm of the coupler. As themode becomes less well -guided, its field spreads out and its attenuation may increaseespecially at any discontinuities or imperfections.

Linear Dynamic Range

In Fig. 8 we show the response of an interferometer with 00 = 89.4° for the TE(ordinary) mode, measured at 8 kHz fundamental frequency with a 100 St load on thedetector. The fundamental and 2nd harmonic were measured on both a spectrum analyzer and alock -in amplifier; the 3rd harmonic was measured on the spectrum analyzer and measurementswere limited to values above the spectrum analyzer noise level, - -124 dBV. The input isthe modulating voltage applied to the interferometer electrodes. The output is the signalfrom the GalnAs /InP detector at which the zero -volt optical power level was - 0.37mW. Thelower limit, VL = 37 pVrms, is where the modulating voltage produces a fundamental outputsignal equal to the noise due to the unmodulated power level and the upper limit, Vu =0.25 Vrms, is where any higher harmonic, in this case the second, equals the noise. Thesecorrespond to a linear dynamic range of 76 dB. The range is thermal noise limited wherethe thermal noise level , -143 dBV, corresponds to a 3 kHz bandwidth and the 100 52 load(the 3 kHz bandwidth is of interest for sensing applications). The modulation voltage V,was 18.0 V.

On another device we measured @o = 91.5° and a linear dynamic range of 70 dB, for theTM (extraordinary) mode, with 0.28 mW incident on the detector at zero voltage. Thedynamic range corresponds to inputs of VL = 13 pV to Vu = 43 mVrms and V, was measured as5.0 V. The voltage sensitivity is greater, i.e. VL is smaller, than for the TE mode caseas the larger r33 electro -optic coefficient is utilized. In each case the upper limit isdetermined by the 2nd harmonic. For 00 = x/2 exactly, the 2nd harmonic becomes negligiblysmall and the 3rd harmonic sets the upper limit, as was observed when a small DC voltagewas applied to adjust the phase bias.

The directional couplers were all symmetric devices. The two arms are identical sothe modes are exactly phase- matched, i.e., Aß = 0, for zero voltage. In order to achievea linear response, the coupler must be "biased" so as to have an appropriate finite eß.This might be achieved passively by making one arm wider than the other, or by varying theTi thickness, or using an overlay on one arm. In our case we used a DC bias voltage toset a directional coupler modulator to its maximum linearity point. In Fig. 9 we show theresponse of a directional coupler modulator for the TM mode, measured at 8 kHz fundamentalfrequency, with a 100 S2 load on the detector and a constant DC bias on the electrodes of-6.3V. The 74 dB linear dynamic range corresponds to input voltages of 89 pV to 0.45Vrms. The electrode length is 4 mm and the gapwidth is 3 pm. The coupling ratioKL = 122 °. The -6.3 V bias was chosen to minimize the 2nd harmonic and sets the powertransferred P1, and the straight- through power P2, to linear portions of their voltageresponses, which are shown in Fig. 7a. The dynamic range was measured on output P2 asits magnitude was greater than P1 at the maximum linearity point. With the -6.3 V DCbias, but no AC modulation, P2 = 0.50 mW.

Photorefractive Effects - Optical Damage

We had previously observed large optical damage effects in interferometers,directional couplers and straight channel waveguides at 0.83 µm.1 At 1.3 pm theseeffects were all very substantially reduced. The transmission of straight channels anddevices was measured as a function of input optical power. Attenuation remained constantfor each polarization and there was no saturation. Up to 2.5 mW was output from achannel. The output at a high power also remained stable with time. The total TM modeoutput of a channel waveguide directional coupler decreased by at most 4% after 10 hr.The directional coupler throughput was slightly higher than for an interferometer, by -0.5 dB. An interferometer at maximum transmission generally had 1.5 -2 dB more loss than asimilar straight channel on the same substrate.

We also measured 00 of interferometers as a function of power and observed it to begenerally constant, unlike at 0.83 pm. On some devices it is absolutely constant withvarying power and with time. On other devices there are some small variations with timeand occasionally power. These instabilities may be temperature -related in part and arenow being investigated further. On directional couplers we checked the coupling ratio KLas a function of power. Any observed changes in KL were < 2.5% as the power was increasedfrom - 2x102 to 2x104 W /cm2 whereas at 0.83 pm an approximately 50:50 coupler becamealmost 100:0 with similarly increased power (change in rL of 45 °). Greater stabilitymeans that a greater dynamic range may be achieved at 1.3 pm compared to 0.83 pm. Forinstance, the dynamic range of an interferometer depends on the accuracy of the phase bias00 (90° is desired) and on the optical power.1 At 1.3 pm we could construct

180 / SPIE Vol. 517 Integrated Optical Circuit Engineering (1984)

At high voltages there is generally some decrease in total coupler throughput. For either voltage polarity, the mode effective index is reduced in one arm of the coupler. As the mode becomes less well-guided, its field spreads out and its attenuation may increase especially at any discontinuities or imperfections.

Linear Dynamic Range

In Fig. 8 we show the response of an interferometer with <|>o = 89.4° for the TE (ordinary) mode, measured at 8 kHz fundamental frequency with a 100 ft load on the detector. The fundamental and 2nd harmonic were measured on both a spectrum analyzer and a lock-in amplifier? the 3rd harmonic was measured on the spectrum analyzer and measurements were limited to values above the spectrum analyzer noise level, ~ -124 dBV. The input is the modulating voltage applied to the interferometer electrodes. The output is the signal from the GalnAs/InP detector at which the zero-volt optical power level was - 0.37mW. The lower limit, VL = 37 jiVrms, is where the modulating voltage produces a fundamental output signal equal to the noise due to the unmodulated power level and the upper limit, Vu = 0.25 Vrms, is where any higher harmonic, in this case the second, equals the noise. These correspond to a linear dynamic range of 76 dB. The range is thermal noise limited where the thermal noise level , -143 dBV, corresponds to a 3 kHz bandwidth and the 100 ft load (the 3 kHz bandwidth is of interest for sensing applications). The modulation voltage Vw was 18.0 V.

On another device we measured $o = 91.5° and a linear dynamic range of 70 dB, for the TM (extraordinary) mode, with 0.28 mW incident on the detector at zero voltage. The dynamic range corresponds to inputs of VL = 13 \iV to Vu = 43 mVrms and V^ was measured as 5.0 V. The voltage sensitivity is greater, i.e. VL is smaller, than for the TE mode case as the larger r33 electro-optic coefficient is utilized. In each case the upper limit is determined by the 2nd harmonic. For (j> 0 = w/2 exactly, the 2nd harmonic becomes negligibly small and the 3rd harmonic sets the upper limit, as was observed when a small DC voltage was applied to adjust the phase bias.

The directional couplers were all symmetric devices. The two arms are identical so the modes are exactly phase-matched, i.e., A3 = 0, for zero voltage. In order to achieve a linear response, the coupler must be "biased" so as to have an appropriate finite A&. This might be achieved passively by making one arm wider than the other, or by varying the Ti thickness, or using an overlay on one arm. In our case we used a DC bias voltage to set a directional coupler modulator to its maximum linearity point. In Fig. 9 we show the response of a directional coupler modulator for the TM mode, measured at 8 kHz fundamental frequency, with a 100 ft load on the detector and a constant DC bias on the electrodes of-6.3V. The 74 dB linear dynamic range corresponds to input voltages of 89 ^V to 0.45 Vrms. The electrode length is 4 mm and the gapwidth is 3 jim. The coupling ratio*rL = 122°. The -6.3 V bias was chosen to minimize the 2nd harmonic and sets the power transferred PI, and the straight-through power ?2/ to linear portions of their voltage responses, which are shown in Fig. 7a. The dynamic range was measured on output ?2 as its magnitude was greater than PI at the maximum linearity point. With the -6.3 V DC bias, but no AC modulation, ?2 = 0.50 mW.

Photorefractive Effects - Optical Damage

We had previously observed large optical damage effects in interferometers, directional couplers and straight channel waveguides at 0.83 jim.l At 1.3 >im these effects were all very substantially reduced. The transmission of straight channels and devices was measured as a function of input optical power. Attenuation remained constant for each polarization and there was no saturation. Up to 2.5 mW was output from a channel. The output at a high power also remained stable with time. The total TM mode output of a channel waveguide directional coupler decreased by at most 4% after 10 hr. The directional coupler throughput was slightly higher than for an interferometer, by ~ 0.5 dB. An interferometer at maximum transmission generally had 1.5-2 dB more loss than a similar straight channel on the same substrate.

We also measured (j> o of interferometers as a function of power and observed it to be generally constant, unlike at 0.83 vim. On some devices it is absolutely constant with varying power and with time. On other devices there are some small variations with time and occasionally power. These instabilities may be temperature-related in part and are now being investigated further. On directional couplers we checked the coupling ratio »cL as a function of power. Any observed changes in trL were < 2.5% as the power was increased from ~ 2xl0 2 to 2x10^ W/cm2 whereas at 0.83 >im an approximately 50:50 coupler became almost 100:0 with similarly increased power (change in rL of 45°). Greater stability means that a greater dynamic range may be achieved at 1.3 >iro compared to 0.83 pirn. For instance, the dynamic range of an interferometer depends on the accuracy of the phase bias <j> 0 (90° is desired) and on the optical power. 1 At 1.3 urn we could construct



interferometers with 00 values in the range 88 -92° which remained unchanged as the powerwas increased (up to at least 5 x 103 W /cm2), whereas at 0.83 Lim a stable phase bias ofclose to 90° could be achieved only at much lower powers (- 102 W /cm2).

Discussion and Conclusions

The responses of two types of channel waveguide modulators, Mach - Zehnderinterferometers and directional couplers, have been described and compared. Theinterferometer output varies sinusoidally with applied voltage. By appropriate biasing tothe mid -point of the sine wave (setting 00 = a /2), a linear response is obtained forsmall voltages. We achieved such a bias passively, in a geometrical fashion, by extendingone interferometer arm relative to the other. The directional coupler output varies in asin2x /x2 fashion where x is the sum of one term determined by the coupling ratioand a second term proportional to the voltage. For a symmetric coupler, as for asymmetric interferometer, the response is identical for voltages of opposite polarity butequal magnitude. With an appropriate bias (creating a finite oß), which depends on thecoupling ratio, a linear response is achieved. We achieved biasing actively, using a DCvoltage. A bias might be realized passively by geometrical means: widening one arm,depositing a greater Ti thickness on one arm or using an overlay. The process would bemore complicated than for an interferometer because the exact bias required would dependon the actual coupling ratio achieved and so would vary with fabrication parameters;whereas, for an interferometer, a 1/2 bias is always required, corresponding to onequarter guide wavelength which varies little with fabrication parameters.

We measured the voltage response of both interferometers and directional couplersand showed them to be in good agreement with theory. We also measured the linear dynamicrange of both devices at 1.3 pm. For an interferometer with 00 = 89.4° we achieved a 76dB range, limited by the 2nd harmonic. For a directional coupler, with a small DC bias,we achieved a 74 dB range. There were no large optical damage effects as were apparent at0.83 pm. Interferometer phase bias and coupler coupling ratio were generally stable withvarying optical power.

Acknowledgment

The authors wish to thank W. K. Burns for useful discussions, R. P. Moeller forvaluable technical assistance and J. P. Gunn, M. L. Rebbert and E. J. West for assistancewith device fabrication.

References

1. C. H. Bulmer and W. K. Burns, "Linear interferometric modulators in Ti:LiNb03," IEEEJ. Lightwave Tech. LT -2, pp. 512 -521, 1984.

2. S. K. Yao, T. Findakly, R. Cordero- Iannarella, S. Thaniyavarn, G. Hayward and B.Chen, "Electromagnetic sensor using integrated optic channel waveguide modulator andpolarization preserving fiber," SPIE Proc., Vol. 412, pp. 154 -159, 1983.

3. See, for example, R. C. Alferness, "waveguide electrooptic modulators," IEEE Trans.MTT -30, pp. 1121 -1137, 1982.

4. W. H. Louisell, "Coupled mode and parametric electronics," Ch. 1, Wiley, 1960.5. J. L. Jackel, V. Ramaswamy and S. P. Lyman, "Elimination of out -diffused surface

guiding in titanium -diffused LiNb03," Appl. Phys. Lett., 38, pp. 509 -511, 1981.6. C. H. Bulmer and W. K. Burns, "Polarization characteristics of LiNb03 channel

waveguide directional couplers," IEEE J. Lightwave Tech., LT -1, pp. 227 -236, 1983.

< 4t Figure 1 Schematic of channelwaveguide Mach -Zehnderinterferometer

SPIE Vol 517 Integrated Optical Circuit Engineering (1984) / 181

interferometers with <j>o values in the range 88-92° which remained unchanged as the power was increased (up to at least 5 x 10^ W/cm^), whereas at 0.83 um a stable phase bias of close to 90° could be achieved only at much lower powers (~ 10^ W/cm^).

Discussion and Conclusions

The responses of two types of channel waveguide modulators, Mach-Zehnder interferometers and directional couplers, have been described and compared. The interferometer output varies sinusoidal!^ with applied voltage. By appropriate biasing to the mid-point of the sine wave (setting <j> o = */2), a linear response is obtained for small voltages. We achieved such a bias passively, in a geometrical fashion, by extending one interferometer arm relative to the other. The directional coupler output varies in a sin^x/x^ fashion where x is the sum of one term determined by the coupling ratio and a second term proportional to the voltage. For a symmetric coupler, as for a symmetric interferometer, the response is identical for voltages of opposite polarity but equal magnitude. With an appropriate bias (creating a finite AB) , which depends on the coupling ratio, a linear response is achieved. We achieved biasing actively, using a DC voltage. A bias might be realized passively by geometrical means: widening one arm, depositing a greater Ti thickness on one arm or using an overlay. The process would be more complicated than for an interferometer because the exact bias required would depend on the actual coupling ratio achieved and so would vary with fabrication parameters? whereas, for an interferometer, a ir/2 bias is always required, corresponding to one quarter guide wavelength which varies little with fabrication parameters.

We measured the voltage response of both interferometers and directional couplers and showed them to be in good agreement with theory. We also measured the linear dynamic range of both devices at 1.3 >im. For an interferometer with <{> o = 89.4° we achieved a 76 dB range, limited by the 2nd harmonic. For a directional coupler, with a small DC bias, we achieved a 74 dB range. There were no large optical damage effects as were apparent at 0.83 jim. Interferometer phase bias and coupler coupling ratio were generally stable with varying optical power.

Acknowledgment

The authors wish to thank W. K. Burns for useful discussions, R. P. Moeller for valuable technical assistance and J. P. Gunn, M. L. Rebbert and E. J. West for assistance with device fabrication.

References

1. C. H. Bulmer and W. K. Burns, "Linear interferometric modulators in Ti:LiNb03," IEEE J. Lightwave Tech. LT-2, pp. 512-521, 1984.

2. S. K. Yao, T. Findakly, R. Cordero-Iannarella, S. Thaniyavarn, G. Hayward and B.Chen, "Electromagnetic sensor using integrated optic channel waveguide modulator and polarization preserving fiber," SPIE Proc., Vol. 412, pp. 154-159, 1983.

3. See, for example, R. C. Alferness, "Waveguide electrooptic modulators," IEEE Trans. MTT-30, pp. 1121-1137, 1982.

4. W. H. Louisell, "Coupled mode and parametric electronics," Ch. 1, Wiley, 1960.5. J. L. Jackel, V. Ramaswamy and S. P. Lyman, "Elimination of out-diffused surface

guiding in titanium-diffused LiNb0 3 ," Appl. Phys. Lett., 38, pp. 509-511, 1981.6. C. H. Bulmer and W. K. Burns, "Polarization characteristics of LiNb03 channel

waveguide directional couplers," IEEE J. Lightwave Tech., LT-1, pp. 227-236, 1983.

Figure 1 Schematic of channelwaveguide Mach-Zehnder interferometer



Figure 2(a) Interferometer output Po asfunction of total phase differ-ence ct. For cpo = 0, this isPo as a function of KV, whereV is the voltage.

(b) Output Po as function of KV foran interferometer with a 7/2intrinsic phase bias.

(a)

(b)

-2H -H

0.5

1-5II -3II -II H 3H 511

2 2 2 2 2 2

II 2II 3H

KV

= [00 + KV]

Figure 3 Schematic of asymmetric inter-ferometer with optical pathdifference AL between the armsand vertical field electrodeconfiguration.

SINGLE MODECHANNEL

WAVEGUIDE : `1.2° 6pm

g7Nm

Figure 4 Schematic of channel waveguidedirectional coupler withvertical field electrodeconfiguration.

Pin

Figure 5 Computed directional coupler outputs as a function of 4ßL (proportionalto voltage) for coupling ratio KL = 7/4, 7/2, 37r/4, - --27. The solidcurve is P1, the power transferred. The dashed curve is P2, the straight -through power. A lossless coupler with unity input power is assumed.

xL=II/4

-8H - 4H

P2

P1

4H 8II

AßL (RADIANS)

182 / SPIE Vol. 517 Integrated Opt ;cal Circuit Engineering (1984)

x L = II/2

.Th I\ 1'

0.5

I^\ /i \.i P2

Pl

4H 8H

0ßL (RADIANS)

Figure 2(a) Interferometer output Po asfunction of total phase differ ence cf>f For (j> 0 = 0, this is P0 as a function of KV, where V is the voltage.

(b) Output P0 as function of KV for an interferometer with a ir/2 intrinsic Dhase bias.

(a)

Figure 3 Schematic of asymmetric inter ferometer with optical path difference AL between the arms and vertical field electrode configuration.

SINGLE MODECHANNEL

WAVEGUIDE

KV]

-2n -n n 2n

(b)

Figure 4 Schematic of channel waveguide directional coupler with vertical field electrode configuration.

-sn -an -n n an sn22222 2

w

w ',

XX

H^'/

xxxxxxxxJ d *

''XXXXXXX

1

11

;

Figure 5 Computed directional coupler outputs as a function of A$L (proportional to voltage) for coupling ratio KL = ir/4, IT/2, Sir/4, 2ir. The solid curve is P]_, the power transferred. The dashed curve is P2, the straight- through power. A lossless coupler with unity input power is assumed.

XL = n/4

XL = n/2

4D BIT

A0L (RADIANS)

-sn 4nA0L (RADIANS)



Figure 5 continued

xL = 311/4

f` n ..1 1

1 1 211 1\`I

5

I

1 ¡\ +

PI

-811 -411 0 411 811

xL = 511/4

,.: 1\ I.\+ 1 1v

1 /1

y+ I

0ßL (RADIANS)

¡1 i si r,% '".I

1 1 1.!I I p

1 1/ 2

PI

-811 -411 0 411 811

0ßL (RADIANS)

AO_ (RADIANS)

xL=11

-' ..% 1 1vr1 j I \i P2

1t 1

I I 1 1

1 I 1 1

\ / \`r

/e

0.5

-811 -411 0 411 811

OßL (RADIANS)

XL = 311/2

/ 1 I\ 1 I 1v

1

11

1/ I

r1

1 \I I

1 111% P

I2

I l1

V

P1

-811 -411 0 411 811

43L (RADIANS)

xL=211

% 11 i 1 \I ; \/ f`t,

I I I 1 ' 1 P2

V I - I 1 v

LIAIPI

-811 -411 411 811

0ßL (RADIANS)


Figure 5 continued

XL = n

-sn -4n 4n snA0L (RADIANS)

-sn 4n snA(3L (RADIANS)

= 5H/4 XL = 3n/2

-sn -4n snA0L (RADIANS)

-4n 4n snA/3L (RADIANS)

A

-sn snA/3L (RADIANS)

snA/3L (RADIANS)



Figure 6 Experimental plots of interferometer output as a function of DC voltagefor (a) the TM mode (b) the TE mode. In each case ¢o r/2. Thevertical scale is in arbitrary units.

(a) (b)OUTPUTPOWER

Po

-15 -10 -5 0 5 10 15

DC INPUT VOLTAGE (V)

OUTPUTPOWER

Po

A 1 A-60 -20 0 20 40


Figure 7 Experimental plots of directional coupler outputs for the TM mode asa function of DC voltage and corresponding theoretical curves as afunction of A6L, calculated for the measured KL values. In (a) KL =122 °, in (b) KL = 247 °. The solid curves represent P1, the powertransferred, and the dashed curves are P2, the straight- through power.

(a) xL = 122° (EXP.) OUTPUTPOWER

P2

- 80 -20 0 20


184 / SP /E Vol 517 Integrated Optical Circuit Engineering (1984)

(a) XL = 122° (COMPUTED)

w 1

\% 1 / 1 it ,\ / P21 t Xv V

sit

'

0.5

A-8H -4II 4H 8H

0ßL (RADIANS)

Figure 6 Experimental plots of interferometer output as a function of DC voltage for (a) the TM mode (b) the TE mode. In each case $ o « Tr/2. The vertical scale is in arbitrary units.

OUTPUT POWER

po

-505

DC INPUT VOLTAGE (V) -20 0 20


Figure 7 Experimental plots of directional coupler outputs for the TM mode as a function of DC voltage and corresponding theoretical curves as a function of A3L, calculated for the measured xL values. In (a) KL = 122°, in (b) KL = 247°. The solid curves represent P]_, the power transferred, and the dashed curves are P 2 , the straight-through power.

(a) XL = 122° (COMPUTED)(a) XL = 122° (EXP.) OUTPUT

POWER

/\

-40 -20 0 20


40 60

-4n 4n snA0L (RADIANS)



Figure 7 continued

(b) xL = 247° (EXP.) OUTPUTPOWERi'

1 It it

; ', :i

r 1

it rII ``. : i

I /

,,\, /

i i -.

,I _

/ P2

-80 -00 -40 -n 0 20

DC INPUT VOLTAGE IVI

40 60 80

Figure 8 Interferometer response at 8 kHz(fundamental). There is no DCbias. (po = 89.4° because of theasymmetric arms.

-40

-160

o FUNDAMENTALD 2nd HARMONICA 3rd HARMONIC

76 dB

37NV rmsII I 1 I

THERMAL NOISEI LIMIT

IR =10040.25 V rms B = 3 kHz)

I I

-100 -80 -60 -40

INPUT IdBVI

-20 o 20

(b) xL = 247° (COMPUTED)

1 ^ i I ^ . ,\ / l I I I // / v.. \J I

iP

1 I 1 IiI

1 I 2

\J/ I \v/

I (I I

1

-8H -4n 411 an

zia. (RADIANS)

Figure 9 Directional coupler responseat 8 kHz (fundamental). TheDC bias is -6.3V.

-40

_BO

-120

-160

o FUNDAMENTAL

a 2nd HARMONIC

A 3rd HARMONIC

89uV rms

74 dB

045Vrmsr

ca

00THERMAL NOISELIMITIR = 100 R,B = 3 kHz)

-80 -60 -40 -20

INPUT I48V)

20

SPIE Vol 517 Integrated Optical Circuit Engineering (1984) / 185

Figure 7 continued

(b) XL = 247° (COMPUTED)

- 20 0 20


40 60 80

-sn -4n 40 snA(3L (RADIANS)

Figure 8 Interferometer response at 8 kHz (fundamental). There is no DC bias. <j> 0 = 89.4° because of the asymmetric arms.

_ -80

-160

O FUNDAMENTALa 2nd HARMONICA 3rd HARMONIC

0.25 V rms j

THERMAL NOISE LIMIT

(R = 100 Q B = 3 kHz)

I

Figure 9 Directional coupler response at 8 kHz (fundamental). The DC bias is -6.3V.

-100 -80 -40

INPUT (dBV)

O FUNDAMENTAL

0 2nd HARMONIC

A 3rd HARMONIC



spie proceedings [spie 1984 cambridge symposium - cambridge (tuesday 23 october 1984)] integrated...

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