The thermo-optic ~TO! effect is useful for constructingwaveguide-type optical switching devices because itcan be utilized even in passive materials such asglass and polymers.1–3 Since organic polymers havea lower thermal conductivity and a greatertemperature-dependent refractive index than inor-ganic materials, polymer TO switches require lessswitching power. Several kinds of polymerwaveguide TO switch have been studied by use ofMach–Zehnder interferometers ~MZI’s!,4,5 Y branch-es,6,7 and directional couplers.8 They all have asmall switching power of less than 0.1 W. In partic-ular, MZI-type switches incorporating TO phaseshifters in their waveguide arms need less switchingpower than do other types of switch.
Recently we reported a MZI-type 2 3 2 switch witha switching power of 4.8 mW and a switching time of9 ms.9 The advantage of the switch is that it has alow insertion loss of 0.6 dB at a communication wave-
Y. Hida and S. Imamura are with the NTT Opto-electronicsLaboratories, Tokai-Mura, Naka-Gun, Ibaraki-Ken 319-11, Japan.K. Onose is with the NTT Electronics Technology Corporation atthe same address.
Received 27 February 1996; revised manuscript received 27 No-vember 1996.
6828 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997
length of 1.3 mm. This is achieved by use of deuter-ated and fluorinated methacrylate ~FMA! polymersin which the C–H bonds are eliminated.10 Further-more, we obtained polarization-independent opera-tion and a low cross talk of approximately 240 dB.However, we observed a drift phenomenon in switch-ing that remains to be solved.
Here, we report on the phase drift in a TO phaseshifter composed of deuterated methacrylate andFMA polymers, and we ascribe the drift phenomenonto moisture desorption–sorption in the waveguidecaused by heating–cooling. In Section 2 we describethe fabrication of the TO phase shifter and its normalresponse and then the observed drift phenomenon.We characterize the drift phenomenon with regard toambient humidity in Section 3. In Section 4 we dis-cuss the mechanism of the phase drift with someexperimental and calculated results.
2. Fabrication and Characterization of Thermo-OpticPhase Shifter
A. Circuit Configuration
We evaluated a TO phase shifter installed in a MZI-type TO switch. The switch consists of two identicaldirectional couplers linked by two waveguide arms ofequal length @Fig. 1~a!#. Phase shifters are formedin each of the arms in the regions covered with thin-film heaters. A silicon ~Si! wafer is used as a sub-strate because it has a much larger thermal
conductivity than polymers and acts as a heat sink@Fig. 1~b!#. The output powers from throughport P1and crossport P2 are given by
P1
P05 ~1 2 2K!2 cos2 Sf
2D 1 sin2 Sf
2D , (1.1)
P2
P05 4K~1 2 K!cos2 Sf
2D , (1.2)
respectively, where P0 is the input power, K is thepower-coupling ratio of the directional couplers, andf is the phase shift caused by the TO effect. Here weassume that the waveguides have no losses. If K 550%, the circuit works as an ideal switch for boththroughport and crossport. When K Þ 50%, the out-put power from the throughport is not completelyextinguished. However, the crossport power can al-ways be extinguished when u f u 5 p, 3p, 5p, . . . , andtherefore we can characterize the phase shifter bymeasuring the crossport output power.
B. Waveguide Polymers
The polymers used for waveguide formation were co-polymerized from deuterated methyl methacrylateand FMA monomers.10 The absorption loss of thesemonomers was low at communication wavelengths ofapproximately 1.3 mm. This was achieved by elim-ination of C–H bond vibrational absorption. Wecontrolled the refractive index of the polymers byadjusting the co-polymerization ratio of the twomonomers since the refractive index decreases withincreasing fluorine content. A polymer without flu-orine, which is usually referred to as poly~methylmethacrylate! ~PMMA!-d8, was used for the core, anda polymer with 2 wt% of fluorine was used for the
Fig. 1. ~a! Top view of a test circuit that consists of a Mach–Zehnder interferometer with TO phase shifters in its waveguidearms. ~b! Cross section of the TO phase shifter.
cladding. Their relative index difference was 0.3%.These polymers were dissolved in an organic solventfor spin coating and passed through a 0.1-mm filter toremove impurities.
C. Fabrication Process
The fabrication process of the polymer waveguide TOphase shifter is shown in Fig. 2. First an underclad-ding layer and then a core layer were spin coated ona Si wafer @Fig. 2~a!#. After each spin coating, thepolymer film was baked at 90 °C for more than 30min to remove the solvent. The circuit pattern wasformed by conventional photolithography in silicone-based photoresist coated over the core layer. Thenthe core ridges were formed by O2-gas reactive-ionetching with the resist used as a mask @Fig. 2~b!#.An overcladding layer was spin coated to embed thecore ridges @Fig. 2~c!#, and then channel waveguideswere obtained with the circuit pattern. Next, a flu-orinated UV-curable resin was spin coated on theovercladding as a buffer layer to protect thewaveguides from degradation during heater forma-tion @Fig. 2~d!#. Finally, thin-film heaters wereformed by the electron-beam evaporation of Cr andwet etching @Fig. 2~e!#.
D. Circuit Specification
Figure 3 shows a cross-sectional photograph of thefabricated waveguide. The core was 8-mm wide and
Fig. 2. Fabrication process of the TO phase shifter: ~a! spincoating of undercladding and core layer, ~b! formation of core ridgesby photolithography and O2 dry etching, ~c! spin coating of over-cladding to embed core ridges, ~d! covering of overcladding withUV-resin buffer layer, ~e! Cr thin-film heater formation byelectron-beam evaporation and wet etching.
20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 6829
7.5-mm high. The undercladding was 5.5-mm thick,and the total cladding thickness was 19 mm. TheUV-resin layer was 7-mm thick. The propagationloss of the waveguide was 0.7 and 3 dBycm for the TEand the TM polarization modes, respectively. Theselosses are higher than the value of 0.1 dBycm re-ported in Ref. 10, and the loss for the TM mode isnoticeably higher than that for the TE mode. Thesehigh losses are ascribed to a leak of optical power intothe Si substrate through the thin undercladding. Inour study we used a thinner undercladding than wasused in Ref. 10 in an attempt to obtain a shorterresponse time. This effort, however, led to higherlosses. We believe that these losses could be re-duced to 0.1 dBycm if a thicker undercladding were tobe used.
We fabricated the Cr thin-film heaters on bothwaveguide arms in the MZI. The heaters were1000-Å thick, 26-mm wide, and 4.8-mm long. Theresistance was 6.0 kV. This value is much largerthan the calculated value of 240 V from the resistiv-ity11 of Cr ~12.9 3 1028 V m! and the heater size. Wethink the high measured resistance is due to theinhomogeneity or porousness of the films, becausemicroscope observations revealed surface roughnessand many wrinkles. This is caused by thermal dam-age to the UV-resin buffer layer during Cr evapora-tion.
E. Measurement Setup
The test circuit was mounted on a temperature-controlled Peltier device for the measurements. ATE polarized light at 1.3 mm was coupled to the inputport through a polarizer and a polarization-maintaining fiber. Output lights from the through-port and crossport were detected with a photodiodethrough a conventional single-mode fiber. We ap-plied a functional electric voltage to one of the thin-film heaters and a dc-offset voltage to the other toremove any optical-path difference between the twoarms caused by fabrication errors.
F. Normal Response of Thermo-Optic Phase Shifter
We characterized the normal response of the TOphase shifter by applying a square-wave pulsed volt-age to one of the heaters. Figure 4 shows the pulseresponse when a 7.8-V ~10-mW! pulse was applied tocause a p phase shift. The pulse had a 20-ms width
Fig. 3. Cross-sectional photograph of the fabricated waveguide.
6830 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997
and a 25-Hz repetition rate, as shown in the bottomtrace. The upper and middle traces are the cross-port and throughport responses, respectively. Sincethe directional couplers are not 50% couplers, thethroughport output is not extinguished even when novoltage is applied ~f 5 0!. The response time is 4ms. The p phase-shift power is approximately dou-ble and the response time is approximately half thatin the TO switch reported in Ref. 9. This resultsfrom the fact that the cladding in the TO phaseshifter in our study was thinner than that in the TOswitch in Ref. 9.
G. Phase-Drift Phenomena
We observed a deformation of the response trace withtime t, as shown in Fig. 5. The initial response @Fig.5~a!, t 5 0 min# was turned over by a p phase driftafter 4 min @Fig. 5~b!, t 5 4 min# and finally reachedequilibrium @Fig. 5~c!, t 5 45 min#. The correspond-ing phase shift is shown in Fig. 5~d! as a function oftime t. Assuming that this drift phenomenon has anexponential time dependence of exp~2tytm! where tmis the time constant, Fig. 5~d! also shows an extrap-olated curve where tm 5 3 min.
To study this phase drift, we measured the long-term response by applying a step-index electric powerto the heater. The optical output from the crossportand the calculated phase shift are shown in Figs. 6~a!and 6~b!, respectively, when an electric power of 5.1mW was supplied for 15 min ~on-state! and then elim-inated ~off-state! @Fig. 6~c!#. Before the measure-ment no electric power was supplied to the heaters formore than 1 h. At the moment the electric powerwas applied to one of the heaters, the optical outputdecreased quickly. After that the output power con-tinued to decrease slowly and became constant in;10 min. When the electric power supply was cutoff, the optical output increased quickly and thenreturned to its initial value slowly over ;10 min. Itis clear that there are two components in the phase
Fig. 4. Pulse response of the TO phase shifter. The upper andmiddle traces are the crossport and the throughport responses,respectively. The bottom trace is for an applied electric powerwith a 20-ms pulse width and a 25-Hz repetition rate.
shift. The fast component is caused by the TO effect.The slow component has the same origin as the phasedrift in the pulse response shown in Fig. 5. Thisslow phase shift changes in the same direction as thefast one, and so it is caused by a slow decrease inrefractive index because the temperature-dependentindex is negative in the polymers.
Figure 7 shows the relationship between slowphase shift fs and time t. The vertical axis is rep-resented by 2ln~1 2 fsyfm! for the on-state and2ln~fsyfm! for the off-state, where fm is the maxi-mum value of fs. Both 2ln~1 2 fsyfm! and 2ln~fsyfm! are proportional to time, with rates of 0.38 and0.36 min21, respectively. These rates correspond totime constants of 2.6 and 2.8 min for the on and theoff states, respectively. The time constants are al-most the same as that of the phase drift in the pulse-response measurement @Fig. 5~d!#.
Fig. 5. Drift phenomenon measured in the crossport response ~a!at t 5 0 min ~initial state!, ~b! at t 5 4 min ~The response trace isturned over by a p phase drift.!, ~c! at t 5 45 min ~equilibriumstate!. ~d! Corresponding phase shift.
3. Influence of Moisture Sorption–Desorption
At first we suspected that the phase drift was causedby a further temperature increase in the waveguidethat was induced by heat accumulated in the Si sub-strate. But this assumption does not seem correct,because the Si substrate has a much higher thermalconductivity than the polymers and was controlled at25 °C by the Peltier device. The temperature in-crease in the Si substrate was therefore negligible.Furthermore, there has been no report on such aphase drift in silica-based TO switches whose struc-ture is almost the same as that of the polymer TOphase shifter.2 As a result we concluded that thephase drift originated from properties peculiar to ourwaveguide polymers.
Fig. 6. Step-index response of the TO phase shifter: ~a! outputpower change of the crossport, ~b! corresponding phase shift, ~c!applied electric power.
Fig. 7. Relationship between the slow phase shift and time forboth the on state and the off state. The vertical axis is repre-sented by 2ln~1 2 fsyfm! for the on state and 2ln~fsyfm! for theoff state.
20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 6831
Based on the above consideration, we assume thatthe phase drift resulted from a refractive-indexchange caused by an alteration in moisture in thewaveguide when the waveguide temperature waschanged. This assumption was inferred from thefact that PMMA, which has a structure similar to ourwaveguide polymers, sorbs moisture of ;2 wt%.12–15
Furthermore, our recent investigation has revealedthat our polymers sorb moisture of ;1 wt%, and theeffective refractive index of the waveguide is in-creased by moisture sorption.16 In this section wedemonstrate the humidity dependence of the phaseshift of the TO phase shifter. We also report themoisture sorption–desorption caused by a change inthe waveguide temperature by measuring the tem-perature and humidity dependence of OH-absorptionloss.
A. Setup for Humidity-Dependence Measurements
To measure the humidity dependence of the phaseshift, we placed the test circuit, the Peltier device,and the manipulators for the fiber-waveguide align-ments in a closed box. The relative humidity couldbe changed from 13% to 100% by adjusting the flow ofdry and humid air into the box. We monitored thehumidity with a ceramic sensor to an accuracy of63% RH ~relative humidity!. We performed themeasurements after the humidity in the box hadreached a steady state. This period is ;30 min andis longer than the period required by the slow phaseshift to reach equilibrium ~;10 min!. The temper-ature in the box was held at 25 6 1 °C.
B. Humidity Dependence of Phase Shift
Figure 8 shows phase shifts measured at 22%, 40%,and 66% RH when an electric power of 5.1 mW wassupplied to one heater for 15 min and then elimi-nated. It is seen that the slow phase becomes largeras the humidity becomes higher. The time con-stants are ;3 min at every humidity. An initialphase of 20.1p ~dashed line! is due to the path dif-ference between two waveguide arms caused by afabrication error. Figure 9 shows the equilibriumvalues of the fast and slow phase shifts as a function
Fig. 8. Phase shifts at 22, 40, and 66% RH when an electric powerof 5.1 mW was applied. The initial phase of 20.1p ~dashed line!is due to the path difference between two waveguide arms causedby a fabrication error.
6832 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997
of relative humidity. The fast phase shift is causedby the TO effect, so its equilibrium value is indepen-dent of humidity. On the other hand, the equilib-rium value of the slow phase shift increases withincreasing humidity.
Figure 10 shows the applied power dependence ofthe equilibrium values of the fast and slow phaseshifts measured at 63% RH. The equilibrium valueof the fast phase shift is proportional to the appliedpower because it is caused by the TO effect. More-over, the equilibrium value of the slow phase shift isalso proportional to the applied power.
C. Moisture Sorption
We studied the influence of humidity on thewaveguide polymers to learn more about the relation-ship between the slow phase shift and humidity.First we measured the moisture content sorbed in thewaveguide polymers as a function of relative humid-ity. The moisture content is defined as the fractionof the weight of the moisture sorbed in a polymer tothat of the polymer when it contains no moisture.We prepared the samples with the same configura-tion as the waveguide—that is, we prepared them byspin coating the polymers onto 4-in. Si wafers. Fig-ure 11 shows the humidity dependence of the mois-ture content in the waveguide polymers. The
Fig. 9. Humidity dependence of fast and slow phase shifts. Thesymbols indicate fast phase shifts for on-state ~E! and off-state ~F!and slow phase shifts for on-state ~h! and off-state ~■!.
Fig. 10. Applied power dependence of fast and slow phase shiftsmeasured at 63% RH. The symbols have the same meaning as inFig. 9.
moisture content of the core and the cladding poly-mers both increase almost linearly with increasinghumidity. The ratios of the increase for the core andthe cladding polymers are almost the same: 0.0097and 0.0095 wt %y% RH, respectively.
We also found that the humidity affected thewaveguide loss at 1.41 mm, as shown in Fig. 12. Inthis measurement we used a waveguide with athicker cladding than the TO phase shifter to obtaina low propagation loss. The peak at 1.41 mm, whichis caused by the second overtone of the O–H stretch-ing vibration of water, increases proportionally withhumidity. The ratio of the increase with humidity is0.037 dBy~cm % RH!. Using the results shown inFigs. 11 and 12, we can estimate the change in themoisture content in the waveguide from the changein the absorption peak at 1.41 mm. A loss change of1 dBycm at 1.41 mm corresponds to a moisture-content change of 0.26 wt% in the core. Further-more, note that the loss value at 1.41 mm alsochanged with a change in humidity even when thewaveguide was covered with the UV resin used in theTO phase shifter. This result suggests that the UV-resin buffer layer is not moisture-proof.
D. Effect of Temperature Change
To discover the effect of waveguide temperaturechange on moisture content, we measured the tem-perature dependence of the OH-absorption loss at
Fig. 11. Humidity dependence of moisture content in waveguidepolymers. Circles and squares represent the moisture content forthe core and cladding polymers, respectively.
Fig. 12. Loss spectrum change caused by a change in relativehumidity. The peak at 1.41 mm is caused by moisture sorbed inthe waveguide.
1.41 mm. The waveguide was heated by a Peltierdevice, whereas the air temperature was constant.We used this method to simulate the situation whensupplying electric power to a thin-film heater at roomtemperature, except that the temperature of thewaveguide heated by the Peltier device is assumed tobe uniform.
Figures 13~a!, 13~b!, and 13~c! show loss spectrumchanges measured at 13%, 40%, and 70% RH, respec-tively. The OH peak at 1.41 mm decreases as thewaveguide temperature increases at every humidity,and the peak change is greater at a higher humidity.These results mean that the moisture in thewaveguide is released into the air when thewaveguide is heated, and the amount is larger at ahigher humidity. We believe that this moisture de-sorption is caused by a decrease in relative humiditynear the waveguide owing to the waveguide temper-ature increase. This assumption can also explainthe fact that the OH-peak loss decreases more at ahigher humidity, since a change in relative humiditycaused by a temperature change is greater at a higherrelative humidity. We also believe that the sameinterpretation can be applied to the slow phase shiftin the TO phase shifter—that is, the slow phase shiftis induced by the moisture desorption owing to a
Fig. 13. Loss spectrum change caused by a change in waveguidetemperature at ~a! 13% RH, ~b! 40% RH, ~c! 70% RH.
20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 6833
decrease in relative humidity when the waveguide isheated.
To investigate the effect of the waveguide temper-ature change in detail, it is necessary to measure theloss spectra for different air temperatures at thesame relative humidity and to estimate the temper-ature dependence of the moisture solubility in thewaveguide polymers. We think, however, that suchtemperature dependence is negligible in ourwaveguide polymers, because it is reported that thewater sorption of PMMA13,14 and of plastic opticalfiber with a PMMA-d8 core17 depends only on relativehumidity not on temperature.
E. Mechanism of the Phase Drift
From the experimental results described above, themechanism of the phase drift or slow phase shift forthe on-state can be explained as follows. When elec-tric power is supplied to a thin-film heater, thewaveguide temperature increases, and then the re-fractive index of the waveguide polymers decreases.This causes a fast or normal phase shift. Simulta-neously, the temperature increase induces a decreasein relative humidity close to the waveguide surface.As a result moisture in the waveguide is released intothe air, and its concentration decreases. This re-sults in a further decrease in the refractive index ofthe waveguide polymers, and, finally, a slow phaseshift or phase drift occurs. The slow phase shift thatoccurs when the electric power to the heater isswitched off can be explained in a similar way.
4. Discussion
In this section we provide additional evidence for thephase-drift mechanism described above. We ex-plain the relationships that exist among the humid-ity, the waveguide temperature, the moisturesorption–desorption, and the refractive-index changethat we estimated from calculated and experimentalresults.
A. Temperature and Moisture Content
First we characterize the change in the moisture con-tent caused by a change in the waveguide tempera-ture. From the result shown in Fig. 11, moisturecontent m can be expressed approximately by m 5SHa, where S is a coefficient that is connected withthe solubility of moisture in the polymer and Ha is therelative humidity of the surrounding atmosphere.When there is a temperature difference between theatmosphere and the waveguide, the moisture contentat a waveguide temperature Tw is expressed by
m 5 SHa@ps~Ta!yps~Tw!#, (2)
where Ta is the atmospheric temperature and ps~T! isthe saturation vapor pressure at a temperature T.When the waveguide temperature is changed fromTw to Tw9, the moisture content is changed to thevalue m9 expressed by
m9 5 m@ps~Tw!yps~Tw9!#, (3)
6834 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997
where we assume that the coefficient S is indepen-dent of temperature, as described in the previoussection. Using Eq. ~3! and the relationship betweenthe water content and the OH-peak loss described inSubsection 3.C, we can explain well the change inOH-peak loss caused by a change in waveguide tem-perature. The rectangles, triangles, and circles inFig. 14 represent OH-peak losses at 13%, 40%, and70% RH, respectively, obtained from Fig. 13. Thecurves can be extrapolated by use of Eq. ~3!, the tem-perature dependence of the saturation vapor pres-sure of water,18 and a constant loss of 0.4 dBycm thatis independent of the moisture sorption.
B. Refractive Index and Moisture ContentyConcentration
Although we did not directly measure the moisture-dependent refractive index of the waveguide poly-mers, we can estimate it from a Lorentz–Lorenzformula,
n2 2 1n2 1 2
5 Skm 1kp
mDCm, (4)
where n is the refractive index and km and kp are themolar refractions divided by the molecular weight ofwater and the polymer, respectively. Moisture con-centration Cm is defined by the ratio of moisture massto the volume of the polymer including moisture andis given by
Cm 5mrp
1 1 f ~mrpyrm!, (5)
where rp is the density of the polymer without mois-ture, rm is the water density, and f ~0 # f # 1! is thefraction of sorbed moisture that contributes to anincrease in polymer volume.15 We calculated a kmvalue of 0.2006 cm3yg by using a water index of 1.324at a wavelength of 1.3 mm ~Ref. 19! and a waterdensity of 0.9997 gycm3 at 25 °C.20 We estimatedother parameters by measuring the density and therefractive index of the polymers at a certain humid-ity. The density and the refractive index of the corepolymer were 1.27 gycm3 at 50% RH ~m ' 0.48 wt. %!and 1.484 at 30% RH ~m ' 0.29 wt. %!, respectively,
Fig. 14. Waveguide temperature dependence of OH-peak lossmeasured at 13 ~squares!, 40 ~triangles!, and 70% RH ~circles!,obtained from Fig. 13. We calculated the curves by using Eq. ~3!.
and those of the cladding polymer were 1.28 gycm3 at50% RH ~m ' 0.47 wt. %! and 1.480 at 30% RH ~m '0.28 wt. %!, respectively. Using these values, weobtained the relationships between n and m, includ-ing an unknown factor of f. They are expressed ap-proximately by
n 5 ~20.0071f 1 0.0050!~m 2 0.29!
1 1.484 for the core polymer, (6.1)
n 5 ~20.0072f 1 0.0051!~m 2 0.28!
1 1.480 for the cladding polymer, (6.2)
where m is in units of weight percent. We also ob-tained the relationship between n and Cm:
n 5 ~20.0057f 1 0.0040!~Cm 2 0.37!
1 1.484 for the core polymer, (6.3)
n 5 ~20.0056f 1 0.0040!~Cm 2 0.36!
1 1.480 for the cladding polymer, (6.4)
where Cm is in units of grams per cubic centimeter.Using f 5 0.5, which is a typical value for PMMA14,15;we obtained 0.0014 wt%21 as the ratio of the indexchange to the moisture-content change and 0.0011cm3yg as the ratio of the index change to themoisture-concentration change for both polymers.
C. Temperature Distribution
Here we show the calculated temperature distribu-tion that is essential for understanding the moisturedesorption by heating. The sizes of the waveguideand the heater we used for the calculation are thesame as those in the fabricated TO phase shifter.We assumed that the core polymer, cladding polymer,and UV-resin buffer layer all have the same thermalconductivity as PMMA ~0.17 W m21 °C21!.3 In ad-dition, we assumed that the Si substrate and the airare completely conductive and adiabatic, respec-tively. Figure 15 shows the calculated temperaturedistribution in the equilibrium state when an electric
Fig. 15. Calculated temperature distribution in the equilibriumstate when an electric power of 5.1 mW was applied to a thin-filmheater.
power of 5.1 mW is applied to a thin-film heater.The waveguide surface temperature is ;29 °C, justbelow the middle of the heater when the substrateand air are at 25 °C. This temperature increase atthe upper surface of the waveguide induces the mois-ture desorption.
The temperature increase at the core center is1.0 °C. The corresponding phase shift is 0.74p,where we used a temperature-dependent index of21.0 3 1024 °C21.16 This phase shift is a littlehigher than the experimental value of 0.5p shown inFig. 9. This is ascribed to the assumption we madefor the calculation.
D. Moisture Concentration and Slow Phase Shift
Using the calculated temperature distribution at theupper surface of the waveguide in Fig. 15, we esti-mated a moisture concentration in the waveguideand the slow phase shift caused by the moisture de-sorption during the on-state. Since the measuredtime constant for the slow phase shift ~;3 min! ismuch larger than that for the fast one ~;4 ms!, themoisture-desorption process begins after the temper-ature change reaches equilibrium. The moisture isreleased into the air through the heated surface, andthe moisture concentration in the waveguide can beobtained by a two-dimensional diffusion equation,
~]Cm!y~]t! 5 ¹~D¹Cm!, (7.1)
where D is the moisture diffusion coefficient in thepolymer. To simplify the problem, we adopt the fol-lowing assumptions: ~1! The UV-resin buffer layerhas the same characteristics as the cladding becauseit is not particularly moisture-proof, as described inSubsection 3.C. ~2! The core polymer also has thesame characteristics as the cladding polymer, be-cause it exhibits almost the same moisture-sorptioncharacteristics, as shown in Fig. 11. ~3! The thin-film heater is permeable by moisture because itseems porous, as described in Subsection 2.D. Fur-thermore, we ignored such values as the dependenceof the D coefficient on temperature or moisture con-centration, the surface temperature change causedby the heat of desorption, and the volume changewhen the moisture is desorbed, because they are allsmall. Using the cross section of the TO phaseshifter shown in Fig. 1~b!, we give the following initialand boundary conditions:
Cm 5 C0, t 5 0,
Cm 5 C0, x 5 6`,
Cm 5 Cs~x!, y 5 d,
]Cmy]y 5 0, y 5 0, (7.2)
where C0 is the moisture concentration before heat-ing and Cs~x! is the moisture concentration at theupper surface of the waveguide. This Cs~x! value isgiven by the waveguide temperature distributionshown in Fig. 15 and Eqs. ~3! and ~5!.
Figure 16 shows the moisture distribution in the
20 September 1997 y Vol. 36, No. 27 y APPLIED OPTICS 6835
equilibrium state when an electric power of 5.1 mWwas supplied to the heater at 66% RH. We appliedD 5 1.17 3 10212 m2ys for PMMA14 to the core,cladding, and UV-resin buffer layer. The moistureconcentration at the core was reduced to 0.70 gycm3
from an initial value of 0.81 gycm3 by moisture de-sorption through the waveguide surface. Thischange corresponds to a core index change of 0.00012.
Finally, we show in Fig. 17 the calculated slowphase shifts at 22%, 40%, and 66% RH. The slowphase shifts increase with time and are finally satu-rated. The time constants are all 3.4 min, and theequilibrium phase shifts are 0.30p, 0.55p, and 0.90pat 22%, 40%, and 66% RH, respectively. These val-ues are almost the same as those measured for thefabricated TO phase shifter.
5. Conclusion
We have described a drift phenomenon or slowphase shift in a waveguide TO phase shifter com-posed of deuterated methacrylate and FMA poly-mers. The phase drift had a time constant of ;3min, and its equilibrium value was larger at higherrelative humidity. We observed this drift when anelectric power supply was switched both on and off.We have also reported that the waveguide polymers
Fig. 16. Calculated moisture distribution at the equilibrium statewhen an electric power of 5.1 mW was applied to a thin-film heaterat 66% RH.
Fig. 17. Calculated phase drift ~slow phase shift! owing to mois-ture desorption by heating when an electric power of 5.1 mW wasapplied to a thin-film heater at 22, 40, and 66% RH.
6836 APPLIED OPTICS y Vol. 36, No. 27 y 20 September 1997
sorbed moisture at a rate of ;0.01 wt. %y% RH, andthe sorbed moisture caused an OH-absorption lossat a wavelength of 1.41 mm. Using the OH-peakloss, we found that the moisture in the waveguidedecreased with increasing waveguide temperatureand that this change was greater at higher relativehumidity. From these results we have concludedthat the phase drift was caused by moisturedesorption–sorption in the waveguide by heating–cooling.
Although we have reported a moisture-inducedphase drift in a polymer waveguide TO phase shifter,this problem is thought to be peculiar to polymerssuch as PMMA, which sorbs as much as ;1 wt. % ofmoisture. Therefore the drift phenomenon can beavoided by use of water-proof packaging during mod-ule fabrication and is not observed in polymers withlittle moisture sorption, such as fluorinated polyim-ide and silicone.
We thank T. Izawa, M. Kawachi, Y. Ohmori, and H.Kozawaguchi for their encouragement throughoutthis study. We also thank H. Nakagome and R. Yo-shimura for useful discussions.
References1. H. Nishihara, M. Haruna, and T. Suhara, “Thermooptic
waveguide devices,” in Optical Integrated Circuits ~McGraw–Hill, New York, 1989!, pp. 325–330.
2. A. Sugita, K. Jinguji, N. Takato, K. Katoh, and M. Kawachi,“Bridge-suspended silica-waveguide thermo-optic phaseshifter and its application to Mach–Zehnder type opticalswitch,” Trans. IEICE E73, 105–109 ~1990!.
3. M. B. J. Diemeer, J. J. Brons, and E. S. Trommel, “Polymericoptical waveguide switch using the thermooptic effect,” J.Lightwave Technol. 7, 449–453 ~1989!.
4. B. L. Booth, “Low loss channel waveguides in polymers,” J.Lightwave Technol. 7, 1445–1453 ~1989!.
5. M. J. McFarland, K. W. Beeson, K. A. Horn, A. Nahata, C. Wu,and J. T. Yardley, “Polymeric optical waveguides for deviceapplications,” in Integrated Optical Circuits, K. Wong, ed.,Proc. SPIE 1583, 344–354 ~1991!.
6. F. M. M. Suyten, M. B. J. Diemeer, and B. Hendriksen. “Adigital thermo-optic 2 3 2 switch based on nonlinear opticpolymer,” in Nonlinear Optical Properties of Organic Mate-rials VI, G. R. Moehlmann, ed., Proc. SPIE 2025, 479–487~1993!.
7. G. F. Lipscomb, R. Lytel, W. Horsthuis, and M. KleinKoerkamp, “Packaged thermo-optic polymer 1 3 2 switch,” inOptical Fiber Communication, Vol. 2 of 1995 OSA TechnicalDigest Series ~Optical Society of America, Washington, D.C.,1995!, pp. 221–222.
8. N. Keil, H. H. Yao, C. Zawadzki, and B. Strebel, “Rearrange-able nonblocking polymer waveguide thermo-optic 4 3 4switching matrix with low power consumption at 1.55 mm,”Electron. Lett. 31, 403–404 ~1995!.
9. Y. Hida, K. Onose, and S. Imamura, “Polymer waveguide ther-mooptic switch with low electric power consumption at 1.3mm,” Photon. Technol. Lett. 5, 782–784 ~1993!.
10. S. Imamura, R. Yoshimura, and T. Izawa, “Polymer channelwaveguides with low loss at 1.3 mm,” Electron. Lett. 27, 1342–1343 ~1991!.
11. J. Babiskin and J. R. Anderson, “Properties of metals,” in
American Institute of Physics Handbook, 3rd ed., D. E. Gray,ed., ~McGraw–Hill, New York, 1972!, Sec. 9d.
12. J. A. Barrie, “Water in polymers,” in Diffusion in Polymers, J.Crank and G. S. Park, eds. ~Academic, London, 1968!, Chap. 8,pp. 259–313.
13. A. M. Thomas, “Moisture permeability, diffusion, and sorption inorganic film-forming materials,” J. Appl. Chem. 1, 141–158 ~1951!.
14. K. Kawasaki and Y. Sekita, “Sorption and diffusion of watervapor in polymethyl methacrylate,” Jpn. J. Appl. Phys. 26,678–680 ~1957!.
15. D. T. Turner, “Polymethyl methacrylate plus water: sorptionkinetics and volumetric changes,” Polymer 23, 197–202 ~1982!.
16. Y. Hida and S. Imamura, “Influence of temperature and hu-midity change on optical waveguide circuits composed of deu-
2
terated and fluorinated methacrylate polymers,” Jpn. J. Appl.Phys. 34, 6416–6422 ~1995!.
17. T. Kaino, “Influence of water absorption on plastic optical fi-bers,” Appl. Opt. 24, 4192–4195 ~1985!.
18. E. W. Washburn, “The vapor pressures of ice and water up to100 °C,” in International Critical Tables of Numerical Data,Physics, Chemistry, and Technology, E. W. Washburn, ed.~McGraw–Hill, New York, 1928! Vol. 3, p. 210.
19. K. F. Palmer and D. Williams, “Optical properties of water inthe near infrared,” J. Opt. Soc. Am. 64, 1107–1110 ~1974!.
20. V. Stott and P. H. Bigg, “Density and specific volume of water,”in International Critical Tables of Numerical Data, Physics,Chemistry, and Technology, E. W. Washburn, ed. ~McGraw–Hill, New York, 1928! Vol. 3, p. 24.
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