A detailed theoretical and experimental study of the depth dependence of buried ion-exchanged waveguides on waveguide width is reported. Modeling, which includes the effect of nonhomogeneous time-dependent electric field distribution, agrees well with our experiments showing that burial depth increases linearly with waveguide width. These results may be used in the proper design of integrated optical circuits that need waveguides of different widths at different sections, such as arrayed waveguide gratings

Geraghty, David F.

Honkanen, Seppo

Madasamy, P.

Morrell, Michael M.

Peyghambarian, Nassar

West, Brian R.

English

Scholars Commons

Buried Ion-Exchanged Glass Wavelengths: Burial-Depth Dependence on Waveguide Width

Wilfrid Laurier University

Wilfrid Laurier University Scholars Commons @ Laurier Physics and Computer Science Faculty Publications Physics and Computer Science 2003 Buried Ion-Exchanged Glass Wavelengths: Burial-Depth Dependence on Waveguide Width P. Madasamy University of Arizona Brian R. West Wilfrid Laurier University, bwest@wlu.ca Michael M. Morrell Unviersity of Arizona David F. Geraghty Unviersity of Arizona Seppo Honkanen University of Arizona See next page for additional authors Follow this and additional works at: https://scholars.wlu.ca/phys_faculty Recommended Citation Madasamy, P.; West, Brian R.; Morrell, Michael M.; Geraghty, David F.; Honkanen, Seppo; and Peyghambarian, Nassar, "Buried Ion-Exchanged Glass Wavelengths: Burial-Depth Dependence on Waveguide Width" (2003). Physics and Computer Science Faculty Publications. 94. https://scholars.wlu.ca/phys_faculty/94 This Article is brought to you for free and open access by the Physics and Computer Science at Scholars Commons @ Laurier. It has been accepted for inclusion in Physics and Computer Science Faculty Publications by an authorized administrator of Scholars Commons @ Laurier. For more information, please contact scholarscommons@wlu.ca. Authors P. Madasamy, Brian R. West, Michael M. Morrell, David F. Geraghty, Seppo Honkanen, and Nassar Peyghambarian This article is available at Scholars Commons @ Laurier: https://scholars.wlu.ca/phys_faculty/94 1132 OPTICS LETTERS / Vol. 28, No. 13 / July 1, 2003Buried ion-exchanged glass waveguides: burial-depthdependence on waveguide widthP. Madasamy, B. R. West, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. PeyghambarianOptical Sciences Center, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85721Received January 27, 2003A detailed theoretical and experimental study of the depth dependence of buried ion-exchanged waveguideson waveguide width is reported. Modeling, which includes the effect of nonhomogeneous time-dependentelectric field distribution, agrees well with our experiments showing that burial depth increases linearly withwaveguide width. These results may be used in the proper design of integrated optical circuits that needwaveguides of different widths at different sections, such as arrayed waveguide gratings. © 2003 OpticalSociety of AmericaOCIS codes: 130.0130, 230.7390, 290.1990, 000.4430.Buried silver-ion-exchanged glass waveguides areused extensively in integrated optical devices foroptical communications because they feature very lowloss, are well matched with single-mode fibers, andcan have negligible birefringence.1 – 3 These buriedchannel waveguides are fabricated by first perform-ing a thermal silver-ion exchange through a maskpatterned on the glass surface. At the surface silverions are exchanged for sodium ions, and the refractiveindex is locally increased. The resulting surfacechannel waveguides are then buried by an electric-field-assisted, unmasked ion exchange. In this stepthe silver ions migrate deeper into the glass, and thewaveguides are buried below the glass surface.In many cases it is necessary to use waveguidesof different widths in different sections of an inte-grated optical circuit. Good examples of such devicesare arrayed waveguide gratings4 and devices basedon multimode interference.5 If these devices arefabricated with buried ion-exchanged waveguides, sig-nificant losses are expected due to vertical waveguidemisalignment at the junction between two waveguideswith different widths. It has been suggested6 thatthe burial depth would be different for a channelwaveguide and a slab waveguide with no lateralconfinement.In this Letter we report on a detailed study of thedependence of the burial depth on the initial mask-opening width in the case of buried silver-ion-exchanged glass waveguides. We first present theresults of our theoretical modeling, which takes intoaccount the nonhomogeneous time-dependent electricfield distribution in glass during the burial process.Then we describe a simple technique that we de-veloped to accurately measure the burial depths offabricated waveguides. The experimental resultsare in good agreement with our modeling, and weshow that the burial depth increases with increasingwaveguide width. This behavior is explained by thedifferent mobilities of silver and sodium ions in theglass used in the experiments.A binary ion exchange, such as Ag1-Na1 exchange,involves a system with two kinds of monovalent ions:indiffusing ions (A) and outdiffusing ions (B) in theglass substrate. There are two types of force thatdrive the exchange of ions. One is due to the concen-tration gradient of ions (diffusion) and the other isdue to the drift of ions resulting from the electric f ieldin the glass during the exchange. The electric f ieldcan be an externally applied f ield or an internalfield built by the local charge imbalances caused bythe difference in mobilities of the exchanging ions.The development of concentration distribution intime can be given by7≠CA≠tDA1 aCA∑=2CA 1a=CA21 aCAeEext=CAkT∏.(1)The first two terms result from the concentration gra-dient of ions and the internal f ield due to the local dis-tribution of ions with different mobilities, respectively.The third term results from the external applied elec-tric field. Here CA  cAco is the normalized concen-tration of A ions, where cA is the ionic concentration ofA ions and co is the total ionic concentration. DA andDB are the self-diffusion coefficients of A ions and Bions, respectively, and a  1 DADB is a measure ofthe difference in ion mobilities. DA1 aCA is theinterdiffusion coeff icient, which for small values of M(the ratio between the self-diffusion coefficient of twoions, DADB ) is strongly concentration dependent.To solve Eq. (1), usually a time-independent cur-rent with homogeneous conductivity in the glass isassumed. However, it has been reported8,9 that the in-homogeneity of the conductivity due to the exchangedions perturbs the f ield and results in variations in theconcentration profile. Since these variations canaffect the burial depth of a waveguide mode and theeffect of field perturbations will be slightly differentfor different mask-opening widths, the inhomogeneityin conductivity has to be taken into account in themodeling. We follow the approach of Ref. 8 to obtainthe nonhomogeneous field distribution. The fieldhas to be evaluated for each time step and insertedinto Eq. (1), which is then solved by the Peaceman–Rachford alternating direction implicit method.0146-9592/03/131132-03$15.00/0 © 2003 Optical Society of AmericaJuly 1, 2003 / Vol. 28, No. 13 / OPTICS LETTERS 1133In our calculations we use the diffusion parametersand refractive indices estimated for 3-in. BGG31 glasssubstrates (1 in.  2.54 cm). These values were ob-tained from slab waveguide and prism-coupling experi-ments.10 To study the burial-depth dependence onthe mask-opening width, the same process parameterswere used to simulate eight buried waveguides withdifferent mask-opening widths during the first step,ranging from 2 to 9 mm. The estimated self-diffusioncoeff icient of silver ions is 13 10 15 m2s at T  553 Kand 3.5 3 10 16 m2s at T  523 K. The value ofM for the glass is 0.2. The first step, thermal ionexchange, is done for 4500 s at T  553 K. Thesecond step, field-assisted burial, is done for 2400 s atT  523 K with an applied voltage of U  3.2 V acrossthe 20-mm-thick substrate. The small values usedfor voltage and thickness correspond to the values of320 V and 2 mm used in the experiment. Note thata small value for the thickness of the glass is used toreduce the number of points in the calculation; themodeling results would not be different if we used alarger substrate thickness and correspondingly largervoltages.We define the burial depth of the waveguidein terms of the mode profile since that is morerelevant in practical applications. The mode pro-file of the waveguide was solved by the scalarfinite-difference method, with a substrate index of1.4525 at 1.55 mm and a maximum index changeof 0.03. Figure 1 gives the concentration and in-tensity profiles of waveguides with 3- and 9-mmmask-opening widths. The electric f ield lines shownwith the concentration profiles clearly demonstratethat the field lines deviate from the homogeneous case.For comparison with the experiments done using afiber, we take a convolution of the waveguide modeprofile and a Gaussian function approximating thefiber mode. The distance from the surface of the glassto the peak of the convolution is defined as the burialdepth of the waveguide. The results of the burial-depth modeling as a function of mask-opening widthare given in Fig. 2. The error bars are a result of thefinite grid spacing. For M  0.2 the burial depthincreases linearly with the mask-opening width. Thisbehavior can be explained from the strong concentra-tion dependence of the interdiffusion coeff icient forsmall values of M , which affects the drift velocityof the peak concentration of waveguides during theburial step. It should be noted that even though thediffusion depth in terms of concentration changeswith the mask-opening width after the f irst step,as has been similarly observed in other studies,11 – 13the waveguide depth in terms of the mode profiledoes not change with the mask-opening width. Thisdifference in diffusion depths does not inf luence theburial depths, as can be seen from the case for M  1,where there is no concentration dependence on theinterdiffusion coefficient, and there is no differencein burial depth for different mask openings. Whenwaveguides formed from different mask-openingwidths are buried, the concentration values of thenarrower waveguides become smaller faster since thegradient in the transverse direction is larger for nar-rower waveguides. The interdiffusion coeff icient islarger for higher concentrations, and hence the widerwaveguides become buried deeper than the narrowerwaveguides. The results for M  0.5 and M  1 arealso plotted in Fig. 2. The concentration dependenceof the interdiffusion coefficient is stronger for smallerM and disappears for M  1. Hence the slope of thevariation in burial depth is larger for M  0.2 thanfor M  0.5, and there is no variation in burial depthfor M  1.To experimentally investigate burial-depth de-pendence on waveguide width, we fabricated buriedwaveguides in BGG31 glass and used parameters simi-lar to those used in modeling. Mask widths rangingfrom 2 to 9 mm were patterned onto the sample. Thefirst step, thermal ion exchange, was performed in a50:50 AgNO3NaNO3 melt at T  553 K for 4500 s.The second step, unmasked field-assisted burial,was done at T  523 K for 2400 s, with an appliedFig. 1. Concentration profile with the electric field linesat the end of the burial process for the 3- and 9-mm wave-guides are given in the top row with the 3-mm waveguideon the left and the 9-mm waveguide on the right. The con-tours for the concentration profile represent the relativesilver-ion concentration and go as 0.1, 0.2, . . . , 0.4 for the3-mm waveguide and 0.1, 0.2, . . . , 0.5 for the 9-mm wave-guide. The corresponding intensity prof iles solved by thefinite-difference method are given below the concentrationprofiles. The contour lines for the intensity profile go as0.1, 0.3, . . . , 0.9 of the normalized intensity.Fig. 2. Burial-depth variation as a function of mask-opening width. The solid line corresponds to the linear f itfor the experimental data, and the dashed lines correspondto the linear fit for the modeled data.1134 OPTICS LETTERS / Vol. 28, No. 13 / July 1, 2003Fig. 3. Experimental setup for measuring burial depthbased on the Newport AutoAlign System.voltage of 320 V across a 2-mm substrate thickness.Taking advantage of the high accuracy of the NewportAutoAlign system, we developed a simple procedurefor measuring the burial depth.14 The data weretaken with a resolution of 0.1 mm. The measurementconsists of two steps: one is to f ind the center of themode, and the other is to find the surface of the glassrelative to the center of the mode. The setup usedto f ind the center of the mode is given in Fig. 3(a).The input fiber from a 1550-nm superluminescentdiode source and the output f iber to the optical powermeter are butt coupled to the waveguide, and thethroughput is maximized. Then the output f iber isscanned in the vertical y direction, and the centerof the profile gives the center of the mode ( y0). Tofind the surface of the glass the input fiber is movedabout 1 mm from it, as shown in Fig. 3(b). Thisforms a Lloyd’s mirror interferometerlike setup withinterference fringes formed because of the direct lightfrom the input f iber and the ref lected light fromthe glass surface. The intensity in the y directionin the observation plane is I  4I0 sin2paysl fory . 0, where y  0 corresponds to the surface. Theinterference fringe has a minimum at the surface ofthe glass, and there are no fringes below the surface.In the setup in Fig. 3(b) scanning the output fiberin the y direction from the center of the mode givesthe fringes, and the first minimum gives the surfacepoint. The difference between the surface point andthe center of the mode gives the burial depth for thewaveguide. The experimental results are plottedin Fig. 2. The results agree well with the modelingresults for M  0.2.In conclusion, we studied the variations in burialdepths of modes in ion-exchanged glass waveguides fordifferent mask-opening widths. We did an accuratemodeling, including the effect of nonhomogeneous elec-tric f ield distribution in glass, and found the burialdepths to vary linearly as a function of mask-openingwidth. We developed a simple setup to measurethe burial depth and measured them in a samplefabricated with parameters similar to those used inthe modeling. The experimental results were foundto agree well with the modeling. The difference inburial depths arises largely from the concentrationdependence of the interdiffusion coefficient whenM (the ratio of self-diffusion coefficients DA andDB ) is less than 1. This behavior of ion-exchangedglass waveguides must be taken into account whendesigning integrated optical circuits. The loss atthe intersection of a narrow and a wide waveguidecan be eliminated by adding a proper taper at theintersection. Also, as seen from the modeling results,the difference in burial depths becomes negligible forvalues of M close to 1. Therefore the use of glass withM close to 1 will eliminate the difference in burialdepths caused by different mask-opening widths.We acknowledge support from the Center for Opto-electronic Devices, Interconnects, and Packaging andthe Technology and Research Initiative Fund. P.Madasamy’s e-mail address is pmadasamy@optics.arizona.edu.References1. S. Honkanen, Proc. SPIE 53, 159 (1994).2. Y. Jaouen, L. du-Mouza, D. Barbier, J. M. Delavaux,and P. Bruno, IEEE Photon. Technol. Lett. 11, 1105(1999).3. D. F. Geraghty, D. Provenzano, M. M. Morrell, S.Honkanen, A. Yariv, and N. Peyghambarian, Electron.Lett. 37, 829 (2001).4. K. Okamoto, M. Moriwaki, and S. Suzuki, Electron.Lett. 31, 184 (1995).5. L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen,I. Moerman, and M. K. Smit, IEEE Photon. Technol.Lett. 6, 1008 (1994).6. B. Buchold and E. Voges, Electron. Lett. 32, 2249(1996).7. J. Albert and J. W. Y. Lit, Appl. Opt. 29, 2798 (1990).8. D. Cheng, J. Saarinen, H. Saarikoski, and A. Tervonen,Opt. Commun. 137, 233 (1997).9. Jerome Hazart and V. Minier, IEEE J. Quantum Elec-tron. 37, 606 (2001).10. R. G. Walker, C. D. W. Wilkinson, and J. A. H.Wilkinson, Appl. Opt. 22, 1923 (1983).11. R. V. Ramaswamy and R. Srivastava, J. LightwaveTechnol. 6, 984 (1988).12. M. N. Weiss and R. Srivastava, Appl. Opt. 34, 455(1995).13. L. Palchetti, E. Giorgetti, D. Grando, and S. Sottini,IEEE J. Quantum Electron. 34, 179 (1998).14. P. Madasamy, M. M. Morrell, D. F. Geraghty, S.Honkanen, and N. Peyghambarian, in TechnicalDigest: Symposium on Optical Fiber Measurements,2002, P. A. Williams and G. W. Day, eds. (NationalInstitute for Standards and Technology, Boulder,Colo., 2002), pp. 25–28.

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Buried Ion-Exchanged Glass Wavelengths: Burial-Depth Dependence on Waveguide Width

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