Ion-exchanged glass waveguides with lowbirefringence for a broad range of waveguide widths

Sanna Yliniemi, Brian R. West, and Seppo Honkanen

Optical communications networks require integrated photonic components with negligible polarizationdependence, which typically means that the waveguides must feature very low birefringence. Recentstudies have shown that waveguides with low birefringence can be obtained, e.g., by use of silica-on-silicon waveguides or buried ion-exchanged glass waveguides. However, many integrated photonic cir-cuits consist of waveguides with varying widths. Therefore low birefringence is consequently required forwaveguides having different widths. This is a difficult task for most waveguide fabrication technologies.We present experimental results on waveguide birefringence for buried silver–sodium ion-exchangedglass waveguides. We show that the waveguide birefringence of the order of 10�6 for waveguide maskopening widths ranging from 2 to 10 �m can be obtained by postprocessing the sample through annealingat an elevated temperature. The measured values are in agreement with the values calculated with ourmodeling software for ion-exchanged glass waveguides. This unique feature of ion-exchanged waveguidesmay be of significant importance in a wide variety of integrated photonic circuits requiring polarization-independent operation. © 2005 Optical Society of America

OCIS codes: 130.0130, 230.7380, 260.1440.

1. Introduction

Efficient optical routing is a key requirement to meetthe increasing demand for higher system transmis-sion capacities in optical communications networks.Dense wavelength division multiplexing is the lead-ing technology used in optical routing. This technol-ogy is implemented with various integrated opticalcomponents including add–drop filters and phased-array wavelength multiplexers and demultiplexers.Planar waveguides used in these components need tofeature efficient coupling with fiber, low propagationloss, and negligible birefringence. The first two re-quirements are obvious from a power consumptionpoint of view; the last requirement results from thefact that the single-mode optical fiber used in long-haul transmission systems is not polarization main-taining. Therefore polarization insensitivity inconnecting waveguide components is a crucial re-quirement to be fulfilled to avoid polarization-dependent performance. However, this is not a

simple task since, unlike fibers, waveguides typicallylack cylindrical symmetry, increasing form birefrin-gence. In addition, waveguide fabrication processesinduce stresses resulting in birefringence, which isdifficult to eliminate.

Several approaches to reduce or compensate forbirefringence have been suggested in connection withthe leading waveguide technology, silica-on-silicon.These include stress reduction by etching strain-relieving grooves on both sides of the waveguide1,2 orby growing additional material layers on top of thewaveguide.3,4 Albert et al.5 showed that waveguidebirefringence can be reduced by trimming thewaveguide by UV illumination. A similar approachwith CO2 laser ablation was suggested by Canningand Åslund.6 Integration of birefringence-compensating devices into the chip has also beendemonstrated.7 The major drawback common in allthese methods is that they require additional process-ing steps and therefore increase the complexity of thedevice fabrication.

In this paper we study birefringence properties ofburied Ag�–Na� ion-exchanged glass waveguides,the other widely employed glass waveguide technol-ogy. Special emphasis is put on the effect ofwaveguide width on waveguide birefringence, whichis of crucial importance in some devices.8 This tech-nology was chosen since glass waveguides fabricated

The authors are with the Optical Sciences Center, University ofArizona, Meinel Building, 1630 East University Boulevard, Tuc-son, Arizona 85721. The e-mail address for S. Yliniemi issyliniemi@optics.arizona.edu.

Received 3 August 2004; accepted 13 October 2004.0003-6935/05/163358-06$15.00/0© 2005 Optical Society of America

3358 APPLIED OPTICS � Vol. 44, No. 16 � 1 June 2005

by ion exchange feature good mode matching withoptical fibers, low propagation loss, and low birefrin-gence in general.9–13 The processing of ion-exchangedwaveguides is simple, and they can be easily inte-grated with other passive or active waveguide com-ponents on glass substrates. We demonstrate thatlow birefringence, of the order of 10�5 or below, canbe obtained in buried Ag�–Na� ion-exchangedwaveguides for a wide range of waveguide widths.This is in contrast to silica-on-silicon waveguides forwhich low birefringence is attainable only for a ratherlimited range of waveguide widths.14 To further re-duce waveguide birefringence we utilize the featurethat, in Ag�–Na� ion-exchanged waveguides, thestress-induced birefringence can be fully compen-sated by matching the form birefringence throughthermal annealing. The effect of thermal annealingon waveguide birefringence is studied by annealingand characterizing the sample in steps. In Section 2we describe the ion exchange modeling. In Section 3we present the ion exchange and burial processes forwaveguide fabrication and the annealing process forbirefringence reduction. In Section 4 we describe thecharacterization of the waveguides, and in Section 5we present the results and discussion. Finally in Sec-tion 6 we provide a brief conclusion of our results.

2. Modeling

Waveguide birefringence is a sum of form and stress-induced birefringence. In buried silver–sodium ion-exchanged waveguides, birefringence from these twosources has opposite signs. Form birefringence favorsgreater effective refractive index for the quasi-TEmode because the index profile has wider lateral di-mensions. This is in contrast to the stress-inducedbirefringence that favors typically greater effectiverefractive index for the quasi-TM mode. This is due tothe proximity of the glass–air interface that makes itpossible for the glass to expand slightly in the direc-tion normal to the surface, thus relaxing the stressesand induced index increase in that direction. By ad-justing the form and stress-induced birefringence,zero-birefringence waveguides can be created.

In ion exchange the ions participating in the pro-cess have different electronic polarizabilities and dif-ferent ionic radii and therefore produce a usefulrefractive-index change between the substrate andthe exchanged area.15 The differing ionic radii alsoproduce stress that is closely related to the birefrin-gence formation because the thermal expansion ex-perienced by the ion-exchanged glass region and thesubstrate are different.16 In Ag�–Na� exchange, com-pressive stress is produced as the sample cools downsince the ionic radius of the silver ion is larger thanthe ionic radius of the sodium ion. The refractiveindices for quasi-TE and quasi-TM modes depend onthe stress components �x, �y, and �z in the followingway16:

nTE � n0 � C1�y � C2(�x � �z), (1)

nTM � n0 � C1�x � C2(�y � �z), (2)

where n0 is the refractive index without stress, and C1and C2 are the elasto-optical coefficients �C2 � C1�.The x, y, and z directions are defined as in Fig. 1.Since diffusion has a greater extension in the y direc-tion than in the x direction and since the waveguidecan slightly expand along the normal to the surface,the stress component in the x direction is smallerthan in the y direction ��x � �y�.16 It can be thereforeconcluded from Eqs. (1) and (2) that compressivestress favors a larger value for nTM. Exact values forelasto-optical coefficients and stress components inBGG31 glass used in this study are not known, andthe measurement of these constants is an elaborateprocess. Therefore Eqs. (1) and (2) are shown only toqualitatively explain the stress-induced index changein ion-exchanged waveguides, but it is not included inour waveguide modeling.

Modeling of the ion exchange process involves solv-ing for the time evolution of normalized Ag� concen-tration CAg,

�CAg

�t �DAg

1 � (1 � M)CAg�2CAg �

(1 � M)(CAg)2

1 � (1 � M)CAg

�qEext · CAg

kT �, (3)

and is described in detail in Ref. 17. Here, DAg and DNaare the self-diffusion coefficients of silver and sodiumions, respectively, and M � DAg�DNa is their ratio. Eextis the applied electric field and T, k, and q are theabsolute temperature, Boltzmann constant, and theelectron charge, respectively. When M differs fromunity, Eext is nonhomogeneous in the vicinity of thewaveguide and must be determined numerically.

Equation (3) is solved numerically by thePeaceman–Rachford alternating direction implicitmethod,18 which combines efficiency and stabilityover a wide range of processing parameters. After theprocess has been modeled, a semivectorial finite-difference method19 is employed to determine the ef-fective indices of the guided modes. Note thatwaveguide stress is not accounted for in our model.

3. Fabrication

Waveguides with mask opening widths from 2 to10 �m were constructed in BGG31 glass by Ag�–Na�

ion exchange. Surface channel waveguides fabricatedin this way were then buried below the glass surfaceto reduce propagation losses and to obtain circularwaveguides matching well with the fibers. Burial also

Fig. 1. Mode intensity profiles for waveguides with mask openingwidths of (a) 2 �m, (b) 7 �m, and (c) for a single-mode fiber.

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significantly reduces the birefringence by reshapingthe index profile.

The process starts with 200nm-thick titaniumlayer deposition followed by standard lithography.The titanium layer is used as a diffusion mask duringthe thermal ion exchange. Ion exchange was per-formed in a 1:1 AgNO3:NaNo3 melt at T � 280 °C for4500 s. After the ion exchange, the titanium maskwas etched away and the waveguides were buried byfield-assisted burial. The burial was done for 2400 sat T � 250 °C with an applied voltage of U� 320 V across a 2mm-thick substrate. Further de-tails of the process have been described in Ref. 20.With these process parameters, waveguides are bur-ied 5.7–6.8 �m deep in the glass substrate dependingon the mask opening width. Mode intensity profiles ofthe waveguides for two mask opening widths fabri-cated by Ag�–Na� ion exchange are presented in Fig.1. The mode intensity profile for a single-mode fiber isshown as a comparison. The waveguide mode profilesare almost circular and slightly smaller than thesingle-mode fiber mode intensity profile as can beseen from Fig. 1. Further reduction of birefringencecan be obtained through annealing at an elevatedtemperature.

4. Characterization

We determined the waveguide birefringence usingthe difference interferometer approach described inRef. 21. A schematic of the setup is depicted in Fig. 2.First, a linear polarizer at a 45° angle with respect tothe horizontal axis launches orthogonal TE and TMmodes with equal amplitudes into the waveguide.Within the waveguide a phase shift �� between theTE and the TM modes is accumulated:

�� �2

�0(nTE � nTM)L, (4)

where nTE and nTM are the effective refractive indicesof the TE and TM modes, L is the length of the sam-ple, and �0 is the free-space wavelength ��0� 1550 nm�.

After the beam emerges from the output end of thewaveguide, the half-wave plate rotates the polariza-tion state by twice the azimuthal angle. The intensi-ties both in the horizontal and in the verticaldirections are detected with an InGaAs detector.Next, a quarter-wave plate producing a phase shift of �2 between the TE and the TM modes is added tothe setup, and the horizontal and vertical intensitiesare once again measured. The setup also consists ofan infrared camera that is used to check that thelaser power is coupled to the mode under study. Bi-refringence values are extracted from the four inten-sities measured by Jones matrix algebra forpolarization states.22 Details of the procedure arepresented in Appendix A. Since the method describedin Appendix A makes no difference between 2 mul-tiples, the sample was diced into two pieces withlengths of one third and two thirds of the originalsample. Birefringence of both pieces was measured,and the sum birefringence was observed to be equalto the birefringence of the full length sample guaran-teeing that no 2 multiples were included in the orig-inal result.

5. Results

Waveguides with mask opening widths of 2 and 3 �mwere observed to be purely single mode at 1550 nm.Waveguides with mask openings above 3 �m weremultimode but it was still possible to couple lightmainly to the fundamental mode except for thewaveguide made with a 10�m mask opening. Wemeasured propagation losses to be below 0.15 dB forall mask opening widths using the method describedin Ref. 23.

The results of the measured and modeled birefrin-gence as a function of a mask opening width arepresented in Fig. 3. The measured birefringence isvery low, of the order of 10�5 or below, for all maskopening widths. The accuracy of the measurementwas estimated to be 1 � 10�6. Birefringence increaseslinearly as a function of a mask opening width. Thisresults from the fact that the waveguide index profilein wider waveguides is more elliptical, increasing theform birefringence, while the stress-induced birefrin-gence has much smaller dependence on thewaveguide width. The modeled birefringence valuesexhibit the linearly increasing trend as well as a func-tion of a mask opening width. However, the modeledvalues are slightly higher since the effect of the stressis not included in our model.

The ellipticity of the waveguide index profile can besignificantly reduced by thermal annealing. Duringthe annealing, silver ions further diffuse and the in-dex profile becomes more symmetric. The more thesample is annealed, the smaller the form birefrin-gence becomes, and the more dominant the stress-induced birefringence becomes. Since stress-induced

Fig. 2. Measurement setup used to determine the waveguide bi-refringence of channel waveguides. Linearly polarized light at �0

� 1550 nm is coupled to the sample with a 20� objective. After thebeam emerges from the sample it travels through a 20� objective,a ��2 plate at an angle of 22.5°, and a rotatable analyzer to theInGaAs detector. The setup also includes a movable ��4 plate at anangle of 45°. All angles are presented with respect to the horizontalaxis.

3360 APPLIED OPTICS � Vol. 44, No. 16 � 1 June 2005

birefringence favors a larger value for nTM, birefrin-gence eventually changes the sign after annealinglong enough.

We studied the effect of thermal annealing by plac-ing the sample into the oven at 250 °C first for 15 minand then for three successive 30min durations. Bi-refringence was measured after each annealing step.The results are depicted in Fig. 4. After 45-min an-nealing, birefringence for waveguides with maskopening widths below 4 �m is already negative. Also,birefringence for wider waveguides has reduced sig-nificantly. By further annealing, birefringence for allthe waveguides becomes negative and it starts tosaturate to the stress-induced value. It can be con-cluded that for each waveguide there is a point atwhich the form and stress-induced birefringence can-cel each other and zero net birefringence is produced.

The above experiments suggest that, by annealingthe sample long enough, the form birefringence even-

tually disappears and all that is left is the stress-induced birefringence. Annealing has only a minoreffect on the stress-induced birefringence. Because ofthe nature of the diffusion process, the form birefrin-gence is expected to release according to the functiony�t� � a exp�bt2� � c, where a, b, and c are the fittingparameters to be found. To study this statement, thebirefringence values obtained after each annealingstep were fitted to this function for different maskopening widths. Gaussian fits for the narrowest andthe widest waveguide widths are shown in Fig. 5.

The saturation values for birefringence are de-picted in Fig. 6. Birefringence has a Gaussian decayfor all waveguides and saturates between �4.1� 10�6 and �0.38 � 10�6 depending on the maskopening width. The results presented in Fig. 6 sug-gest that stress-induced birefringence is more pro-nounced for waveguides with narrower lateraldimensions, but the dependence on the waveguidewidth is not as strong as in the case of form birefrin-

Fig. 3. Measured birefringence �nTE � nTM� after burial (crosses)and the corresponding modeled values (diamonds).

Fig. 4. Birefringence �nTE � nTM� before annealing (crosses) andafter annealing at 250 °C for 15 min (open circles), 45 min (dia-monds), 75 min (squares), and 105 min (filled circles).

Fig. 5. Exponential fit for birefringence as a function of annealingtime for mask opening widths (a) 2 �m and (b) 10 �m.

Fig. 6. Saturated birefringence values obtained from the expo-nential fitting procedure for different mask opening widths.

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gence. However, it is possible that the widerwaveguides have not yet reached their saturationvalues and further annealing would reduce the de-pendence on waveguide width even more. Small de-viations from the linear dependence can be observedfor the waveguides with mask opening widths of 6and 8 �m. For these two waveguides the saturationvalue is lower than the one predicted by the generaltrend by approximately 1 � 10�6. Both of thewaveguides are multimode, and it is possible thatlight was not coupled optimally to the fundamentalmode during measurements. The uncertainty in thefitting procedure is therefore relatively large due tothe accumulated inaccuracy in the subsequent mea-surements. The fitting procedure would have beenmore accurate if a shorter annealing step had beenused. This was limited by the stability of the anneal-ing oven. Temperature fluctuations in the beginningof each annealing step become more and more pro-nounced for shorter annealing steps.

6. Conclusions

We have demonstrated very low ��10�6� waveguidebirefringence in ion-exchanged glass waveguides formask opening widths from 2 to 10 �m. To our knowl-edge, this is the first time that low birefringence hasbeen presented for such a wide range of waveguidewidths. In silica-on-silicon waveguides low birefrin-gence is achieved only for rather restricted

waveguide widths.14 Also the birefringence in silica-on-silicon waveguides is usually higher, typically ofthe order of 10�5.24,25 This birefringence is low enoughfor most dense wavelength division multiplexingcomponents, but in many sensor applications bire-fringence should be even lower, of the order of10�7.11,12 In our study, waveguides above a 3�mmask opening width are multimode. This is usuallyan unfavorable state of matters, but in some appli-cations, like in an add–drop filter presented in Ref. 8,multimode waveguides with low birefringence arespecifically needed. The observed birefringence is aresult of form and stress-induced birefringence. Wewere able to reduce significantly the form birefrin-gence by annealing the sample. In addition, it wasshown that zero-birefringence waveguides can be cre-ated by properly choosing the annealing time. Lowbirefringence and the consequential minimalpolarization-dependent loss are favorable features inmany dense wavelength division multiplexing com-ponents.

Appendix A: Birefringence Characterization

We extract the retardance angle ��, as defined in Eq.(4), from the data utilizing Jones matrix algebra.22

The polarization state of the incident beam enteringthe sample is

Ein � �Exin

Eyin�� �I0

2 �11�, (A1)

where Ex, yin are the electric field amplitudes along the

x and y directions and I0 is the total intensity of thefield. The polarization state after the sample and thebare half-wave plate can be presented by the electricfield

E1out � J��2JsEin. (A2)

The polarization state after the sample, half-waveplate, and quarter-wave plate is

E2out � J��4J��2JsEin. (A3)

In Eqs. (A2) and (A3), J��2, J��4, and Js are the Jonesmatrices corresponding to the half-wave plate, thequarter-wave plate, and the sample, respectively.The Jones matrix can be represented in a generalform as

where � is the azimuthal angle of the correspondingpolarization element and � is the phase differencecaused by the element. The azimuthal angle and thephase retardance for the half- and quarter-waveplates and for the sample are shown in Table 1.

With Eqs. (A2)–(A4), the values for the four inten-sities at the detector can be presented as

I1x � E1xoutE1x

out* � I0�2�1 � cos(��), (A5)

I1y � E1youtE1y

out* � I0�2�1 � cos(��), (A6)

I2x � E2xoutE2x

out* � I0�2�1 � sin(��), (A7)

I2y � E2youtE2y

out* � I0�2�1 � sin(��). (A8)

From these intensities the value for the phase retar-dance can be derived as

�� � arctan�(I1y � I1x)(I2y � I2x)(I1y � I1x)(I2y � I2x)�. (A9)

Ji(�, �) �exp��i(��2)cos2 � � exp�i(��2)sin2 � �i sin��

2�sin(2�)

�i sin��

2�sin(2�) exp��i(��2)sin2 � � exp�i(��2)cos2 � , (A4)

3362 APPLIED OPTICS � Vol. 44, No. 16 � 1 June 2005

The value for birefringence, defined as nTE � nTM, canbe calculated from Eqs. (4) and (A9).

We thank Mike Morrell and Jason Auxier for theirhelp with measurements. Support from the Technol-ogy and Research Initiative Funding (State of Ari-zona Photonics Initiative) is appreciated. S. Yliniemialso thanks the Academy of Finland and MagnusEhrnrooth’s foundation for financial support.

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Table 1. Azimuthal Angle and Phase Shift used in Eq. (A4) for Half- andQuarter-Wave Plates and the Sample

Element � �

��2 plate 22.5° ���4 plate 45° �2Sample 0° ��

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