JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 4, APRIL 2002 751

Fabrication Tolerance Study of a Compact PassivePolarization Rotator

N. Somasiri, B. M. A. Rahman, Senior Member, IEEE, and S. S. A. Obayya, Associate Member, IEEE

Abstract—In this paper, the expected performance of a compactlow-loss passive polarization rotator is reported by using rigorousnumerical approaches. The effects of waveguide width, slant angle,etch depth, and refractive index variations during its fabrication onthe overall polarization conversion and polarization crosstalk arereported. It is also expected that over the 1.53- to 1.61- m wave-length range, polarization conversion would be more than 99% andpolarization crosstalk would be better than 20 dB.

Index Terms—Finite element method, optical waveguides, pho-tonic devices, polarization rotators.

I. INTRODUCTION

POLARIZATION rotators are essential elements in opto-electronic integrated circuits, which are used to control

the polarization states. They can be used in polarization con-trollers [1] to compensate polarization mode dispersion, in po-larization modulators [2] to avoid polarization hole burning intransoceanic fiber links, in polarization switches [3] for polar-ization division multiplexing, or in polarization diversity hetero-dyne receivers to provide constant 45 operation. In semicon-ductor optoelectronic systems, hybrid optical modes are able toconvert power between the polarization states if the modes arenearly phase matched and have an enhanced overlap. However,in order to obtain this conversion, some means of discontinuityshould exist along the propagation direction, such as junctions,tapers, or bends.

Recent literature shows that there has been great interestin the design of polarization rotators. Polarization rotationin optical systems can be achieved by the electrooptic effectemployed in LiNbO [4] or semiconductor material [5]. How-ever, simple passive polarization rotators are relatively easy tofabricate, quite useful, and satisfactory in many applications[6]–[11]. In early designs, these were fabricated by using anumber of uniform waveguide sections butt coupled to eachother in order to transfer power from a pure transverse electric(TE) to transverse magnetic (TM) mode. Asymmetric loadedsection converters [6], [11] and the asymmetric facet anglewaveguide section converters [10] have also been reportedwith a good polarization conversion ratio and low losses.More recent work [12] shows a significantly more compact400- m-long polarization rotator design with five facet anglesections and a total insertion loss of 0.2 dB.

However, because of the difficulty in fabricating these peri-odic section rotators and the additional losses due to the number

Manuscript received November 21, 2001.The authors are with the City University, London EC1V 0HB, U.K. (e-mail:

B.M.A.Rahman@city.ac.uk).Publisher Item Identifier S 0733-8724(02)03345-5.

of junctions, a single-section polarization rotator would be muchpreferred [13], [14]. Therefore, in this paper, a detailed study tooptimize a single-stage slanted waveguide polarization rotatorin InP–InGaAsP along with the key fabrication tolerances arepresented.

II. THEORY

In the design of a polarization rotator (PR) waveguide, it isnecessary to increase the magnitude of the nondominant fieldcomponents of the fundamental quasi-TE and -TM modes, andthe field profiles of the two dominant modes should be modi-fied in order to enhance the overlap between them. In order toobtain the vectorial field profiles and the propagation constantsfor the TE and TM modes, in the PR waveguide, a full vecto-rial modal solution approach is mandatory. In this study, we useone of the most accurate and efficient vector H-field finite el-ement formulation (VFEM) [15] to carry out the simulations.Because the two propagation constants for the TE- and TM-po-larized modes show a difference, there exists a phase mismatch.In order to obtain maximum polarization rotation, the length ofthe PR waveguide should be exactly equal to the half-beat length

of the two polarized modes; if complete conversion has notbeen achieved, then reversing the phase mismatch will be neces-sary. At that length, as a result of the constructive interference,a complete polarization rotation can be achieved if two hybridmodes are polarized with 45 . The half-beat length is givenby

where and are the propagation constants for the funda-mental TE and TM modes, respectively, or vice versa.

In this study, a single-stage polarization rotator is considered,consisting of two semiconductor rib waveguides with straightside walls, both butt coupled to a polarization rotator waveguidewith a slanted side wall in the middle, as shown in Fig. 1(a).This particular PR waveguide should be designed in such a waythat it supports highly hybrid modes, giving similar and

components. In a standard semiconductor rib waveguide,the dominant field profile of the quasi-TE modes shows asymmetric behavior and the nondominant field shows anasymmetric behavior with a very small field magnitude, as de-scribed in [14]. When a nearly pure TE polarized input field islaunched from a standard rib waveguide to the PR waveguide,two highly hybrid TE and TM modes will be excited in the PRwaveguide. As these two modes propagate along the slantedrib waveguide, at exactly , they become out of phase and

0733-8724/02$17.00 © 2002 IEEE

752 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 4, APRIL 2002

(a)

(b)

Fig. 1. (a) Schematic diagram of the polarization rotator. (b) Cross section ofthe PR waveguide with a slanted wall.

result in a nearly pure TM polarized wave; at this position, itcan be collected by a standard output waveguide (OW). Thiswaveguide, like the input guide, supports nearly pure TE andTM modes. Similarly, if a TM-polarized wave is incident onthe PR waveguide, nearly pure TE-polarized wave can be col-lected by the output waveguide. However, in order to calculatethe modal coefficients at the discontinuity junction, a rigorousjunction analysis approach, the least squares boundary residual(LSBR) method [16], has been employed. The evolution of con-verted power along the propagation direction of the rotator andthe crosstalk at has also been obtained. Here, the crosstalkcan be defined as the unwanted oppositely polarized power, nor-malized to the total input power, which remains at the end ofthe PR waveguide. For example, if a TE-polarized power isincident, then most of the power will be converted into TM-po-larized power at the end of the PR section, although theremight be some amount of power remaining. This particular

, which is normalized to the total input power, is referred toas the crosstalk, in this example.

In this paper, some important characteristics of a single-stageslanted polarization rotator are presented. The effects of ribwidth, slant angle, index difference, and height of the guideand the operating wavelength on the device length and, moreparticularly, on the conversion ratio and crosstalk, have beeninvestigated. Finally, a more clear understanding of the PRwaveguide behavior was obtained when fabrication tolerancewas introduced on each PR waveguide parameter. Section III inthis paper gives all of the simulation results obtained, followedby concluding remarks in Section IV.

III. SIMULATION RESULTS

The cross section of the slanted sidewall semiconductor ribwaveguide considered for evaluation is shown in Fig. 1(b). Theheight of the InP cap layer is fixed at 0.5 m. The height ofthe InGaAsP (1.08 Q) layer grown on InP substrate is 1.3 m.

Fig. 2. Variation of the field component ratios and half-beat length � withthe waveguide width � .

The refractive indexes of InP and InGaAsP are taken as 3.17and 3.27, respectively, at an operating wavelength of 1.55 m.All of the other parameter values of the waveguide are given inFig. 1(b).

The optical modes in a semiconductor waveguide are hybridin nature. For the fundamental quasi-TE mode, theand field components are the dominant field components,and and field components are the dominant field com-ponents of the fundamental quasi-TM mode. However,unlike the normal semiconductor rib waveguide with verticalside walls, the rib waveguide with slanted side wall is capablefor an enhanced field hybridism by destroying symmetry of thestructure. In this study, the H-field based VFEM is used to ob-tain the modal solution of such uniform waveguides.

First, the effect of the waveguide width, , on the modal hy-bridism is evaluated. Fig. 2 shows the variation of the nondomi-nant–dominant field ratios for both and modes, and thehalf-beat length with waveguide width . It can be seen thatwhen is reduced from 1.5 to 1.15 m, the hybridism of themodes is increased. At exactly 1.15- m width, the hybridismreaches its maximum value of nearly one, which indicates thatboth of the transverse field components are almost equal. It hasalso been shown [14] that the hybrid nature of the modes in-creases with the reduction of the waveguide width. However,it is also shown that hybridism not only can reach unity valuebut when is reduced further, in this case, below 1.15 m,the hybridism reduces; to the best of our knowledge, this fea-ture has not yet been reported. TM mode also follows a sim-ilar behavior and the maximum hybridism occurs at

m. However, the hybrid nature of the TM mode isslightly higher than that of the TE mode for a given waveguidewidth.

The half-beat length is an important parameter when de-signing polarization rotators because that is the converter lengththat must reverse the polarization state from one to the other.From Fig. 2, it can be seen that, in this case, reduces asreduces, and at the maximum hybrid position, is equal to403 m. Therefore, in this study, the optimum device lengthfor maximum polarization rotation is considered as 403 m.

SOMASIRI et al.: FABRICATION TOLERANCE OF COMPACT PASSIVE POLARIZATION ROTATOR 753

Fig. 3. Variation of the excited � and � coefficients with waveguidewidth � for input TE polarization.

The waveguide considered here remains single moded untilm and a waveguide wider than that supports higher

order modes.Once the optimum modal hybridism was identified, then the

butt coupling of the input waveguide, which consists of straightside walls and the PR waveguide, was considered because themode conversion can only be expected to happen at waveguidediscontinuities. Here, the junction of the two waveguides wasanalyzed by using the rigorous LSBR method [16]. For theinput waveguide, the rib width is taken as the lower width ofthe slanted PR waveguide and no transverse offset between thewaveguides has been considered in this study. The junctionof the input and PR sections is shown as an inset in Fig. 3.When the TE mode with very small hybridism from the inputguide is incident on the PR section, it excites two highly hybridmodes. The modal coefficients and were obtained byemploying the LSBR method. Here, and are the trans-mission coefficients for TE- and TM-polarized fundamentalmodes respectively. The variation of these two parameters withthe PR rib width is shown in Fig. 3. It can be seen that at

m, is 0.76 and as is reduced, it reachesa minimum value of 0.65 at m. On the otherhand, at m, is 0.55 and it reaches a maximumvalue of 0.66 at m. Around m, thereexist two highly hybrid modes, but the usual definition ofquasi-TE and quasi-TM modes are not useful because both ofthe transverse components are almost equal. At m,the insertion loss at the junction interface is calculated to be0.64 dB. If 0.3- m offset between two uniform sections can beintroduced, then insertion loss would reduce further; however,the fabrication process involved may make the junction lessabrupt, and numerical simulation with lateral offset has notbeen attempted here. If we considered to be m,then modal hybridism would be very small and the wouldreach 1.0 asymptotically and the value would be nearlyzero.

In order to understand how the width of the waveguide affectsthe TE-to-TM power conversion, several power transfer curvesfor different values of were obtained, as shown in Fig. 4.

Fig. 4. Evolution of converted � power along the axial direction of the PRwaveguide for different waveguide widths when TE mode is the incident wave.

Here, the evolution of power was computed from the full vecto-rial modal fields of the two hybrid modes and their propagationconstants, which were obtained from VFEM simulations and thetwo modal coefficients obtained from the LSBR method. Be-cause the input field is nearly pure TE, initially, at the start ofthe PR waveguide, i.e., , the –polarized power isnearly equal to one, and –polarized power is nearly zero.As the excited modes propagate along the PR waveguide sec-tion, slowly the two modes become out of phase, increases,and decreases (which is not shown here), and at a distance

, the half-beat length from the discontinuity along the direc-tion of propagation , nearly pure TM-polarized power can becollected. It can be clearly seen that, for m, thepower reaches a maximum value of 0.998 at m,which is the corresponding value, and then is gradu-ally reduced as the distance deviates further away from the .Therefore, in this case, the length of the single-stage polariza-tion converter should be 403 m. It can be observed, from Fig. 4,if m, then the maximum values at thesepoints will be 0.994 and 0.991, respectively. Therefore, whenfabricating the polarization rotator, 20 m axial tolerance willonly result in an additional loss smaller than 0.1 dB. However,when m, the TM polarized power reaches a max-imum value of 0.983 at a distance m from the discon-tinuity junction. Therefore, when the width of the waveguideis increased to 1.3 m, not only the power transfer is low (dueto a slightly lower hybridism), but also the device length willbe much longer. Similarly, for m, the reachesits maximum value of 0.963 at m. This slightly re-duced power conversion is a result of the poor hybridism of themodes at shorter widths, as shown in Fig. 2. However, it shouldbe noted that, in this case, device length would be much shorter.It can also be noted that if the device length is fixed at 403 mand the width of the PR section deviates from the optimum de-sign during the fabrication process, then the converted powerwill be reduced to 0.910 and 0.301 for and m,respectively.

Hence, when fabricating polarization rotator waveguides, itis important to consider the tolerances and their effect on the

754 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 4, APRIL 2002

Fig. 5. Variation of the converted power � and the crosstalk at � � � and� � ��� �m, with the waveguide width � .

PR behavior. To study the fabrication tolerances of the devicelength, the power conversion and the corresponding crosstalkat specified positions along have been considered for variouswaveguide widths, as shown in Fig. 5. Here, the crosstalk is theunwanted TE polarized power remains at the end of the PRsection. In the numerical simulations, the width has been variedfrom 0.8 to 1.5 m and the optimum device length was fixedat 403 m, because this length corresponds to the ideal designcondition to obtain maximum power conversion. The convertedTM power at their corresponding values increases from0.963 to the maximum value of 0.998, when the width increasesfrom 0.8 to 1.15 m and then gradually decreases up to 0.909with further increase of the width to 1.5 m. This trend ofcan be explained by incorporating the variation of hybridism ofthe modes with the width, which was shown in Fig. 2. Becausethe hybridism increases with the width up to 1.15 m and de-creases as width increases, a similar sort of trend for the powerconversion can be expected because the hybrid nature is directlyrelated to the polarization rotation. It can be seen that if the de-vice is fabricated with a device length of 403 m, then as thewidth varies, power will be very much lower than that atexact . However, at m, the matches withthe exact fabricated device length, therefore giving highest con-version and also lowest crosstalk of 0.00128, which is equal to

28.9 dB. The crosstalk at the specified device length increasesup to 0.698 as reduces to 0.8 m and at m, and thecrosstalk is about 0.32. At the designed device length of 403 m,for a width tolerance of 1.15 0.05 m, converted TM powerwill only show an additional loss of less than 0.05 dB and thecrosstalk value will deteriorate to 20 dB. However, if, duringfabrication, the width of the uniform sections can be controlledwithin 1.15 0.1 m, then the loss would be about 0.3 dBand the crosstalk will deteriorate further at 12 dB.

The effects of the other waveguide parameters, such as angle, the refractive index difference between the guide and the

substrate , and the height were considered to understandtheir effects and to obtain optimized parameter values to achievebetter polarization conversion. First, the variation of the slantangle was considered for evaluation. The nondominant–dom-inant field ratios for both TE and TM modes and the half-beat

Fig. 6. Variation of the field component ratios and half-beat length � withthe slant angle �.

Fig. 7. Variation of the converted power � and the crosstalk at � � � and� � ��� �m with the slant angle �.

length variation with are shown in Fig. 6. Here, the widthof the waveguide was 1.15 m because that width gives the max-imum hybridism and all of the other parameter values were fixedat , m, and m. As the facetangle increases from 48 to 52 , the hybridism increases andit achieves a maximum value at and further increase in

will result in a reduction of hybridism. The half-beat lengthshows a reduction from 420 to 379 m throughout the range ofangles considered. Next, TE-to-TM power conversion and thecrosstalk were investigated varying from 48 to 56 . The con-verted TM power and crosstalk for both at exact and atthe designed device length 403 m are shown in Fig. 7. Bothcurves show a similar kind of trend with a maximum valueof 0.998 at . Because the hybridism is maximum at

, which is shown in Fig. 6, maximum power conversionshould also be expected to happen at 52 . Because is variedaway from 52 , the at m is always lower than the

at , due to the mismatch. However, here, the differencebetween at exact and the output at m, issmaller than that for width variation, as shown in Fig. 5, becauseboth and hybridism were less sensitive with . It can be seenthat, at , the crosstalk is minimum at 28.9 dB. When

SOMASIRI et al.: FABRICATION TOLERANCE OF COMPACT PASSIVE POLARIZATION ROTATOR 755

Fig. 8. Variation of the field component ratios and half-beat length � withthe refractive index difference ��.

fabricating the device, for a tolerance of 52 2 , the powerat the designed length will reduce by 0.05 dB and the crosstalkwill be always better than 19 dB.

The effect of refractive index difference between the guideand the substrate on the hybridism and the device length wasthe next parameter to be considered. Fig. 8 shows the variationof the hybridism for both modes and the half-beat length,with refractive index difference, . In this study, the otherparameters were kept constant at, m, ,

m, and the operating wavelength was kept constantat 1.55 m. It can be seen that the field ratios increase withup to , and reduce when is increased further.reduces from 411 to 393 m as increases and, at the designvalue of 0.1, it shows the maximum hybridism and here theis 403 m. It can be noted that the percentage change in andhybridism is much smaller. In order to investigate the tolerancein index difference over the polarization rotation, converted TMpower , when TE is incident, at and mand the crosstalk were obtained within the range of 0.08 to0.14 as shown in Fig. 9. It can be seen that the maximum powerconversion occurs at with a low crosstalk of about

28.9 dB. However, the two curves are almost similar andthere is hardly any difference between them fromand . This is mostly due to the small difference in

values, i.e., only 2 from the optimized value 403 m,as shown in Fig. 8. For a tolerance of , thepower at designed device length will show less than 0.01-dB ad-ditional loss and a crosstalk value better than 26 dB.

The behavior of the hybridism and the device length werestudied, when the height of the guiding layer, is varied. Asshown in Fig. 10, the height, is varied from 0.8 to 1.25 m.The hybridism decreases as decreases and, at m, itbecomes as low as 0.72. decreases from 480 to 399 m asincreases. At m, shows a percentage difference ofabout 19% from the designed value of 403 m. Because thevariation with is quite large, the converted power at exact

and at the designed length show a very large difference asreduces to 0.8 m, which is clearly seen in Fig. 11. Therefore,at m, the TM power at exact m is0.883 and the power at the designed device length is 0.829.

Fig. 9. Variation of the converted power � and the crosstalk at � � � and� � ��� �m with the refractive index difference ��.

Fig. 10. Variation of the field component ratios and half-beat length � withthe height �.

Fig. 11. Variation of the converted power � and the crosstalk at � � � and� � ��� �m with the height �.

Similarly the crosstalk reaches a higher value of 9.34 dB and7.67 dB at and m, respectively. During

fabrication, when the device length is fixed at 403 m, a change

756 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 4, APRIL 2002

Fig. 12. Variation of the field component ratios and half-beat length � withthe operating wavelength �.

Fig. 13. Variation of the converted power � and the crosstalk at � � � and� � ��� �m with the operating wavelength �.

of m and m will show aloss of 0.0005 dB and 0.01 dB, respectively, and crosstalks of

28.6 dB and 23 dB, respectively.Finally, the polarization rotator behavior, when the operating

wavelength varies from 1.53 to 1.61 m, was investigated.Here, when obtaining the modal solutions for different oper-ating wavelength values, refractive index of the guide, i.e.,n(InGaAsP), has been modified accordingly to include materialdispersion for a given quaternary material at 1.08 Q. Fig. 12shows the variation of the hybridism and with the operatingwavelength, . The hybridism decreases with the increase in

. However, it can be noted that the field ratio difference overthe range of is considerably smaller, giving a value of about0.07. Half-beat length also decreases as increases, givinga minimum of 381.72 m at m. powerand crosstalk curves for different wavelengths are shown inFig. 13. at exact reduces from 0.998 to 0.995 asincreases, because the hybridism reduces as shown in Fig. 12.However, this 0.003 difference hardly affects the behavior ofthe polarization rotator. at m also does not showmuch deviation from the curve at exact , becauseonly shows a change of 30 m along the whole wavelength

range considered. At m, the crosstalk forand m are 23.3 dB and 19.2 dB, respectively. Fora tolerance of m at the designed length of403 m, loss is about 0.006 dB and the crosstalk is about

26 dB.

IV. CONCLUSION

A single-section compact polarization rotator design incorpo-rating a slanted sidewall waveguide in InP has been presented.Numerical simulations based on a rigorous and very efficientvectorial finite element approach have been carried out to an-alyze the polarization rotator waveguide. An optimized designof a polarization rotator waveguide with overall 403- m lengthand a low 0.6-dB insertion loss has been achieved. In this case,99.8% polarization rotation can be achieved, which is one ofthe highest reported so far, with a very low crosstalk value of

29 dB.In this paper, it has also been demonstrated that the critical

fabrication tolerance on each waveguide parameter and the oper-ating wavelength. The simulated results show that there is hardlyany effect on the polarization rotator behavior with the variationof the slant angle , index difference , and height . Whenfabricating the device, the most critical parameter to consideris the waveguide width . It has been shown that, for a guidewidth tolerance of 1.15 0.1 m, the converted power will bereduced by 0.3 dB from the optimum value, and the crosstalkwill be increased up to 12 dB. It has also been shown that thedevice performance is reasonably stable with the variation of theoperating wavelength .

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N. Somasiri, photograph and biography not available at the time of publication.

B. M. A. Rahman (S’80–M’82–SM’93), photograph and biography not avail-able at the time of publication.

S. S. A. Obayya (S’99–A’00), photograph and biography not available at thetime of publication.