Control of optical mode properties in cross-slot waveguides

Control of optical mode propertiesin cross-slot waveguides

Amit Khanna,* Antti Säynätjoki, Ari Tervonen, and Seppo HonkanenPhotonics Group, Department of Micro and Nanosciences, Helsinki University of Technology,

Micronova, Tietotie 3, FI- 02015 Espoo, Finland

*Corresponding author: [email protected]

Received 10 August 2009; revised 27 October 2009; accepted 30 October 2009;posted 4 November 2009 (Doc. ID 115463); published 20 November 2009

A cross-slot waveguide geometry provides high confinement of the mode field of both fundamentalquasi-TE and quasi-TMmodes in geometrically perpendicular slots. A unique possibility to tailor opticalmode characteristics such as effective index and confinement factor quite independently for the two po-larizations with geometric and material parameters is shown. Nonbirefringent cross-slot geometries arepresented. Fabrication related tolerances of the cross-slot geometry for low birefringence operation arestudied. Means to externally tune the birefringence by a thermo-optic effect is also analyzed. Fabricationof a cross-slot waveguide test structure is demonstrated. © 2009 Optical Society of America

OCIS codes: 030.4070, 080.2208, 130.2790, 130.3120, 230.7390, 260.1440.

1. Introduction

A slot waveguide is a high index contrast waveguidefor high confinement of mode field in the low indexslot region [1,2]. This can enable the use of nonsiliconmaterials in silicon photonic devices to realize activeand passive structures for functions such as lightemission and all-optical signal processing [3,4].However, slot waveguide based devices are severelypolarization sensitive. Various polarization diversityapproaches based on polarization splitters and polar-ization rotators have been proposed to overcome thislimitation in high index contrast waveguides [5,6].The cross-slot waveguide as a means to utilize highconfinement by the slot effect for both quasi-TE andquasi-TM polarization modes has been investigated[7]. Such geometry was also studied in [8], which tar-geted finding an optimum practical design that stillhad birefringence; therefore its use was proposedonly as a short access waveguide for a polarizationdiversity scheme.Since the two polarizations (quasi-TE and quasi-

TM) in a cross-slot waveguide are largely confined

into geometrically orthogonal slots, they have smalloverlap. Thus propagation in a cross-slot waveguideis approaching polarization diversity, which providesa possibility of relatively independently tuning theproperties of the two polarizationmodes. Such tuningcan be performed by optimizing the geometry of thewaveguide and by choosing the slot filling materials.

In this paper we investigate the effect of variousgeometrical parameters and analyze the choice of dif-ferent materials to provide a detailed study of thecross-slot waveguide. Characteristics such as singlemode regime, birefringence, optical mode confine-ment, external tuning of birefringence by thermo-optic methods, and fabrication tolerances arediscussed. Finally, simulation results of a more prac-tical geometry, with angled sidewalls, are presented.

2. Properties of Cross-Slot Waveguides

A. Structure

A schematic of the cross-slot waveguide with horizon-tal slotmaterial indexnh andvertical slotmaterial in-dex nv is shown in Fig. 1. When nh ¼ nv, the structureis called a uniform cross-slot waveguide, and whennh ≠ nv it is called a nonuniform cross-slot waveguide.

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A cross-slot waveguide can be fabricated by plasmaenhanced chemical vapor deposition (PECVD) of athree layer sandwich structure to define the horizon-tal slot layer followed by lithography [e-beam litho-graphy, nano-imprint lithography (NIL), or deep-UVlithography (DUV)] and dry etching to fabricate thevertical slots and silicon rails. The entire process canbe CMOS compatible, depending on the lithographicprocedure adopted. The growth of rails and a hori-zontal slot layer by PECVD provides, practically, afree choice for the height of each layer. A vertical slotmay be filled by atomic layer deposition (ALD) [9].The choice of materials for horizontal and verticalslots by PECVD (SiO2, Si3N4, SiON, and a-Si:H)and ALD (TiO2, Al2O3, and ZnO), respectively, isindependent and diverse. This encourages the sepa-rate analysis of uniform and nonuniform cross-slotconfigurations.

B. Simulation Method

We employ a commercial software tool for vectorial,two-dimensional film mode matching (FMM) eigen-mode analysis and finite element method (FEM) ana-lysis [10,11]. To study the characteristics of cross-slotwaveguide with vertical sidewalls, the FMM solver isemployed. The FMM is a highly accurate method tosolve rectangular geometry waveguides [12]. Forangled sidewalls (Fig. 6) the finite element methodis employed, since triangular mesh elements usedin the FEM mode solver are found to yield more ac-curate results in such cases. All simulations are per-formed at the wavelength of 1550nm. Changing theboundary condition from a perfect magnetic to a per-fect electric conductor has negligible influence on ef-fective-index simulation results (accuracy of at least

10−4), indicating sufficient decay of the evanescentfield at the border of the simulation domain.

A single mode regime where both the fundamentalquasi-TE and quasi-TM modes exist is analyzedthroughout this study. As an example, singlemode re-gime for uniform structure with variations in railheight h and rail width wr is shown in Fig. 2. Otherparameters used in simulation are ws ¼ hs ¼ 60nm,c ¼ 100nm, d ¼ ðh − hsÞ=2, and nh ¼ nv ¼ 1:46. Thecurve appears symmetric about the line h ¼ð2wr þwsÞ because the structure is almost symmetricexcept for the slight effect of finite thickness of the cov-er layer. The intensity distribution shows twomaximaof the mode field for both quasi-TE and quasi-TMmodes on either side of the crossing (Fig. 2, top).

C. Birefringence and Fabricational Tolerances

It is possible to choose appropriate geometry wherebirefringence is minimal for both uniform and nonu-niform cross-slot configurations. Birefringence is de-fined as B ¼ nTE − nTM, where nTE and nTM are modeeffective indices for TE and TM polarizations, respec-tively. Since the vertical lithography and etch stepsare most critical from the fabrication aspect, high tol-erance with respect to variations in rail widthwr andvertical slot width ws is desirable. To analyze fabri-cation tolerance, a default structure is assumed,where wr ¼ 160nm, h ¼ 380nm, ws ¼ hs ¼ 60nm,c ¼ 100nm, and nv ¼ nh ¼ 1:46. To maintain

Fig. 1. (Color online) Schematic of a cross-slot waveguide. Railwidth wr, rail height h, vertical slot width ws, horizontal slotheight hs, depth of the horizontal slot d, thickness of the cover ma-terial c, and refractive indices of different material layers areshown.When nh ¼ nv, the configuration is called uniform, whereaswhen nh ≠ nv, it is termed nonuniform. Refractive index of thesubstrate n is 1.46 (SiO2) and the rails nr is 3.58 (Si) for allsimulations.

Fig. 2. (Color online) Single mode regime is shown with varia-tions in rail widthwr and rail height h for uniform cross-slot struc-ture, where ws ¼ hs ¼ 60nm, c ¼ 100nm, d ¼ ðh − hsÞ=2, andnh ¼ nv ¼ 1:46. Top, two maxima can be observed in quasi-TEand quasi-TM mode intensity distributions on either side of thecrossing.

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geometric symmetry in simulations, when rail heighth or horizontal slot height hs is varied, then depth dvaries as d ¼ ðh − hsÞ=2. For simplification, designparameters are assumed to be independent. Table 1shows the order-of-magnitude estimate of slopes ob-tained from the linear regression of variation in bi-refringence with respect to critical parameters.This analysis is useful to understand a generic beha-vior of optical modes; however, it does not take intoaccount multiparameter interdependence.Whereas variation in horizontal slot height hs does

not affect total rail height h, change in vertical slotwidth ws is independent of change in rail width wr(Fig. 1). Thus in Table 1, horizontal slot height hsand vertical slot widthws have significantly differentinfluences on birefringence because of the geometricconvention chosen. Also from Table 1, the most criti-cal parameters are horizontal slot height hs, railwidthwr, and horizontal slot depth d. Although para-meters such as horizontal slot height hs, horizontalslot depth d, and height of the rails h can be variedwith high precision owing to easier control over thePECVD deposition steps, such control is not possiblefor rail width wr.To overcome fabrication related limitations in ver-

tical etch steps, such as a larger value of rail widthwr(slope ¼ 3:1 × 10−3 nm−1, Table 1) horizontal slotheight hs (slope ¼ 2:5 × 10−3 nm−1, Table 1), may bereduced during the design phase to compensate forthe effect on birefringence. In DUV lithography thelinewidth can typically be 120nm [8]. For ws ¼120nm it is possible to achieve zero birefringencefor uniform (nh ¼ nv ¼ 1:46) and nonuniform (nh ¼1:46 and nv ¼ 1:63) configurations, as shown in Fig. 3.For simulations in Fig. 3, wr ¼ 200nm and h ¼400nm for uniform structure, and wr ¼ 160nmand h ¼ 380nm for nonuniform structure. For bothconfigurations, the depth of horizontal slot d ¼ðh − hsÞ=2 and other parameters are the same asthe default structure in Table 1.

D. Confinement Factors

High confinement of the quasi-TMmode into the hor-izontal slot is expected for modes with effective indexvalues (nTM) closer to nh. When the horizontal slotlayer is farther from the center [d ¼ ðh − hsÞ=2], qua-si-TM mode is less confined in the horizontal slot re-gion andhashighmode field overlapwith silicon rails,resulting in a higher effective index [Fig. 4(a)]. Thequasi-TE mode is relatively unaffected by the changein horizontal slot depth because of high confinementin the vertical slot region. InFig. 4(b), at position (і) onthe graph, only one mode intensity maximum is pre-sent, resulting in a smaller quasi-TE mode area, un-like the intensity distribution in position (іi). This isdue tohigher confinement of the quasi-TEmode in thelower part of the vertical slot when d < ðh − hsÞ=2[Fig. 4(b), position (і) on the graph] and in the upperpart of the vertical slot when d > ðh − hsÞ=2. More-over, localization of the quasi-TE mode away fromthe low index horizontal slot also leads to a highereffective-index value at the end points of the effective-index curve in Fig. 4(b). Consequently, both the con-finement and effective index of quasi-TE mode as afunction of horizontal slot depth d have positive valueof the second derivative [Fig. 4(b)]. Other parametersused for simulation results shown in Fig. 4 are thesame as the default structure in Table 1.

The quasi-TE mode confinement for d ¼ 150nm inthe vertical slot region is 45% and in the horizontalslot region is 10% [Fig. 4(b) position (ii)]. Likewise,confinement of the quasi-TM mode in the horizontalslot region is 40% and in the vertical slot region is 7%[Fig. 4(a) position (ii)]. Such selective confinement ofwell confinedmodes in spatially separated regions is adistinct feature of the cross-slot waveguide geometry.

E. Thermo-Optic Tuning

Since silicon has a 20× larger thermo-optic coefficientthan silica [13], it is possible to tune birefringence of

Fig. 3. (Color online) Equal effective indices for quasi-TE andquasi-TM modes, shown by arrow, are observed for both uniform(nh ¼ nv ¼ 1:46) and nonuniform (nh ¼ 1:46 and nv ¼ 1:63) config-urations when vertical slot width ws ¼ 120nm and depth d is cen-tered (d ¼ ðh − hsÞ=2). For uniform structure wr ¼ 200nm andh ¼ 400nm, and for nonuniform structure wr ¼ 160nm andh ¼ 380nm.

Table 1. Slope Depicting Change in Birefringence with Changein Geometric Parametersa

Parameter Slope (nm−1) Range (nm)

hs 2:5 × 10−3 40 < hs < 100wr 3:1 × 10−3 120 < wr < 300ws −0:73 × 10−3 60 < ws < 100h 1:4 × 10−3 300 < h < 400c −0:2 × 10−3 40 < c < 160d 2:8 × 10−3 30 < d < 120d −2:4 × 10−3 200 < d < 260

aSlope is obtained from the linear regression of birefringenceversus parameter curves. All parameters are assumed to be inde-pendent except when either the rail height h or horizontal slotheight hs is varied; then horizontal slot depth d varies asd ¼ ðh − hsÞ=2. The default parameter values for simulations arewr ¼ 160nm, h ¼ 380nm, ws ¼ hs ¼ 60nm, c ¼ 100nm, andnh ¼ nv ¼ 1:46. For 120nm < d < 200nm, the change in birefrin-gence with horizontal slot depth d is much smaller than in otherregions in the range 30nm < d < 260nm.


the cross-slot waveguide thermo-optically. To achievethermo-optic tuning, the noncentered horizontal slot(d ≠ ðh − hsÞ=2) is preferable. A large mode field over-lap with silicon would make the quasi-TM modemore sensitive to thermo-optic tuning in comparisonwith the quasi-TE mode. Figure 5(a) shows tempera-ture tuning to achieve zero birefringence(∂B=∂T ¼ 4 × 10−5 K−1) in nonuniform cross-slotconfiguration. For thermo-optic tuning simulationsshown in Fig. 5(a), wr ¼ 200nm, hs ¼ 56nm,d ¼ 70nm, nv ¼ 1:63, and ∂nv=∂T ¼ 10−5 K−1. Other

parameters are nh ¼ 1:46, ∂nh=∂T ¼ 10−5 K−1, andnr ¼ 3:58, ∂nr=∂T ¼ 2 × 10−4 K−1, for horizontal slotlayer (nh) and rails (nr), respectively. For a differentgeometry with uniform cross-slot configuration, andboth the quasi-TE and quasi-TM modes well con-fined, the thermo-optic coefficient of birefringenceis smaller [∂B=∂T ¼ 8 × 10−6 K−1, Fig. 5(b)]. Thisshows the influence of optical mode confinementon thermo-optic tuning. Parameters for simulationsin Fig. 5(b) are wr ¼ 160nm, hs ¼ 67nm, d ¼ðh − hsÞ=2, and nv ¼ 1:46; other parameters are the

Fig. 4. Variationof effective-indexandconfinement factorof fundamental (a)quasi-TMand(b)quasi-TEmodeswithhorizontal slotdepthd.Minimumeffectiveindexcorrespondstohighestconfinementwithintheslotregionforquasi-TMmode.Quasi-TEmodeisrelativelyunaffectedwith changes in horizontal slot depth d. Intensity distributions for depth d ¼ 30nmare shown, indicated by position (i), and for d ¼ 150nm,indicated by position (ii). Parameters used for simulation are wr ¼ 160nm, h ¼ 380nm, ws ¼ hs ¼ 60nm, c ¼ 100nm, and nh ¼ nv ¼ 1:46.

Fig. 5. (Color online) Variation of effective index is shownwith temperature for the fundamental quasi-TE and quasi-TMmodes. Commonparameters in simulations are h ¼ 380nm, ws ¼ 60nm, c ¼ 100nm, nh ¼ 1:46 at 298K, ∂nh=∂T ¼ ∂nv=∂T ¼ 10−5 K−1 and∂nr=∂T ¼ 2 × 10−4 K−1. (a) wr ¼ 200nm, hs ¼ 56nm, d ¼ 70nm, and nv ¼ 1:63. (b)wr ¼ 160nm, hs ¼ 67nm, d ¼ ðh − hsÞ=2, and nv ¼ 1:46.


same as in Fig. 5(a). Owing to the possibility of tai-loring multiple geometrical parameters (d, hs, h, andc) with high accuracy, stress induced birefringencemay also be compensated by appropriate design [14].

F. Angled Sidewall

The etching process during fabrication typicallyyields angled sidewalls (Fig. 6) [15]. The angle affectsthe fundamental quasi-TE mode more than the qua-si-TM mode since a well confined quasi-TM modedoes not overlap significantly with the vertical slotregion (Fig. 7, top). For achieving low birefringence,mode effective indices can be varied by designing thedepth of horizontal slot d [as in Figs. 4(a) and 4(b)] orthe thickness of the horizontal slot layer hs, (as inFig. 3] to offset the influence of the angled sidewall.Both of these approaches are simple since they can bedetermined by growth of the layer structure, en-abling accurate and independent control over modeproperties such as effective index or confinement fac-tor of quasi-TE and quasi-TM modes. In angled side-wall geometry, vertical slot width ws and rail widthwr are defined at depth of h=2 (Fig. 6). In Fig. 7, bi-refringence as a function of horizontal slot depth d is

shown. For these simulations, vertical slot width wsis 100nm and vertical slot base width wb (Fig. 6) is60nm, representing an example of a typical etch pro-file; other parameters are same as default structurein Table 1. Two horizontal slot depths correspondingto zero birefringence are marked by arrow in Fig. 7.The effect of an angled sidewall on the mode field in-tensity distribution of quasi-TE and quasi-TMmodes

Fig. 6. Schematic of an angled sidewall cross-slot waveguide sec-tion with vertical slot base width wb. In angled sidewall geometry,vertical slot widthws and rail widthwr are defined at depth of h=2.

Fig. 7. Variation of birefringence with horizontal slot depth d, inan angled sidewall cross-slot waveguide. Zero birefringence isshown with an arrow. Other geometrical parameters arewr ¼ 160nm, h ¼ 380nm, ws ¼ 100nm, hs ¼ 60nm, wb ¼ 60nm,c ¼ 100nm, and nh ¼ nv ¼ 1:46. Top, mode intensity distributionsof the quasi-TE and quasi-TM modes.

Fig. 8. (Color online) (a) Confinement factor of the quasi-TE and quasi-TM modes with variation of horizontal slot depth d, in cross-slotwaveguide with angled sidewall. Parameters used for simulation are wr ¼ 160nm, h ¼ 450nm, ws ¼ 100nm, wb ¼ 60nm, hs ¼ 80nm,c ¼ 100nm, and nh ¼ nv ¼ 1:46. (b) Variation of effective index of quasi-TE and quasi-TM modes with temperature. Fine-tuning of bire-fringence externally by thermo-optic means to realize zero birefringence is shown (arrow). Parameters used in simulation arewr ¼ 160nm,h ¼ 380nm, ws ¼ 100nm, wb ¼ 60nm, hs ¼ 100nm, d ¼ 41nm, c ¼ 100nm, nh ¼ 1:46, nv ¼ 1:63, ∂nh=∂T ¼ ∂nv=∂T ¼ 10−5 K−1, and∂nr=∂T ¼ 2 × 10−4 K−1 at 298K.


is shown in Fig. 7, top (also compare with Figs. 2and 4).As shown in Fig. 4, without the consideration of

angled sidewall, confinement factors vary with chan-ging horizontal slot depth d. A similar approach isused to obtain equal confinement for quasi-TE andquasi-TM modes by varying horizontal slot depth din an angled sidewall structure [Fig. 8(a)]. Simula-tion parameters used are h ¼ 450nm, hs ¼ 80nm,and other parameters are the same as in Fig. 7.Zero birefringence may be achieved by thermo-

optic tuning, as presented in Fig. 8(b). As in Table 1,linear regression of change in birefringence withchange in rail width wr yields a slope of 2 ×10−3 nm−1 for the same geometry as in Fig. 8(b).Similarly, the slope for vertical slot width is6 × 10−4 nm−1. Thus it is possible to compensate forfabrication related inaccuracy of around 1:5nm inrail width wr, or around 5nm in vertical slot widthws, by raising the temperature from 300K to400K [∂B=∂T ¼ −3 × 10−5 K−1, Fig. 8(b)]. Parametersused in simulation are wr ¼ 160nm, h ¼ 380nm,ws ¼ 100nm, wb ¼ 60nm, hs ¼ 100nm, d ¼ 41nm,c ¼ 100nm, nh ¼ 1:46, and nv ¼ 1:63. Thermo-opticcoefficients are the same as used for Fig. 5(a).To the best of our knowledge, demonstration of a

cross-slot structure has not been published. Fabricat-ing the cross-slot waveguide involves narrow line-width etching through a stack of Si=SiO2=Si, whichis more challenging than processes in manufacturinghorizontal or vertical slot waveguides. As the first de-monstration of the feasibility of the cross-slot wave-guide approach, test structures are fabricated byPECVD deposition of a sandwich layer over ther-mally oxidized silicon followed by focused ion beam(FIB) milling. A scanning electron micrograph of fab-ricated test structure is shown in Fig. 9.

3. Conclusion

In cross-slot waveguides, well confined quasi-TE andquasi-TM modes are spatially localized with lowoverlap. This feature can be used to selectively alterthe characteristics of one of the modes. We haveshown the possibility of achieving zero birefringence

in the cross-slot structure. It is also shown that ther-mo-optic tuning can be used to fine tune the birefrin-gence of an optimized structure or to overcome minormanufacturing inaccuracies. First test structures ofthe cross-slot geometry are also demonstrated.

We thank Nikolai Chekurov (M.Sc.) for fabricatingthe test structures. The research is supported byAcademy of Finland project 128827 and by Tekes–the Finnish Funding Agency for Technology and In-novation (FiDiPro program).

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Fig. 9. Test structures of cross-slot waveguide with no covermaterial. Sandwich layers of a-Si:H/SiOx/a-Si:H are depositedby PECVD over thermally oxidized silicon. FIB milling is usedto obtain the vertical sections.


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Control of optical mode properties in cross-slot waveguides