Muhammad Alam,* J. Stewart Aitchsion, and Mohammad MojahediDepartment of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario M5S3G4, Canada
Surface plasmon (SP)—a hybrid surface wave thatresults from the coupling of an electromagnetic waveand free electrons in a metal—has attracted a lot ofinterest in recent years for its unique properties andits great potential for practical applications. For ex-ample, SP can offer subdiffraction-limited confine-ment of light not possible by other means [1].Moreover, the presence of metal as a part of the guid-ing structure and the high field confinement on themetal surface make SP very attractive for biosensing[2] and electro-optic applications [3]. However, theapplication of SP is restricted by its large propaga-tion loss. In the optical regime, metals are highlylossy and SP is strongly affected by this loss. One pos-sible way to overcome this problem is to compensatefor the loss by using an optical gain medium [4,5].Another possibility is to integrate plasmonics withother photonic technologies, for example, with sili-con-on-insulator (SOI). In this approach, the low-lossSOI guides will be used to guide light over large dis-
tances on an optical chip and plasmonic devices willbe used locally to execute specific functions. One suchfunction can be polarization control on an SOI inte-grated optical circuit. Given the fact that the highdielectric contrast of SOI waveguides makes themhighly polarization-dependent, good control of thepolarization state is necessary for proper operationof SOI-based integrated optical circuits. This canbe achieved by using a polarizer to extinguish the un-wanted polarization state. Although numerous polar-izer designs are available in the literature, there arerelatively few polarizer designs that are compact andcompatible with SOI technology [6,7]. To implementthe plasmonic waveguide-based polarizer and otherdevices for SOI, a plasmonic guide is needed thatis fully compatible with SOI fabrication technology.The guide dimensions should be comparable withSOI guides so that both technologies can be inte-grated easily. The selected plasmonic guide shouldalso provide a good compromise between loss andconfinement. All these properties can be satisfiedby our (along with others) recently proposed hybridplasmonic waveguide [8–12]. Here, we present a SOIcompatible TM-pass polarizer using the hybrid guid-ing scheme.
Figure 1(a) shows the hybrid guide chosen in thiswork [12]. It consists of a silver layer of dimensionw × t separated from a high-index layer (silicon) of di-mension w × d by a low-index spacer of dimensionw × h. Electric field intensity profiles for the TMand TE modes, obtained by finite element code Com-sol Multiphysics, are shown in Figs. 1(b) and 1(c), re-spectively. Material properties for silica and siliconare taken from [13] and that of silver is from [14].The TM mode supported by the hybrid guide is asupermode resulting from the coupling betweenthe SP mode guided by the silver–silica interfaceand the dielectric waveguide mode guided by the si-licon layer. The supermode is highly concentrated inthe low-index spacer region (silica, in the presentcase). On the other hand, the TEmode is very similarto conventional dielectric waveguide mode and isconcentrated in the high-index region, i.e., in the si-licon layer.
Since the two modes are guided in two differentlayers, changing the dimensions and material prop-erties of these layers will affect the two modes in dif-ferent ways. For designing practical devices usingthe hybrid guide, it is necessary to have a clear un-derstanding of how the choice of waveguide dimen-sions and material properties affect the modecharacteristics. Therefore, we have carried out a de-tailed numerical analysis to investigate these effects.Some of these results are presented in Figs. 2–4.Figure 2 shows the effects of spacer permittivityεspacer on the effective mode index Neff and the pro-pagation distance of the TM mode. Here, Neff is de-fined as Neff ¼ k=k0 where k is the real part of the
propagation constant and k0 ¼ ω=c is the free spacewave number. The propagation distance is defined asthe distance over which guided power drops to 1=e ofits initial magnitude. Increase of spacer permittivityresults in increase of Neff and decrease of propaga-tion distance. Two possible choices of spacer materi-als are silica and silicon nitride, which havepermittivity 2.08 and 4, respectively. In this work,we have chosen silica as the spacer material to en-sure low loss in the hybrid section.
Figures 3(a) and 3(b) show the effects of spacerthickness (h) and silicon thicknesses (d) on effectivemode index (Neff ) for TM and TEmodes, respectively.Reduction of spacer thickness results in an increaseof Neff for the TM mode, but the opposite is true forthe TE mode. When silicon thickness is large (e.g.,d ¼ 200nm), both modes exist for any spacer thick-ness considered here. For small silicon thickness(e.g., d ¼ 100nm), the hybrid waveguide supportsonly the TM mode.
Figure 4 shows the variations of propagation dis-tance for the two modes with varying waveguide di-mensions. The TM mode is lossier than the TE modefor all choices of silicon and spacer thicknesses con-sidered in this work. The propagation distance of theTM mode decreases monotonically with reducedspacer thickness. Propagation distance of the TEmode follows the same trend when silicon thicknessis large (e.g., d ¼ 200nm). For a reduced siliconthickness (e.g., d ¼ 150nm), the propagation dis-tance of the TEmode is small for intermediate valuesof spacer thickness.
To understand the reason behind the variations ofmode characteristics presented in Figs. 3 and 4, wehave examined the field profiles of both modes.Figure 5 shows the electric field intensity of the TMmode for different spacer thicknesses (h). The domi-nant electric field component of the TM mode is per-pendicular to the metal, as shown by the electric fieldarrows in the figures. With reduced spacer thickness,the mode is more tightly confined and Neff , is largeras shown in Fig. 3(a). Like all plasmonic guides, thisincreased confinement is accompanied by reducedpropagation distance, as shown in Fig. 4(a).
Figure 6 shows the electric field intensity of the TEmode for a number of spacer thicknesses. The field isconcentrated in the high-index region (silicon), andsince the silicon film is thin in this case (d ¼ 150nm),the field is loosely confined. For large spacer thick-ness, the mode is not significantly affected by the
Fig. 1. (Color online) (a) Cross section of the hybrid waveguide. (b) Electric field intensity for TM mode. (c) Electric field intensity for TEmode.Waveguide dimensions arew ¼ 350nm, t ¼ 200nm, h ¼ 150nm, d ¼ 150nm, T ¼ 2 μm.Wavelength of operation is 1550nm and thespacer is silica.
Fig. 2. (Color online) Effect of varying spacer permittivity (εspacer)on effective mode index (Neff ) and propagation distance for the TMmode. Waveguide dimensions are w ¼ 350nm, t ¼ 200nm,h ¼ 100nm, d ¼ 100nm and T ¼ 2 μm.
metal and propagation distance is large (propagationloss is low). As the spacer thickness is reduced, themode is more affected by the presence of metal,and propagation distance decreases (propagationloss increases). According to the boundary conditionsof the electric field, the tangential electric field iszero on the surface of a perfect conductor. Though sil-ver is not a perfect conductor in near-IR, it still has alarge negative real part of permittivity and can beconsidered a “good conductor.” Hence, for a smallspacer thickness, the dominant electric field compo-nent of the TEmode, which is tangential to the metalsurface, is pushed away from the metal. The net re-sult is the following: for small spacer and siliconthicknesses, the TE mode is pushed into the sub-strate and approaches the cutoff condition, as shownin Fig. 6(c). Since in this case, the field is mostly inthe substrate (a “good dielectric”), metallic losses arereduced. Therefore, for a thin silicon film (e.g.,d ¼ 150nm), the propagation distance is minimizedfor an intermediate choice of spacer thickness asshown in Fig. 4(b).
Since the TE mode can be cut off by properly se-lected dimensions while the TM mode is still wellguided, it is possible to implement a TM-passpolarizer using the hybrid plasmonic waveguide.Figure 7(a) shows the schematic of such a device.Figure 7(b) shows the cross sections of the hybrid sec-tion and Fig. 7(c) depicts the input/output siliconwaveguides. By properly choosing the dimensions,it is possible to force the TE mode into cutoff whilethe TMmode is well guided. The hybrid guide in thiscase acts as a TM-pass polarizer.
Finite-difference time-domain (FDTD) code fromLumerical was used to investigate the performanceof the polarizer. Lumerical code has been widely usedfor analyzing plasmonic devices in the past and hasshown good agreement with experimental results[15]. To obtain a good compromise between speedand memory requirements, a nonuniform mesh witha mesh accuracy level of 6 and a minimummesh-stepsetting of 0:25nmwas used. Details of the simulationcan be found in [15]. The computational volumeis 35 μm× 4 μm× 4:5 μm and is terminated with
Fig. 3. (Color online) (a) and (b): Variations of effective mode index (Neff ) for TM and TE modes with spacer thickness (h) for a number offixed silicon thicknesses (d). Other dimensions are w ¼ 350nm, t ¼ 200nm, T ¼ 2 μm. Wavelength of operation is 1:55 μm.
Fig. 4. (Color online) (a) and (b): Variations of propagation distance for TM and TE modes with spacer thickness (h) for a number of fixedsilicon thicknesses (d). Other dimensions are w ¼ 350nm, t ¼ 200nm, T ¼ 2 μm. Wavelength of operation is 1:55 μm.
Fig. 5. (Color online) Variations of electric field intensity for the TM mode with spacer thickness h. (a) h ¼ 150nm, (b) h ¼ 100nm,(c) h ¼ 50nm. The other dimensions are w ¼ 350nm, t ¼ 200nm, d ¼ 150nm, T ¼ 2 μm. Wavelength of operation is 1:55 μm.
perfectly matched layers (PML). Simulations werecarried out on multiple processors in parallel onthe high-performance computer cluster Westgrid.Details of the simulation process can be found in[15]. Figures 8(a) and 8(b) show the electric field in-tensity profiles of the TM and TE modes, respec-tively, along the polarizer for 1:55 μm wavlengthfor an 18-μm-long polarizer. The hybrid polarizer sec-tion is located between z ¼ 0 μm and z ¼ 18 μm. TheTMmode is well guided from the input to the output,although it suffers some propagation losses. The TEmode, on the other hand, is below cutoff, and hence isunable to propagate through the hybrid section.
In Fig. 9, we have plotted the variations of inser-tion losses of the TM and TE modes with polarizerlength for two different values of T. The extinctionratio (difference between the insertion losses of TMand TEmodes) is high for both cases. Insertion loss ofthe TMmode, however, is not negligible, and for largevalues of T, the polarizer described in [6] outper-forms our hybrid polarizer in terms of both TM inser-tion loss and extinction ratio. However, there are
practical applications, such as optical amplifiers im-plemented on a SOI substrate, where a thin oxidelayer is required [16]. For T ¼ 1 μm, the extinctionratio for our 18-μm-long hybrid polarizer is 21dB,compared to 14dB for the polarizer described in[6]. Therefore, for a thin oxide substrate, the use ofthe hybrid polarizer is more advantageous thanthe polarizer described in [6]. The hybrid polarizercan also provide a high extinction ratio for a shorterpolarizer length. For example, a 13-μm-long hybridpolarizer (with all other dimensions the same as inFig. 9 caption) provides 21:8dB and 3:2dB insertionloss for the TM and TE modes, respectively, i.e., anextinction ratio of 18:6dB. If (h) is increased from50nm to 150nm, the TE mode is no longer far belowcutoff, and hence the extinction ratio for a 18-μm-longpolarizer drops from 21dB to 7:7dB. Choosing asmall value of h, therefore, is essential for proper op-eration of the polarizer.
The insertion loss of the TM mode is caused bythree factors: material loss due to the presence of me-tal, mismatch of mode profile between the hybridsegment and input/output silicon waveguides, andreflection caused by the mode index mismatch be-tween the hybrid guide and input/output wave-guides. Less than one-third of the insertion lossresults from material loss. The mode size in the hy-brid waveguide is very similar to that in the siliconinput/output waveguide, and hence losses resultingfrom mode-size mismatch are expected to be low.However, because of the difference in the effectivemode indices for the TM modes in the hybrid sectionfrom those in the input/output silicon waveguide sec-tions, significant reflection occurs. One solution tothis is to use a taper section between the input/output waveguides and the hybrid plasmonic section.Design of tapers for mode matching is a well-studiedand understood topic, and hence will not be discussedin this work.
Fig. 6. (Color online) Variations of electric field intensity for the TE mode with spacer thickness h. (a) h ¼ 150nm, (b) h ¼ 100nm,(c) h ¼ 50nm. The other dimensions are w ¼ 350nm, t ¼ 200nm, d ¼ 150nm, T ¼ 2 μm. Wavelength of operation is 1:55 μm.
Fig. 7. (a) Three-dimensional schematic of the complete TM polarizer. (b) Cross section of the hybrid section. (c) Cross section of the inputand output silicon waveguides. The coordinate system is defined with respect to (b) and (c) with the xz plane coinciding with the siliconwaveguide-buried oxide interface and its origin located at the beginning of the hybrid waveguide section.
Fig. 8. (Color online) Electric field intensity plot for the lightpropagating through the polarizer. (a) TM mode, (b) TE modefor the TM-pass polarizer. Device dimensions are w ¼ 350nm, t ¼200nm, h ¼ 50nm, d ¼ 100nm, T ¼ 1 μm. Dimensions of inputand output waveguides are D ¼ 350nm and H ¼ 300nm. Spaceris silica. Wavelength of operation is 1:55 μm.
We have proposed a compact hybrid TM-pass polar-izer that is fully compatible with SOI technology. Theeffectiveness of the proposed polarizer is confirmedby FDTD simulations. To the best of our knowledge,the proposed device is the first application of thehybrid plasmonic waveguide as a polarizer for inte-grated optics. Many other hybrid devices, for exam-ple, TE-pass polarizer, polarization-independentdirectional coupler, and polarization rotator, can beimplemented using this technology and will be re-ported in our future publications.
We would like to acknowledge the use of computingresources from WestGrid. This work was supportedby the Natural Sciences and Engineering ResearchCouncil (NSERC) of Canada under grant no. 480586and BiopSys Network under grant no. 486537.
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Fig. 9. (Color online) Insertion losses of the TM-pass polarizer for two different buried oxide thicknesses. (a) TM mode, (b) TE mode.Device dimensions are w ¼ 350nm, t ¼ 200nm, h ¼ 50nm, d ¼ 100nm. Spacer is silica. Dimensions of input and output waveguides areD ¼ 350nm and H ¼ 300nm. Spacer is silica. Wavelength of operation is 1:55 μm.
