Copper nanorod array assisted silicon waveguide polarization beam splitter

We present the design of a three-dimensional (3D) polarization beam splitter (PBS) with a copper nanorod array placed between two silicon waveguides. The localized surface plasmon resonance (LSPR) of a metal nanorod array selectively cross-couples transverse electric (TE) mode to the coupler waveguide, while transverse magnetic (TM) mode passes through the original input waveguide without coupling. An ultra-compact and broadband PBS compared to all-dielectric devices is achieved with the LSPR. The output ports of waveguides are designed to support either TM or TE mode only to enhance the extinction ratios. Compared to silver, copper is fully compatible with complementary metal-oxide-semiconductor (CMOS) technology. © 2014 Optical Society of America OCIS codes: (230.3120) Integrated optics devices; (130.5440) Polarization-selective devices; (250.5403) Plasmonics. References and links 1. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16, 4872–4880 (2008). 2. D. Dai, L. Liu, S. Gao, D. X. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013). 3. T. Pfau, R. Peveling, J. Hauden, N. Grossard, H. Porte, Y. Achiam, S. Hoffmann, S. K. Ibrahim, O. Adamczyk, S. Bhandare, D. Sandel, M. Porrmann, and R. Noe, “Coherent digital polarization diversity receiver for real-time polarization-multiplexed QPSK transmission at 2.8 Gb/s,” IEEE Photon. Technol. Lett. 19, 1988–1990 (2007). 4. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1, 57–60 (2006). 5. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61, 44 (2008). 6. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442–2446 (2004). 7. S. Kim, Y. Xuan, V. P. Drachev, L. T. Varghese, L. Fan, M. Qi, and K. J. Webb, “Nanoimprinted plasmonic nanocavity arrays,” Opt. Express 21, 15081–15089 (2013). 8. V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, “Plasmonic Fabry-Pérot nanocavity,” Nano Lett. 9, 3489 (2009). 9. L. T. Varghese, L. Fan, Y. Xuan, C. Tansarawiput, S. Kim, and M. Qi, “Resistless nanoimprinting in metal for plasmonic nanostructures,” Small 9, 3778–3783 (2013). 10. R. F. Oulton, V. J. Sorger, D. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008). 11. Y. Bian, Z. Zheng, X. Zhao, Y. Su, L. Liu, J. Liu, J. Zhu, and T. Zhou, “Guiding of long-range hybrid plasmon polariton in a coupled nanowire array at deep-subwavelength scale,” IEEE Photon. Technol. Lett. 24, 1279–1281 (2012). 12. Y. Bian and Q. Gong, “Low-loss light transport at the subwavelength scale in silicon nano-slot based symmetric hybrid plasmonic waveguiding schemes,” Opt. Express 21, 23907–23920 (2013). #207131 $15.00 USD Received 25 Feb 2014; revised 2 Apr 2014; accepted 2 Apr 2014; published 11 Apr 2014 (C) 2014 OSA 21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009508 | OPTICS EXPRESS 9508 13. X. Guan, H. Wu, Y. Shi, L. Wosinski, and D. Dai, “Ultracompact and broadband polarization beam splitter utilizing the evanescent coupling between a hybrid plasmonic waveguide and a silicon nanowire,” Opt. Lett. 38, 3005–3008 (2013). 14. Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on siliconon-insulator waveguides,” Sci. Rep. 3 (2013). 15. E. D. Palik, Handbook of Optical Constants of Solids, vol. 3 (Academic press, 1998). 16. D. M. Pozar, Microwave Engineering (Wiley, 2009). 17. C. Tserkezis and N. Stefanou, “Calculation of waveguide modes in linear chains of metallic nanorods,” J. Opt. Soc. Am. B 29, 827–832 (2012). 18. A. Sure, T. Dillon, J. Murakowski, C. Lin, D. Pustai, and D. Prather, “Fabrication and characterization of threedimensional silicon tapers,” Opt. Express 11, 3555–3561 (2003).


Introduction
Chip scale photonic integrated circuits (PICs) offer the miniaturization and integration of large amount of optical devices on a stable substrate.Silicon photonics utilizes the high refractive index contrast between Si and SiO 2 to confine and guide optical modes at telecommunication wavelength, and can take advantage of mature CMOS manufacturing technology to achieve large-scale PICs [1][2][3][4].Among various device components, a polarization beam splitter (PBS), which separates the TM and TE mode, is an important building block for the realization of polarization-multiplexing [1,2], coherent optical communications [3], and polarization transparent PICs [4].However, the sizes of reported PBSs are typically on the order of tens of wavelengths because they require large birefringence and long coupling length [1][2][3][4].Plasmonics has attracted substantial research interest with its ability to squeeze light down to the subwavelength and to enhance the field strength [5][6][7][8][9][10][11][12].Various optical components such as waveguides [5,6,[10][11][12] and resonant nanocavities [7,8] have been demonstrated in subwavelength scale for the realization of chip scale PICs on a metal nanostructure platform [9].Compared to dielectric structure, however, plasmonic structures typically suffer from high losses in metal.To achieve a lower propagation loss and a longer propagation length, a hybrid plasmonic waveguide (HPW), which confines the light within the gap between a metal and a high index dielectric, was suggested [10], and various HPW configurations such as a symmetric hybrid waveguide were also investigated [11,12].
A hybrid structure combining the advantages of both silicon photonics and plasmonics may provide a solution to the issues of large device footprints and high losses.Waveguides platform can be based on silicon-on-insulator (SOI) to take the benefit of CMOS compatible manufacturing and to avoid the undesired propagation losses from metal.Still, to achieve small device footprints, we can utilize plasmonics to reduce the device size and to enhance some (but probably not all) performance metrics.Indeed, several hybrid PBS structures utilizing surface plasmons have been proposed [13,14].A bent Si/SiO 2 /Ag HPW is utilized to support TM mode (electric field perpendicular to the platform surface) while TE mode (electric field parallel to the platform surface) couples to a closely spaced Si/SiO 2 waveguide [13].Dimensions of each waveguide are carefully chosen so that the phases for TE mode match, while those for TM mode do not.However, to realize this structure, selective layer depositions are necessary; to avoid propagation losses from the HPW, an additional coupler or taper at the HPW ports must be designed.A directional coupler-based PBS structure where silver cylinders are sandwiched between two Si waveguides has also been proposed [14].In this work, a TE mode input field excites metal cylinders and couples to the other waveguide, while a TM mode input passes through the original waveguide.However, this work was simulated in two dimensions (2D), which assumes infinite length in height.When the structure is truncated to form a practical 3D structure, the extinction ratio for TM mode will be significantly reduced due to the finite height of the structure.An additional issue with the hybrid structure is that so far most of the plasmonic devices are designed for or implemented with silver, which is not compatible with

CMOS technology.
In this paper, we present the design of a 3D PBS structure that is composed of two silicon waveguides with the gap filled with a copper nanorod array.The localized surface plasmon resonance (LSPR) introduces large birefringence to the directional coupler, selectively coupling and splitting TE or TM mode.Two output ports (port 2 and port 3) are designed to couple TM or TE mode only in order to improve the extinction ratio for each excitation mode.The device size is significantly reduced because of the subwavelength resonant coupling that comes from the LSPR.The bandwidth of the device is broad because it is dictated by the bandwidth of the LSPR, which too is broad.

LSPR assisted PBS
Figure 1 shows (a) top (xy-plane) and (b) cross-sectional (yz-plane) view of the simulated domain and its corresponding parameters.In Fig. 1(b), above is the yz-plane at port 1 and below is at port 2 and port 3. Si, SiO 2 , Cu, and air regions are colored in blue, cyan, yellow, and grey, respectively.L c is the coupling region length, where the coupling between two Si waveguides occur, and L s is the splitter arm length in x-direction.θ is the separation angle between x-axis and splitter arm.w i and h i represent width and height of i-th port, respectively.The Cu nanorod dimensions chosen to be 50 × 50 × 400 nm, which match the coupler waveguide gap and height.The nanorods are arrayed in x-direction through the coupling region.The spacing between rods are set to 40 nm (the period in x-axis is 90 nm) for high coupling efficiency.L s and θ are set to 1.1 μm and 20 • , respectively, so that the separated modes can be guided to each port without any significant bending loss.
3D finite element method (FEM) simulations are conducted using the COMSOL Multiphysics.Either TE 0 or TM 0 mode is excited at port 1, then the resulting power transmissions to ports 2 and 3 are measured.Boundary mode analysis is conducted along the simulations to excite the desired mode.The free space wavelength is set to λ 0 =1550 nm, which is used in optical telecommunication.We choose Cu as a plasmonic material because of its compatibility in current CMOS manufacture technology.The refractive index of Si, SiO 2 , and air are chosen to be n Si =3.476, n SiO 2 =1.444, and n air =1 assuming lossless, and a complex refractive index of Cu is used in consideration of both material dispersion and loss [15].We define key performance parameters such as coupling factor (CF), insertion loss (IL), and extinction ratio (ER) as the following (expressed in dB): [16]: Here, T represents the power transmission and the subscripts TE and TM represent each mode of excitation.P1 is the input power at port 1 while P2 and P3 are the output powers at port 2 and port 3 respectively.The output port for CF and IL on TE or TM excitation is switched because, in our design, the port 3 is designed to a TE port and the port 2 is to a TM port.
Both the width w i and height h i of all the waveguides are set to 400 nm as an initial design (Design 1).In this case, either TE 0 or TM 0 mode supports comparable propagation constant (phase), and essentially the effective refractive indexes for both input and coupler waveguides are matched.
The coupling region length L c , where two Si waveguides are closely spaced and Cu nanorods are arrayed, is optimized to have the highest ERs. Figure 2 shows the power transmission T of Design 1 (Fig. 1) from port 1 to port 2 and port 3 as a function of L c for TE 0 (black) and TM 0 (red) mode excitations.CFs and ILs are plotted with a solid and dashed line respectively.For the TE 0 mode (black lines), if the L c is too short, the coupling efficiency to the coupler waveguide (and hence to the port 3) is low and fields just pass through their original input waveguide.Hence, the low CF TE and high IL TE .However, if the L c is too long, the cross-coupled fields  couple back to the original input waveguide because the structure is symmetric.Also, more exposure to Cu rods introduces higher losses, resulting in a lower transmission.For the TM 0 modes (red lines), the power transmission is not so sensitive to L c as TE mode.Shorter L c tends to result higher ERs because it reduce the undesirable coupling to port 3, i.e., IL TM .We choose L c =980 nm as an optimal value, and will use this coupling length through the rest of the paper.
Figure 3 shows the normalized field plots of Design 1 (Fig. 1) for (a) TE 0 (E y ) and (b) TM 0 (E z ) mode excitations when λ 0 =1550 nm.Insets show the corresponding mode excitations at port 1.In Fig. 3(a), we can observe that the TE 0 mode is effectively coupled to the additional coupler waveguide (toward port 3) while, in Fig. 3(b), the TM 0 mode just passes through its original input waveguide (toward port 2) having some portion of undesired coupling to the coupler waveguide.Here, the Cu nanorods array plays a role for subwavelength scale resonant coupling between two Si waveguides at TE mode, reducing the L c and dramatically enhancing the coupling efficiency.The LSPR at Cu nanorod array is essentially polarization selective, i.e., the degree of excited LSPR, hence the coupling efficiency, for the TE and TM modes are significantly different [5,7,17].This polarization selective strong resonance at subwavelength scale leads to the polarization sensitive coupling, and hence enhances the PBS functionality.
Figure 4 shows the T of Design 1 which is similar to Fig 2, but as a function of λ 0 .Notice that, for the TE 0 mode excitation (black lines), the CF TE is high (∼ −1.5 dB) and the IL TE is low (∼ −25 dB), hence making ER TE high (> 23 dB) through 1.48 μm to 1.68 μm.However, for the TM 0 mode excitation (red lines), the ER TM is low (< 10 dB).This is because port 3 also can support the TM 0 mode with the same phase as the port 1. Hence some portion of the TM 0 mode are coupled to port 3 reducing the ER TM .We can observe this undesired coupling from Fig. 3(b) also.

Output ports design
To enhance the ER TM of the initial design (Design 1), waveguide dimensions of port 3 are modified so that the phase for TE 0 mode is matched with that of port 1, while the phase for TM 0 mode is mismatched.The modified port 3 structure reduces the undesired coupling to port 3 for TM 0 mode (IL TM ) while maintaining high enough coupling efficiency to port 2 (CF TM ).Port 2 dimensions are also modified so that the phase for TM 0 mode is matched with that of port 1, and mismatched for TE 0 mode.Figure 5 is the modified PBS structure (Design 2) that shows similar schematic views as Fig. 1.The waveguide widths and heights are modified to w 2 =250 nm and h 2 =540 nm for port 2, and w 3 =540 nm and h 3 =250 nm for port 3. Different waveguide dimensions between port 1 and other output ports (port 2 and port 3) are linearly tapered through the coupling region, as shown in Fig. 5(a).Other dimensions are fixed to the same numbers shown in Fig. 1.
The port 3 dimensions are chosen by evaluating the TE 0 and TM 0 modes for different geometries, so that the effective refractive index (n eff ) for TE 0 mode is same as that of port 1 while the n eff for TM 0 mode is sufficiently different.However, the n eff for TM 0 mode at port 2 is matched with that of port 1 while the n eff for TE 0 mode is mismatched.Figure 6   that the TE 0 mode can be coupled well to port 3 (increasing the CF TE ), while a huge gap in the n eff between port 1 and port 2 prevents the undesired coupling to port 2 (lowering the IL TE ).TM 0 mode goes through a similar process.In Fig 6(b), the n eff at port 1 and port 2 are matched while there is a substantial mismatch at port 3.
Figure 7 shows the normalized field plots of Design 2 (Fig. 5) for (a) TE 0 (E y ) and (b) TM 0 (E z ) mode excitations when λ 0 =1550 nm.Insets show the corresponding mode excitations at port 1.Notice the clear beam splitting for TM 0 mode, in Fig. 7(b), compared to the undesired coupling toward port 3 in Fig. 3(b).Figure 8 shows the T of the Design 2 (Fig. 5) which is similar to Fig. 4. Notice in Fig. 8, the ER TM (red lines) of the Design 2 has greatly improved compared to that of the Design 1 in Fig. 4. Red lines in Fig. 8 show the high ER TM (> 15 dB) and CF TM (> −3 dB) over broadband wavelength ranges (1420∼1890 nm).The bandwidth of the ER TE (black lines) has also broadened by reducing the IL TE for longer wavelength regime.The ER TE is over 20 dB within the 1520∼1920 nm range.Overall, for both TE and TM modes, output ports (ports 2 and 3) dimensions reduce the undesired ILs while maintaining high CFs.From a device point of view, if we define the operating criteria of PBS as ER > 15 dB and CF > −3 dB, Design 2 operates well through 1440 to 1720 nm for TE 0 mode and through 1420 to 1890 nm for TM 0 mode.Thus, for a bandwidth of 280 nm (from 1440 nm to 1720 nm), Design 2 splits TE 0 and TM 0 modes successfully, and couples TE 0 to Port 3, and TM 0 to port 2.
Our design could be fabricated in state-of-the-art CMOS facility capable of achieving minimum features of 32 nm or below (our structure has minimum feature of 40 nm).For vertical tapers, one could use grey-scale lithography [18].Using silver instead of copper may improve the operating bandwidth from 280 nm to 360 nm.However, substituting silver for copper will result in a loss of fabrication compatibility with CMOS technology as silver would not be allowed in CMOS processing for the foreseeable future.

Conclusion
In summary, we designed a directional coupler-based 3D PBS structure enhanced by LSPR.An array of metal nanorods is used for the excitation of LSPR on a SOI platform.Output ports dimensions are designed to support a desired TE 0 or TM 0 mode only for higher ERs.We used copper as a metal component, which is fully compatible with current CMOS technology.The device size is ultra-compact compared to full dielectric implementations (the coupling region length is only about 1 μm), and the operating bandwidth (ER > 15 dB and CF > −3 dB for both TE 0 and TM 0 mode) is about 280 nm.This LSPR assisted PBS will substantially reduce the entire device size in PIC while maintaining the PBS functionality over a broad bandwidth.Similar conceptual plasmonics-assisted Si devices with reduced device size and enhanced efficiency could be designed.

Fig. 2 .
Fig. 2. Power transmission T (expressed in dB) of Design 1 (Fig. 1) from port 1 to port 2 and port 3 as a function of L c for TE 0 (black) and TM 0 (red) mode excitations.CFs and ILs are plotted with solid and dashed lines respectively.

Fig. 4 .
Fig.4.Power transmission T (expressed in dB) of Design 1 (Fig.1) from port 1 to port 2 and port 3 as a function of λ 0 for TE 0 (black) and TM 0 (red) mode.CFs and ILs are plotted with solid and dashed lines respectively.

Fig. 8 .
Fig.8.Power transmission T (expressed in dB) of the Design 2 (Fig.5) from port 1 to port 2 and port 3 as a function of λ 0 for TE 0 (black) and TM 0 (red) mode.CFs and ILs are plotted with solid and dashed lines respectively.