1. 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 SiO₂ to confine and guide optical modes at telecommunication wavelength, and can take advantage of mature CMOS manufacturing technology to achieve large-scale PICs [1–4]. 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 [1–4]. Plasmonics has attracted substantial research interest with its ability to squeeze light down to the subwavelength and to enhance the field strength [5–12]. Various optical components such as waveguides [5, 6, 10–12] 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/SiO₂/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/SiO₂ 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.

2. 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, SiO₂, 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.

 

Fig. 1 (Design 1) (a) Top view (xy-plane) and (b) cross-sectional view (yz-plane) at each port of the simulated domain and its corresponding parameters: L_s=1.1 μm, θ =20°, and w_i=h_i=400 nm for i=1,2, and 3. The Cu nanorod dimensions are 50 × 50 × 400 nm, and the gap spacing between rods are fixed to 40 nm.

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3D finite element method (FEM) simulations are conducted using the COMSOL Multi-physics. Either TE₀ or TM₀ 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 λ₀=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, SiO₂, and air are chosen to be n_Si=3.476, n_SiO2 =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 TE₀ or TM₀ 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 TE₀ (black) and TM₀ (red) mode excitations. CFs and ILs are plotted with a solid and dashed line respectively. For the TE₀ 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 TM₀ 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.

 

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 TE₀ (black) and TM₀ (red) mode excitations. CFs and ILs are plotted with solid and dashed lines respectively.

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Figure 3 shows the normalized field plots of Design 1 (Fig. 1) for (a) TE₀ (E_y) and (b) TM₀ (E_z) mode excitations when λ₀=1550 nm. Insets show the corresponding mode excitations at port 1. In Fig. 3(a), we can observe that the TE₀ mode is effectively coupled to the additional coupler waveguide (toward port 3) while, in Fig. 3(b), the TM₀ 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.

 

Fig. 3 Normalized field plots of Design 1 (Fig. 1) for (a) TE₀ (E_y) and (b) TM₀ (E_z) mode excitations when λ₀=1550 nm. Insets show the corresponding mode excitations at port 1.

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Figure 4 shows the T of Design 1 which is similar to Fig 2, but as a function of λ₀. Notice that, for the TE₀ 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 TM₀ mode excitation (red lines), the ER_TM is low (< 10 dB). This is because port 3 also can support the TM₀ mode with the same phase as the port 1. Hence some portion of the TM₀ mode are coupled to port 3 reducing the ER_TM. We can observe this undesired coupling from Fig. 3(b) also.

 

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 λ₀ for TE₀ (black) and TM₀ (red) mode. CFs and ILs are plotted with solid and dashed lines respectively.

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3. 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 TE₀ mode is matched with that of port 1, while the phase for TM₀ mode is mismatched. The modified port 3 structure reduces the undesired coupling to port 3 for TM₀ 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 TM₀ mode is matched with that of port 1, and mismatched for TE₀ 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 w₂=250 nm and h₂=540 nm for port 2, and w₃=540 nm and h₃=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.

 

Fig. 5 (Design 2) (a) Top view (xy-plane) and (b) cross-sectional view (yz-plane) at each port of the simulated domain and its corresponding parameters: w₂=250 nm, h₂=540 nm, w₃=540 nm, and h₃=250 nm. Other parameters are same as Fig. 1.

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The port 3 dimensions are chosen by evaluating the TE₀ and TM₀ modes for different geometries, so that the effective refractive index (n_eff) for TE₀ mode is same as that of port 1 while the n_eff for TM₀ mode is sufficiently different. However, the n_eff for TM₀ mode at port 2 is matched with that of port 1 while the n_eff for TE₀ mode is mismatched. Figure 6 shows the numerically calculated n_eff for (a) TE₀ and (b) TM₀ mode at different ports: port 1 (black), port 2 (red), and port 3 (blue). Notice that, in Fig 6(a), the n_eff for TE₀ mode at port 1 and port 3 are matched so that the TE₀ 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). TM₀ 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.

 

Fig. 6 Effective refractive index (n_eff) of the Design 2 (Fig. 5) for (a) TE₀ and (b) TM₀ mode as a function of λ₀ at different ports: port 1 (black), port 2 (red), and port 3 (blue).

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Figure 7 shows the normalized field plots of Design 2 (Fig. 5) for (a) TE₀ (E_y) and (b) TM₀ (E_z) mode excitations when λ₀=1550 nm. Insets show the corresponding mode excitations at port 1. Notice the clear beam splitting for TM₀ 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 TE₀ mode and through 1420 to 1890 nm for TM₀ mode. Thus, for a bandwidth of 280 nm (from 1440 nm to 1720 nm), Design 2 splits TE₀ and TM₀ modes successfully, and couples TE₀ to Port 3, and TM₀ to port 2.

 

Fig. 7 Normalized field plots of Design 2 (Fig. 5) for (a) TE₀ (E_y) and (b) TM₀ (E_z) mode excitations when λ₀=1550 nm. Insets show the corresponding mode excitations at port 1.

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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 λ₀ for TE₀ (black) and TM₀ (red) mode. CFs and ILs are plotted with solid and dashed lines respectively.

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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.

4. 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 TE₀ or TM₀ 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 TE₀ and TM₀ 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.