Mode-evolution-based polarization rotation and coupling between silicon and hybrid plasmonic waveguides

Hybrid plasmonic (HP) modes allow strong optical field confinement and simultaneously low propagation loss, offering a potentially compact and efficient platform for on-chip photonic applications. However, their implementation is hampered by the low coupling efficiency between dielectric guided modes and HP modes, caused by mode mismatch and polarization difference. In this work, we present a mode-evolution-based polarization rotation and coupling structure that adiabatically rotates the TE mode in a silicon waveguide and couples it to the HP mode in a strip silicon-dielectric-metal waveguide. Simulation shows that high coupling factors of 92%, 78%, 75%, and 73% are achievable using Ag, Au, Al, and Cu as the metal cap, respectively, at a conversion length of about 5 μm. For an extremely broad wavelength range of 1300–1800 nm, the coupling factor is >64% with a Ag metal cap, and the total back-reflection power, including all the mode reflections and backscattering, is below −40 dB, due to the adiabatic mode transition. Our device does not require high-resolution lithography and is tolerant to fabrication variations and imperfections. These attributes together make our device suitable for optical transport systems spanning all telecommunication bands.

of about 70% at a gap size of 50 nm, from TM mode (electric field perpendicular to the surface) to HP mode 29 . However, in Si photonic devices, TE mode (electric field parallel to the surface) is dominant due to its higher confinement and ease of fabrication. Thus, to fully utilize the HP waveguide in Si photonic devices, it is essential to have an efficient coupler between TE mode and HP mode, that is, to rotate the TE mode in a Si waveguide and simultaneously couple the rotated mode to the HP mode. Achieving simultaneously high coupling efficiency (> 90% with metal propagation loss), low reflection (< 30 dB as on-chip isolators are not readily available), broad bandwidth (preferably > 500 nm to cover all telecommunication bands), and high tolerance to fabrication imperfections is highly desirable for such devices to be incorporated into large-scale silicon photonics integration and manufacturing. Unfortunately, to the best of our knowledge, no such couplers have been reported.
In purely dielectric photonic systems, mode-evolution based polarization splitter and rotators have been demonstrated with high performance [30][31][32] . Such devices usually include tapers to adiabatically splitting or rotating modes. However, simply tapering out the metal layer into sharp tips in a similar fashion does not achieve mode-evolution. Rather, the tapered sharp metal tip focuses and confines the light into the plasmonic mode 33,34 .
Several polarization rotators consisting of plasmonic structures have been proposed 13,35 or fabricated 14 to reduce the device length for Si photonic applications. Such devices utilize asymmetric HP structures, covering the top and one side-wall of Si waveguide with oxide and metal 35 or tapering out the metal layer of HP waveguide 13,14 . However, these designs did not focus on the coupling to hybrid modes and are based on mode-coupling 35 or a combination of mode-coupling and mode-evolution 13,14 . For example, in Fig. 2 of ref. 13, the oscillation in polarization extinction ratio (PER) from 2 μm to 7 μm for the case of 90 nm spacer thickness is a signature of mode-coupling. Therefore it remains interesting to find a scheme to achieve pure mode-evolution when plasmonic effect is involved, and conduct a systematic investigation on the mechanism of transition between a dielectric mode and a HP mode.
In this paper, we present a truly mode-evolution-based polarization rotation and coupling (PRC) scheme that rotates the TE mode adiabatically and couples the rotated mode to the HP mode. When material absorption by metals is ignored, the coupler achieves almost 100% of efficiency with a proposed perfectly-phase-matched taper design. The performance of different metal caps (Cu, Au, Ag, and Al) with a linear Si taper is evaluated, and their spectral responses are assessed. Compared to mode-evolution structures in purely dielectric systems, our coupler has an upper limit of 92% efficiency when using silver as the metal cap, but it does have a much more compact size (~5 μm) and broader bandwidths (~500 nm), which are desirable in future dense optical integration. Figure 1 shows the schematic view of the mode-evolution-based PRC structure, and geometric parameters; w 1 and w 2 are the widths of Si waveguide at port 1 and HP waveguide at port 2, respectively, and h 1 , h 2 , and h 3 are the heights of Si core, SiO 2 spacer, and metal cap, respectively. The conversion/coupling region has a length of L c , and starts when the lateral shift between the metal cap and Si core is d, and ends when the metal cap is exactly on top of the Si core. Through the conversion length L c , the width of the Si core waveguide tapers from w 1 to w 2 , while that of the metal cap is fixed to w 2 .

Device design
We first calculate and plot the effective refractive indices of each mode in Fig. 2 as a function of Si core width (w 1 or w 2 ). Finite element method (FEM) is used for the calculation with a free space wavelength of λ 0 = 1550 nm. The refractive indices of Si and SiO 2 are chosen to be n Si = 3.445 and n SiO 2 = 1.445. For the metal cap we choose Cu for its CMOS compatibility, and the dispersive complex refractive index of Cu is used 36 . Waveguide heights are fixed to h 1 = 220 nm, h 2 = 30 nm, and h 3 = 100 nm. Here, the thickness of SiO 2 spacer is chosen to strike a balance between the field confinement and propagation length for the subsequent hybrid mode 8,9,18 . In general, a small spacer thickness is desirable as it would lead to strong field confinement in the spacer, which is one of the motivations to incorporate hybrid modes into the silicon photonics platform 8,9,18 . A thinner spacer also requires an optimized coupler design as direct butt coupling would cause stronger reflection and scattering. Other thickness can also be selected to promote confinement over propagation loss or vice versa, and the coupler can be designed accordingly. The thickness of Si core is chosen to be compatible with common silicon-on-insulator (SOI) wafers. TE 01 (blue) and TM 01 (green) are the fundamental TE and TM modes at port 1, respectively, and HP 02 (red) and TE 02 (cyan) are the fundamental HP and TE modes at port 2, respectively. Our goal is to match the propagation constants (phases) between TE 01 and HP 02 , while having a wide phase gap between TE 01 and TE 02 . Here, we choose w 2 = 300 nm and w 1 = 405 nm as the port widths so that the phases of TE 01 and HP 02 modes are matched. Figure 3(a) shows, from left to right, the normalized mode profiles (|E|) at the cross-sections of the device with the separation distance d = 600 nm, 200 nm, and 0 nm, respectively, and the corresponding Si core width w 1 = 405 nm, 335 nm, and 300 nm. Note that the case of d = 0 nm is the same as the cross-section of port 2, and d = 600 nm is the cross-section at the beginning of the conversion region. TE 01 and SP 01 are the TE and surface plasmon modes at the interface between port 1 and PRC, respectively, and HP 02 and TE 02 are the HP and TE modes at port 2, respectively. PRC i is the i-th PRC mode in a hybrid state. Upper figures (TE 01 , PRC 0 , and HP 02 ) are the main modes that play important roles in mode-evolution. This is an advantage over mode-coupling-based PRCs, where both PRC 0 and PRC 1 modes are excited for the rotation of polarization 33,35 .
To see the phase variations of mode-evolution in more detail, the effective refractive indices of main (blue line) and secondary (dashed green line) modes are plotted in Fig. 3(b) as a function of separation distance d, and corresponding Si core width along the device. Notice that TE 01 mode is adiabatically evolved into HP 02 mode through PRC 0 mode (blue line), while simultaneously maintaining a large phase gap to their secondary modes (dashed green line).

Results and Discussion
The performance of mode-evolution-based PRC with linear Si taper is evaluated by calculating the coupling factor to the HP mode (CF HP ), which is defined as , where P TE 01 is the input power of TE 01 mode at port 1 and P HP 02 is the output power of HP 02 mode at port 2. 3D FEM simulations are conducted by exciting TE 01 mode at port 1; then output fields of HP 02 mode is decomposed to calculate the P HP 02 33,37 . Figure 4(a) shows the calculated CF HP of the linearly tapered PRC as a function of L c , with different metal caps: Cu (blue), Au (green), Ag (red), and Al (cyan). Simulation results with the output port width w 2 = 300 nm are plotted with plain lines, and those with different port widths w 2 − 20 nm and w 2 + 20 nm are also presented with dotted and dashed lines, respectively. To show the designed PRCs are truly based on mode-evolution, Cu metal cap without metallic absorption loss is also evaluated (circled blue line), and its CF HP converges to about 97% after L c = 5 μm. This is distinctively different from mode-coupling-based polarization rotation, which relies on the mode interference and the coupling factors show a sinusoidal oscillation as the conversion length increases 13,14,33,35 . In reality when metal absorption cannot be ignored, CF HP , decreases monotonously as the L c increases, after reaching a maximum point. The trend for CF HP is similar with other metal caps, i.e., CF HP 0 hits the maximum point then decreases as L c increases; however, each metal cap shows different maximum point and descent rate. Especially, with a Ag cap, the maximum CF HP is ~92% and the descent rate is very slow, having over 80% of CF HP throughout the conversion lengths of 4 μm to 15 μm. Furthermore, simulations for w 2 varied by ± 20 nm show almost identical results for each material, suggesting that the devices are tolerant to fabrication variations. This is an another signature of the mode-evolution-based device and advantage over the mode-coupling-based one 30,31 . Also, the conversion lengths for the maximum CF HP are ultrashort with L c ~ 5 μm. Typically, a mode-evolution-based device    requires a long device length, e.g., hundreds of micrometers, to smoothly convert the mode adiabatically 30,31 ; however, an ultrashort conversion length is achieved here, with a higher degree of field confinement in the HP mode In addition to high coupling efficiency, couplers need to have broad bandwidth to cover a wide range of operating wavelengths. The spectral responses of the linearly tapered PRC are shown in Fig. 4(b), for Cu (blue), Au (green), and Ag (red) metal caps. For each metal cap, different conversion lengths are chosen, which correspond to their maximum CF HP in Fig. 4(a): 4.5 μm, 5.0 μm, and 5.5 μm for Cu, Au, and Ag, respectively. Notice that, in every case, the spectral ranges with CF HP ≥ 50% are at least over 500 nm, covering the entire telecommunication bands.
In optical telecommunication systems, low back-reflection, or high return loss is also an important factor, especially for the emerging coherent transmission schemes. Despite recent advances 38,39 , on-chip optical isolators are not readily available, so a close-to-zero reflection is highly important if a device is to be considered for practical use. Figure 4(c) shows the calculated back reflection power of the linearly tapered PRC as a function of free space wavelengths. Cu is used as the metal cap, and the device length is set to L c = 4.5 μm. Solid lines are the total back-propagation power (R total ), accounting all possible reflections and scatterings. Dashed lines are the TE mode component of the total back-propagation (R TE ). Simulations with two different mesh grid sizes (Δ ) were included: Δ = 5 nm (blue lines) and Δ = 3 nm (red lines), and the results are almost identical, suggesting high likelihood of truthfulness. Overall the total back-propagating power is below − 40 dB for the entire telecommunication wavelength range of 1300-1800 nm. Note that previous HP mode couplers showed about 2 ~ 4% of back-reflections 29 , but our mode-evolution based HP coupler shows an extremely low back-reflection, because our coupling mechanism is based on the mode-evolution, which allows an adiabatic and smooth mode transition.

Taper shape optimization.
To further optimize the mode-evolution, the effective refractive indices of the main modes are calculated as functions of both w 1 and d, while the other geometric parameters are fixed; then the index map is plotted in Fig. 5(a), again with Cu as the metal cap. The blue line on the figure is the case of linear tapering as in Fig. 3(b), and the green curved line delineate the contour of the Si waveguide taper whose main mode (PRC 0 ) has the same effective refractive index as the HP 02 mode. Note that the lower-right corner (d = 0 nm and w 1 = 300 nm) is the point of pure HP 02 mode, and the end-points on top (w 1 = 405 nm) are the points of pure TE 01 mode. Keeping the separation distance d linearly, the Si waveguide core width w 1 is tapered along the contour green line in Fig. 5(a); this tapering results in a perfect-phase-matching through the device. While there is a small phase deviation on PRC 0 mode with a linear tapering (as the blue line in Fig. 3(b)), such deviation is removed with the contoured taper, which gives a perfect-phase-matching throughout the device. Figure 5(b) shows the calculated CF HP as a function of L c for both tapers: blue lines for linear taper and green lines for perfectly-phase-matched (optimized) taper. Cases without considering the metal absorption are also plotted with dashed lines. Compared to linearly tapered design, perfectly-phase-matched tapering has shorter L c for the maximum CF HP point, and a little bit higher coupling factor for the case without metal absorption. The shorter L c of perfectly-phase-matched tapering is due to the optimized separation distance d, making the effective interaction length longer. In terms of the coupling factor, even in the case without metal absorption, there is about 3% of loss with linear tapering (dashed blue line); this loss is due to the scattering that comes from the phase-mismatch, and is removed by an optimized taper which gives the perfect phase-matching (dashed green line). After including absorption losses (thick lines), however, there is no appreciable improvement in coupling factor. This indicates that, in this mode-evolution-based PRC, the phase-mismatch is not a significant factor that determines the maximum coupling factor. Rather, as we've seen in Fig. 4(a,b), the metallic losses are the dominant factor that determines the maximum CF HP . The polarization conversion efficiency (PCE), which is defined as , is also plotted in Fig. 5(c). Notice that the PCEs are almost 100% after L c = 5 μm for every case. This shows that there are no remaining TE mode for these mode-evolution based PRCs after a short conversion length of merely L c = 5 μm. Outline of device fabrication. In this section we describe briefly a potential route of fabrication for our proposed device. The fabrication can start from the deposition of a thin (e.g. 70 nm-thick) sacrificial silicon nitride (SiN) layer on top of the 220 nm-thick Si layer of a silicon-on-insulator (SOI) wafer. After the definition of Si waveguide via lithography and etching through the SiN and Si layers, a thick SiO 2 layer will be deposited to cover the Si waveguides. Chemical mechanical polishing (CMP) can be applied to planarize the SiO 2 top surface and the polishing will stop at the height of the top surface of the Si waveguide, using silicon nitride as the etch/ polish stop. After removing the remaining SiN sacrificial layer, a 30 nm-thick layer of SiO 2 can be deposited on the planarized surface with high precision in thickness to form the spacer between the Si and metal layers. The metal layers can be subsequently formed with lithography and lift-off to complete the fabrication of our device. To make the structure more robust, we propose to over clad the metal structures with SiO2 so that the metal is encapsulated between two SiO2 layers. The fabrication process does not require high-resolution lithography as all lateral features are above 300 nm, which can be achieved with any deep-UV projection lithography tools currently available in most CMOS manufacturing facilities.

Conclusion
In summary, we present a mode-evolution-based polarization rotation and coupling scheme that has a high coupling efficiency (the maximum CF HP is about 92% using Ag), an ultra-broad bandwidth (the spectral range with CF HP > 64% is over 500 nm), and near-zero reflection. Also, the device length is very short (L c ~ 5 μm) and is tolerant to fabrication errors. The material property of plasmonic metal cap is important to the device performances such as the maximum coupling factor and the bandwidth. The Si waveguide core widths are also optimized with a perfect-phase-matching, reducing the conversion length and removing the scattering loss. This mode-evolution-based PRC scheme could meet the stringent requirements in optical communications systems and should be useful in HP-waveguide-based applications such as electro-optical modulators 15 , nano-lasers 10 , ring-resonators 19 , nonlinear optical devices 20 , and quantum plasmonic devices [40][41][42] .