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We present a polarization rotation and coupling scheme that rotates a TE0 mode in a silicon waveguide and simultaneously couples the rotated mode to a hybrid plasmonic (HP0) waveguide mode. Such a polarization rotation can be realized with a partially etched asymmetric hybrid plasmonic waveguide consisting of a silicon strip waveguide, a thin oxide spacer, and a metal cap made from copper, gold, silver or aluminum. Two implementations, one with and one without the tapering of the metal cap are presented, and different taper shapes (linear and exponential) are also analyzed. The devices have large 3 dB conversion bandwidths (over 200 nm at near infrared) and short length (< 5 μm), and achieve a maximum coupling factor of ∼ 78% with a linearly tapered silver metal cap.
© 2015 Optical Society of America
1. Introduction
Silicon photonics [1–5] and plasmonics [6–8] are two of the most actively investigated research fields that are promising in realizing low-cost and high-density photonic integrated circuits (PICs). The significant benefit of silicon photonics is that it can utilize the well-established CMOS manufacturing technology. However, sizes of most silicon photonic devices are relatively large compared to current electronic devices. Plasmonics has attracted extensive research interest due to its ability to confine the light tightly, bringing down the plasmonic device size to subwavelength scale. However, the main drawback of plasmonics is the high absorption loss from metals. To mitigate the challenges of large device footprint and high loss, a promising approach is to integrate silicon photonics and plasmonics into a hybrid system [9–14]. To that end, an efficient coupler between dielectric waveguides and plasmonic devices is an essential component.
A typical plasmonic waveguide consists of a metallic waveguide and one or more layers of dielectric loading, which can be either patterned or blanket. Recently, several designs of Si to plasmonic waveguide couplers have been reported [15–17]. A Si waveguide to dielectric-loaded plasmonic waveguide coupler was demonstrated with a high coupling efficiency (∼ 80%) [15]. Also, an efficient coupler between Si and metal-insulator-silicon-metal waveguides was demonstrated with a coupling loss of 2.5 dB [16]. A broadband coupler between Si and hybrid plasmonic (HP) waveguides with a tapered structure was suggested with a maximum coupling efficiency of ∼ 70% [17]. This work has practical importance because the HP waveguide is a relatively efficient plasmonic waveguide with its long propagation length and high field confinement [9–11]; the HP configuration has also been used as an ultracompact electro-optical modulator [12] and a nano-laser [13] with a great potential for future PICs. However, in [17], the coupler was designed for TM mode (electric field perpendicular to the surface) to HP mode only. In silicon photonics in general, TE modes (electric field parallel to the surface) are more desirable and widely used due to their higher coupling efficiency and ease of fabrication. Thus, to utilize the Si waveguide to HP waveguide coupler scheme in [17], an additional polarization rotator is required, which decreases coupling efficiency and increases the device size.
For the rotation of polarization, exciting a hybrid eigenmode with an angled optical axis is necessary, and the waveguide structure essentially requires an asymmetric cross-section. Various types of asymmetric waveguide structures have been proposed and demonstrated as a polarization rotator (PR), such as a twisted waveguide [3], a slanted sidewall waveguide [4], and a corner cut waveguide [5]. There are, in general, two types of PR schemes, based on mode-evolution [3] or mode-coupling [4, 5]. The mode-coupling based PRs use the multimode interference [4,5,18] of two hybrid modes in a PR, and usually have shorter conversion length compared to the mode-evolution based PRs. However, the performance is sensitive to the phases of coupled modes, making the device wavelength-sensitive and difficult to fabricate. On the other hand, the mode-evolution based PRs are more tolerant to the fabrication errors and inherently broadband [3]. Plasmonic metal nanostructure can confine light down to the subwavelength scale [19], and may reduce the device size and enhance the operating bandwidth [14]. For the PR applications, an asymmetric waveguide cross-section can be introduced by covering the top or side-wall surfaces of silicon waveguide, with a metal, asymmetrically [20–22]. In these cases, hybrid modes with a plasmonic structure introduce a large effective refractive index differences, resulting an ultrashort conversion length.
In this paper, we present ultrashort polarization rotation and coupling (PRC) structures that rotate the TE0 mode in a Si waveguide (TE0,Si) and couple it to the HP0 mode in a HP waveguide. We use an asymmetric hybrid plasmonic waveguide structure for the rotation of polarization and coupling; the metal and low-index material cap area is etched partially. Two PRC schemes are presented without (Fig. 1) and with (Fig. 8) metal tapers. The effects of different metal caps (copper, silver, gold, and aluminum) and taper shapes (linear and exponential) are evaluated, and spectral responses are also presented.
Fig. 1 Schematic of the polarization rotation and coupling (PRC) structure. The inset shows the cross-sectional view and parameters; hSi, hSiO2, and hCu are the heights of Si, SiO2, and Cu, respectively. w1 is the width of both Si and HP waveguides, and w2 is the width of Cu and SiO2 in the PRC region. Si, SiO2, Cu, and PMMA regions are colored in blue, grey, yellow, and cyan respectively. The PMMA cladding is not shown in the 3D illustration.
2. Polarization rotation and coupling (PRC)
2.1. Design of the PRC
Figure 1 shows the schematic of the PRC structure. A Si waveguide and a HP waveguide are connected with the PRC structure, where the TE0 mode is converted to the HP0 mode. The inset shows the cross-sectional view and parameters; hSi, hSiO2, and hCu are the heights of Si, SiO2, and Cu, respectively. w1 is the width of both Si and HP waveguides, and w2 is the width of Cu and SiO2 on PRC region. We first choose Cu as the plasmonic material for its compatibility with CMOS processing, and cover it with PMMA to avoid its oxidation. Waveguide heights are fixed at hSi=230 nm, hSiO2 =50 nm, and hCu=100 nm, and width w1 is chosen to be 380 nm so that the phase of TE0,Si mode is matched with the phase of HP0 mode.
Figure 2 shows the normalized mode profiles (|E|) at Si waveguide, PRC (w2=200 nm), and HP waveguide regions from left to right. The free space wavelength is λ0=1550 nm throughout the paper. Notice that the effective refractive index (neff) of TE0,Si mode and the neff of HP0 mode are identical (neff = 2.19) so as to match the phase of both modes. Hybrid modes (PRC0 and PRC1) are excited in the PRC region, due to the asymmetry of the structure with w2. These two lowest hybrid modes have a large overlap in field components, and experience interference with each other through the conversion length of Lc. The conversion length of this multimode interference can be estimated by Lc = π/(β0 − β1) [18], where β0 and β1 are the propagation constants of PRC0 and PRC1 modes, respectively, which are given by βi = nPRCik0. Figure 3 shows the calculated neff for PRC0 (red circle line) and PRC1 (black square line) modes, and corresponding Lc (blue line) as a function of w2. Notice that the conversion length is very short (between 3 μm and 6 μm), compared to that of other conventional polarization rotators (typically, tens or hundreds of micrometers). Previously, an asymmetric Si nanowires were used to rotate the polarization with a conversion length of ∼ 22.1μm [5]. Here, a shorter polarization conversion lengths are achieved (∼ 4.5μm) by using the asymmetric HP waveguide, simultaneously coupling to the HP0 mode. The short conversion length is due to the large neff difference between the two lowest order modes (PRC0 and PRC1). However, there is a trade-off between conversion length and coupling factor. The green line indicates the position of neff = 2.19, which corresponds to the neff of TE0,Si and HP0 modes. The coupling factors, at the interfaces between PRC and Si or HP waveguide, will be reduced as the neff of PRC0 and PRC1 modes deviate from this green line, because of the phase mismatch at the interfaces. On the other hand, the more deviations from this green line result in the shorter conversion length because of the larger neff difference between PRC0 and PRC1 modes.
Fig. 2 From left to right, normalized mode profiles showing the |E|, at Si waveguide, PRC, and HP waveguide cross-sections. Geometric parameters are set to hSi=230 nm, hSiO2 =50 nm, hCu=100 nm, w1=380 nm, and w2=200 nm.
Fig. 3 Effective refractive index (neff) of the two lowest modes in PRC (red circle line for PRC0 mode and black square line for PRC1 mode), and corresponding coupling length of Lc (blue line) as a function of w2. Green line represents the neff=2.19, which corresponds to the neff of TE0,Si and HP0 modes.
2.2. Numerical method
To evaluate the performance of the designed PRC, 3D finite element method (FEM) simulations are conducted using the COMSOL Multiphysics®. The refractive indices of Si, SiO2, and PMMA are chosen to be nSi=3.445, nSiO2 =1.445, and nPMMA=1.481 assuming them to be lossless, and the complex refractive index of Cu is used considering both material dispersion and loss [23, 24]. The TE0 mode is excited at port 1, and the coupling factor to the HP0 mode (CFHP0) is evaluated by the power transmission to the HP0 mode at port 2, i.e., CFHP0 = PHP0,2/PTE0,1, where PTE0,1 is the input power of the TE0 mode at port 1, and PHP0,2 is the output power of the HP0 mode at port 2. The output power of the TE0 mode at port 2 (PTE0,2) is also calculated to evaluate the polarization conversion efficiency (PCE), which is defined as PCE = PHP0,2/(PHP0,2 + PTE0,2). Boundary mode analysis is conducted to excite the TE0 mode at port 1 and to decompose the HP0 and TE0 modes at port 2. The output power of the HP0 mode is evaluated by the field decomposition as the following [25]:
where EFEM and HFEM are, respectively, the electric and magnetic fields components of the 3D FEM simulations, and EHP0 and HHP0 are, respectively, the electric and magnetic fields components of the HP0 mode calculations for the same geometric dimensions. The surface integrations of the output power in propagation direction (z-direction) are conducted over the waveguide cross-sections. The process for evaluating PTE0,2 is similar, but EHP0 and HHP0 are replaced by ETE0,2 and HTE0,2, respectively.2.3. Results and discussion
Figure 4 shows the normalized field plots at the middle of waveguide width w1 (yz-plane), when w2=180 nm, Lc=4 μm, and λ0=1550 nm. Above is the real Ex and below is the real Ey. Notice that, in the Re(Ex) plot (above), the excited TE0 mode at the port 1 (left side of the figure) gradually disappears as wave propagates (in z-direction) through the PRC region. On the other hand, in the Re(Ey) plot (below), the HP0 mode begins to appear as the TE0 mode disappears, and couples to the port 2 (right side of the figure). Here, the TE0 mode is rotated and coupled to the HP0 mode through the conversion length Lc of the PRC structure.
Fig. 4 Normalized field plots of real Ex (above) and Ey (below) components at the middle of waveguide width w1 (yz-plane), when w2=180 nm, Lc=4 μm, and λ0=1550 nm.
Figures 5(a) and 5(b) show the calculated CFHP0 and PCE, respectively, as a function of Lc for different waveguide width w2: w2 = 160 nm (blue), w2 = 180 nm (green), w2 = 200 nm (red), w2 = 220 nm (cyan), and w2 = 240 nm (purple). Notice that the maximum CFHP0 is over 60% with an ultrashort conversion length Lc of ∼ 4 μm. Also, the maximum PCE is ∼ 100% with w2 = 180 nm and w2 = 200 nm. The ripples on the graph are due to the Fabry-Pérot type resonances from the reflected lights within the PRC region. As w2 increases, the conversion lengths Lc of the maximum CFHP0 and PCE increase; this is consistent with our previous finding on conversion length in Fig. 3. The degree of CFHP0 is affected by the coupling efficiencies between other waveguides and the PCE, which depend on the w2 significantly. There are two loss factors that determine the coupling efficiencies. One is the reflection or scattering loss that comes from the modes mismatch between two different waveguide schemes, and the other is the material loss from the metal. As we increase the w2, the reflection or scattering loss will be reduced because the phases of PRCi modes approach to the phases of TE0,Si and HP0 modes as shown in Fig. 3. Also, increasing the w2 will enhance the mode overlap between PRCi and HP0 modes, improving the CFHP0. However, the material loss will be increased due to more exposure to the metal. The PCEs also vary for different w2, because w2 determines the field distribution of PRC0 and PRC1 modes, and essentially the modes overlap between them. The PCE of polarization rotator, which is based on hybrid modes interference, depends on the rotational angle of the optical axis θ and conversion length Lc as the following [4]:
where, L is the actual length of the structure. The rotational angle of optical axis θ can be defined by the distributions of the transverse magnetic field components as follows [4, 26]:Fig. 5 (a) CFHP0 and (b) PCE as a function of Lc for different w2 and tapered PRC: w2 = 160 nm (blue), w2 = 180 nm (green), w2 = 200 nm (red), w2 = 220 nm (cyan), w2 = 240 nm (purple), and tapered PRC (dashed black).
FEM mode calculations are conducted to find the field distributions for different w2, then θ is obtained using the Eq. (3). Figure 6 shows the estimated PCE of using the Eq. (2) for different w2. Here, we assume the device length L = Lc; the PCE depends solely on the optical axis rotation angle θ, which is determined by the field distributions of the hybrid mode PRC1. Notice that, in Fig. 6, the maximum PCE occurs around w2 = 180 nm, and the PCE decreases as w2 increases. This is consistent with the rigorous 3D FEM simulation results in Fig. 5(b), where the degree of PCE has the maximum value when w2 is between 180 nm and 200 nm, and then decrease as w2 increases. As a result of these related effects of coupling efficiencies and PCE, the maximum CFHP0 increases from w2 = 160 nm to w2 = 200 nm because of the reduced reflection or scattering loss, then starts to decrease after that because of the reduced PCE and increased material loss.
Fig. 6 Estimated PCE of PRC1 mode as a function of w2, using the Eq. (2). FEM mode calculations are conducted for different w2, and the rotation angle of the optical axis θ is obtained using the Eq. (3). Device length is assumed to be Lc.
3. Tapered polarization rotation and coupling (TPRC)
3.1. Design of the TPRC
To reduce the reflection or scattering loss at the interfaces, a metal taper can be introduced into the PRC structure. Figure 7 shows the schematic of the tapered polarization rotation and coupling (TPRC) structure. The geometric parameters and material components are set to the same as the PRC in Fig. 1. The CFHP0 and PCE as a function of Lc for the TPRC are plotted in Fig. 5(a) and 5(b), respectively, with dashed black lines. Notice that the CFHP0 of TPRC (the maximum CFHP0 ∼ 64%) is higher than the previous PRC designs, and the PCE of TPRC is comparable (the maximum PCE ∼ 100%) with other PRC designs. Furthermore, the TPRC has a broader fabrication tolerance in Lc. In tapers, an abrupt phase difference at the interface between TPRC and HP waveguide is avoided, thus improving the coupling efficiency at this interface. However, there will still be an abrupt phase difference at the interface between Si waveguide and TPRC, where a sharp metal tip exists. Typically, in all-dielectric waveguide, a gradual taper that keeps an asymmetric waveguide cross-section gives an adiabatic polarization rotation [3], as the underlying principle of polarization rotation is mode-evolution, and the transmission power of the rotated mode increases as the device length increases (no sinusoidal trend as in Fig. 5). However, the TPRC design that we present here is not based solely on mode-evolution, rather it is a combination of mode-coupling and mode-evolution. The critical difference from the purely dielectric taper is that highly confined plasmonic modes are excited at the narrow metal tip. This gives an abrupt phase difference and as a result, two different modes can be excited and converted into either PRC0 or PRC1. This would cause mode-coupling based interference and hence the sinusoidal trend. There is, still, an adiabatic mode-evolution between TPRC and HP waveguide (from PRC0 to HP0 mode); and this gives a higher fabrication tolerance in Lc compared to PRC as shown in Fig. 5. The Lc for the peak coupling factors (∼ 4.5 μm) is a little bit longer than PRC designs, but it is still very short compared to other dielectric polarization rotators.
Fig. 7 Schematic of the tapered polarization rotation and coupling (TPRC) structure. Geometric parameters and material composition are same as Fig. 1.
3.2. Different metal caps
Up to now, we have employed Cu as the plasmonic material due to its low resistivity and widespread use in current CMOS manufacturing technology. However, the material loss can be reduced by replacing the Cu with other plasmonic materials such as silver, gold, and aluminum [23, 24, 27]. To compare the performance of other plasmonic metals, more simulations are conducted on the same TPRC structure, but with different port widths of w2 = 380 nm (Cu), 375 nm (Ag), 380 nm (Ag), and 355 nm (Al), which corresponds to the optimized value for each material. Figure 8 shows the calculated CFHP0 as a function of Lc, which is similar to Fig. 5(a), but for the TPRC with different metal caps: Cu (blue), Ag (green), Au (red), and Al (cyan). Notice that, in Fig. 8, the TPRC with Ag, Au, or Al metal cap has higher CFHP0 (> 70%) than that with Cu metal cap. Ag and Au are well known as good plasmonic materials, with less absorption losses compared to other materials [27]. Here, the maximum CFHP0 of about 78% is achieved with Ag metal cap, and about 71% with Au. For Al, even though Al has higher material loss (larger imaginary permittivity) compared to other metals, it is highly metallic with a large negative permittivity (εAl = −229.78 + i46.12 at λ0 = 1550 nm [24]). Thus, the skin depth of Al is very low and less percentage of the total optical power is propagating in Al. This reduces the overall material absorption loss and yields lower propagation loss for the HP mode with Al cap than those with Au or Cu metal caps [27]. As a result, TPRC with Al shows higher CFHP0 than TPRC with Au or Cu, achieving the maximum CFHP0 of about 73%.
3.3. Different taper shapes
The effect of taper shapes is also evaluated with a linear [Eq. (4)] and exponential [Eq. (5)] taper shapes which can be described as the following:
where z0 and z1 are the starting and ending points in z direction, and a determines the degree of growth rate in exponential taper function. Figure 9(a) shows the contour of tapers in xy-plane with different taper shapes: linear (blue) and exponential tapers with a = 1 (green) and a = −1 (red). Here, z0 and z1 are set to 0 and Lc, respectively, and the width w1 is multiplied to each taper function. Cu is used as the metal cap. Figure 9(b) is the calculated CFHP0 as a function of Lc, which corresponds to each taper shape in Fig. 9(a). Calculations show that the exponential taper with a = 1 has higher CFHP0 than liner taper and exponential taper with a = −1; this is because, for the exponential taper with a = 1, more gradual tapering (slowly increasing w2) is introduced at narrow edge region where the mode changes abruptly. With the exponential taper (a = 1), about 5 % increase in CFHP0 has been achieved.Fig. 8 Calculated CFHP0 as a function of Lc for the TPRC with different metal caps and w2: Cu (w2 = 380 nm, blue), Ag (w2 = 375 nm, green), Au (w2 = 380 nm, red), and Al (w2 = 355 nm, cyan). The free space wavelength is λ0 = 1550 nm.
Fig. 9 (a) Taper shapes according to shape function in Eq. (4) and Eq. (5), and (b) Corresponding CFHP0 as a function of Lc for different taper shapes: linear (blue), and exponentials with a = 1 (green) and a = −1 (red).
4. Bandwidths of PRC and TPRC
The bandwidths of PRC and TPRC are also evaluated, and Fig. 10 shows the calculated CFHP0 as a function of the free space wavelength λ0, ranging from 1400 nm to 1700 nm, for PRC (blue line) and TPRC (green line). Cu is used as the metal cap for every case, and the geometric dimensions are chosen to have the maximum CFHP0 for each case: the PRC with w2 = 180 μm and Lc = 4 μm and the TPRC with Lc = 5 μm and linear taper. Other parameters are set to the same as in the original designs for each case. Notice that the TPRC has broader bandwidth than PRC. In general, the mode-evolution based PR has broader bandwidth than the mode-coupling based PR [3], and this is consistent with our results as TPRC is based on a combination of mode-evolution and mode-coupling, while PRC is solely based on mode-coupling. Nevertheless, even the mode-coupling based PRC has a relatively large bandwidth compared to a typical all-dielectric mode-coupling based PR; this is because the plasmonic modes (HP0, PRC0, and PRC1 modes) are relatively less sensitive to the wavelength compared to other all-dielectric waveguide modes. If we define an operating 3-dB bandwidth as CFHP0 ≥ 50 % (coupling loss is below 3 dB), the operating bandwidths are ∼ 200 nm and ∼ 250 nm for PRC and TPRC, respectively.
Fig. 10 The CFHP0 as a function of the free space wavelength λ0 for the PRC (w2 = 180 μm and Lc = 4 μm, in blue) and the TPRC (Lc = 5 μm, in green).
5. Conclusion
In conclusion, we presented a class of polarization rotation and coupling designs that rotate the TE0 mode and simultaneously couple it to the HP0 mode. With a Cu metal cap, which is compatible with current CMOS technology, the coupling factor to the HP0 mode can be over 60% and the PCE is almost 100%. About 2% or 5% higher coupling factors can be achieved with a linear or exponential metal taper, respectively. The device sizes are very short with a conversion length of about 4.5 μm, and the 3 dB bandwidths are over 200 nm. Higher performance can be achieved with different metal caps, and about 78% of coupling factor is achieved with a Ag metal cap. The polarization rotation and coupling scheme that we presented here has potential in future Si/plasmonic hybrid PICs.
Acknowledgments
This work is supported in part by National Science Foundation grant CMMI-1120577, Defense Threat Reduction Agency grants HDTRA110-1-0106 and HDTRA1-07-C-0042, National Institute of Health grant 1R01RR026273-01, Air Force Office of Scientific Research grant FA9550-12-1-0236, and DARPA PULSE program grant W31P40-13-1-0018 from AMRDEC.
References and links
1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006). [CrossRef]
2. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron 12, 1678–1687 (2006). [CrossRef]
3. M. Watts and H. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30, 138–140 (2005). [CrossRef] [PubMed]
4. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23, 432 (2005). [CrossRef]
5. Z. Wang and D. Dai, “Ultrasmall Si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B 25, 747–753 (2008). [CrossRef]
6. V. J. Sorger, R. F. Oulton, R.-M. Ma, and X. Zhang, “Toward integrated plasmonic circuits,” MRS bulletin 37, 728–738 (2012). [CrossRef]
7. M. L. Brongersma and V. M. Shalaev, “Applied physics the case for plasmonics,” Science 328, 440–441 (2010). [CrossRef] [PubMed]
8. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007). [CrossRef] [PubMed]
9. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Supermode propagation in low index medium,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2007), paper JThD112.
10. M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photon. Rev. 8, 394–408 (2014). [CrossRef]
11. R. F. Oulton, V. J. Sorger, D. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nature Photon. 2, 496–500 (2008). [CrossRef]
12. V. J. Sorger, N. D. Lanzillotti-Kimura, R.-M. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1, 17–22 (2012). [CrossRef]
13. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009). [CrossRef] [PubMed]
14. S. Kim and M. Qi, “Copper nanorod array assisted silicon waveguide polarization beam splitter,” Opt. Express 22, 9508–9516 (2014). [CrossRef] [PubMed]
15. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10, 4851–4857 (2010). [CrossRef] [PubMed]
16. A. Emboras, R. M. Briggs, A. Najar, S. Nambiar, C. Delacour, P. Grosse, E. Augendre, J. Fedeli, B. de Salvo, H. A. Atwater, and R. Espiau de Lamaestre, “Efficient coupler between silicon photonic and metal-insulator-silicon-metal plasmonic waveguides,” Appl. Phys. Lett. 101, 251117 (2012). [CrossRef]
17. Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, “Broadband coupler between silicon waveguide and hybrid plasmonic waveguide,” Opt. Express 18, 13173–13179 (2010). [CrossRef] [PubMed]
18. L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995). [CrossRef]
19. 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). [CrossRef] [PubMed]
20. J. Zhang, S. Zhu, S. Chen, G.-Q. Lo, and D.-L. Kwong, “An ultracompact surface plasmon polariton-effect-based polarization rotator,” IEEE Photon. Technol. Lett. 23, 1606–1608 (2011). [CrossRef]
21. J. N. Caspers, M. Alam, and M. Mojahedi, “Compact hybrid plasmonic polarization rotator,” Opt. Lett. 37, 4615–4617 (2012). [CrossRef] [PubMed]
22. J. N. Caspers, J. S. Aitchison, and M. Mojahedi, “Experimental demonstration of an integrated hybrid plasmonic polarization rotator,” Opt. Lett. 38, 4054–4057 (2013). [CrossRef] [PubMed]
23. E. D. Palik, Handbook of Optical Constants of Solids, Vol. 3 (Academic, 1998).
24. A. D. Rakic, A. B. Djurišic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]
25. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University, 2006).
26. V. P. Tzolov and M. Fontaine, “A passive polarization converter free of longitudinally-periodic structure,” Opt. Commun. 127, 7–13 (1996). [CrossRef]
27. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795–808 (2010). [CrossRef]
