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Mode-coupling polarization rotator based on plasmonic waveguide Lin Jin, Qin Chen,* and Long Wen Key Laboratory of Nanodevices and Applications-CAS & Collaborative Innovation Center of Suzhou Nano Science and Technology, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences (CAS), Suzhou 215123, China *Corresponding author: [email protected] Received January 22, 2014; revised March 14, 2014; accepted April 3, 2014; posted April 3, 2014 (Doc. ID 205228); published April 30, 2014 A novel polarization rotator (PR) based on mode coupling in plasmonic waveguides is demonstrated by simulation. A silicon waveguide with asymmetric claddings of silicon oxide and metal is applied to induce a hybridization of the polarization modes. Operating at the telecommunication wavelength of 1.55 μm, polarization conversion efficiency of 99.7% can be achieved in a device at a length of 9.7 μm with an insertion loss of 2.2 dB. This PR can be easily fabricated by oblique deposition of the claddings after etching the silicon waveguide without precise alignment for two-step lithography as required in a previous design. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5440) Polarization-selective devices; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.39.002798
Photonic integrated circuit (PIC) is a ground-breaking technology for optical fiber communications due to its high bit rate for data processing. Silicon-on-insulator (SOI) technology provides a promising platform for developing PIC because of the compatibility with mature complementary metal-oxide-semiconductor technologies and its high-index-contrast (HIC) for compact microphotonic/nanophotonic devices. However, the considerable difference of propagation constant resulting from the HIC in these devices induces polarization-dependent dispersion and loss, which are severe issues because the polarization state changes randomly in optical fibers [1]. In addition, polarization division multiplexing has attracted much attention recently [2,3]. Therefore, a polarization diversity system with polarization manipulating capability is becoming more and more important for PIC [4,5]. A polarization rotator (PR) is a key component in which the input light in one polarization state is converted to the other polarization state at the output by mode coupling [6–8] or mode evolution [9–11]. The modecoupling-based PRs utilizing the mode beating behavior are more compact [8]. Although active PRs or passive PRs with longitudinally periodic structures have been reported [12,13], single-section passive PRs are preferred for practical applications because there is loss at the junction between the neighboring sections in multisection PRs and the active PRs have more power consumption [6]. Tzolov and Fontaine proposed an asymmetric waveguide PR in which the cross section of the waveguide has a slanted sidewall allowing the generation of two hybrid modes that induce the polarization rotation [6]. In this case, the input light first couples to two hybrid modes in the PR and the two modes have a relative phase shift of π after propagating for a half-beat length. As a result, light coupled to the output waveguide completely changes its polarization state compared to the input one. Wang et al. proposed a waveguide PR with a stair-like cross section instead of the slanted sidewall [8] and the device was experimentally demonstrated by Aamer et al. with a polarization conversion efficiency of −0.85 dB in a 25 μm long device [14]. The PCE is defined as the output power 0146-9592/14/092798-04$15.00/0
ratio of the desired polarization to the sum of both polarizations. For transverse electric (TE) input, PCETE P TM ∕P TE P TM , P TE , and P TM are the output powers of TE and transverse magnetic (TM) polarizations, respectively. Although the stair-like waveguide PRs can be relatively easier for fabrication compared to the slanted waveguide ones, two-step lithography and etch processes are required with precise alignment. Alternative designs for PRs also suffer from the complex waveguide structure that is difficult to fabricate [15,16]. Recently, Gao et al. proposed a plasmonic waveguide PR with a metal film partially covering the silicon waveguide [17]. The asymmetric cross section induces a hybridization of the polarization modes and a large mode index contrast between the two plasmonic waveguide modes was observed. As a result, an ultracompact (3.2 μm) PR shows a PCE of 99.5% in simulation. Because the PCE is sensitive to the width and position of the metal film on the silicon waveguide, the fabrication of this device is still challenging due to the precise alignment in lithography. Some other PRs based on mode evolution in plasmonic waveguides were also reported [18,19]. However, the fabrication is very difficult due to the complex structures. In this Letter, we present a mode-coupling PR based on a silicon waveguide partially cladded by a thin film of silica and metal. Lithography with a large tolerance of alignment and a one-step etch are required to fabricate this device. The asymmetric cross section for mode hybridization can be realized by oblique deposition process. In an optimized structure, sub-10 μm waveguide length is enough to achieve a PCE over 99% for a TE polarization input with a reasonably low insertion loss [IL, −10 logP TM ∕P Input , P Input is the input power]. The present design is shown in Fig. 1, where a thin film of silicon oxide and silver covers the top plane and the right-hand-side sidewall of the silicon waveguide. As well known, this metal/insulator/silicon (MIS) waveguide has excellent propagating properties, such as low loss and strong field confinement [20]. Our previous work on full-cladding silicon plasmonic waveguides shows that this type of waveguide could support mode propagation © 2014 Optical Society of America
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Fig. 1. Schematic cross section of the proposed modecoupling plasmonic waveguide PR.
of both polarizations and have very low difference of propagation constant [21]. When the metal and silicon oxide layers are removed from one sidewall of the silicon waveguide as shown in Fig. 1, hybridization of the two polarization modes occurs and ensures the polarization rotation along the propagation. By controlling the deposition condition, the film thickness on the top plane and the sidewall could be nearly the same. As a result, the whole waveguide has a quasi-45° symmetry due to the strong confinement of the modes inside the silicon oxide layer. The full symmetry could be obtained by depositing additional silicon oxide cladding over the whole structure as [14]. After propagating for a conversion length LC π∕β1 − β2 λ∕2Δn, where β1 and β2 are the propagation constants of the two hybrid modes, Δn is the hybrid mode index difference, λ is the wavelength, the two modes have a relative phase shift of π, which results in a complete polarization conversion. A figure-of-merit of a PR is PCE. As discussed in [7], in a mode-coupling scheme the PCE is related to the hybrid mode optical axis rotation angle θ and LC : 2 2 πL : (1) PCE sin 2θsin 2LC In [3,4], the rotation angle θ is defined by the transverse electric fields. However, the calculation accuracy of the electric fields in the case of a MIS waveguide is very sensitive to the mesh allocation due to the discontinuity of the normal component of the electric field at the interface [22]. Here, we define θ by the transverse magnetic fields: ZZ 2 H x x; ydxdy : (2) tanθ R H 2y x; ydxdy The mode property was investigated by threedimensional FDTD simulation (3D-FDTD, Lumerical Solutions, Inc.) [23]. The refractive indices of silicon and silicon dioxide are 3.48 and 1.44, respectively, the dielectric constant of a silver cladding is assumed to be −86.64 8.74i at 1.55 μm [24]. The calculated electric and magnetic fields of the two hybrid modes are shown in Fig. 2. It is clear that the electric fields are confined in the thin oxide layer. The half-cladding oxide and metal layers provide an asymmetric field profile that is necessary for polarization mode hybridization. The magnetic field profiles indicate a large overlap of the two modes and a near −45° rotation angle, which results in a PCE close to 100% at a device length of LC . For the structure shown in Fig. 2,
Fig. 2. (a), (b) Electric and (c), (d) magnetic field profiles of hybrid mode 1 (a) and (c), hybrid mode 2 (b) and (d). W Si H Si 310 nm, W SiO2 H SiO2 50 nm, W Ag H Ag 80 nm.
the calculated Δn is 0.08 and θ 47.9°. Therefore, we have TE polarization (with a main electric field in the x direction) input. TM polarization (with a main electric field in the y direction) has approximately the same results. Notice that the theoretical result of PCE by Eq. (1) is an approximate result and it is only valid if the optical axes of the two hybrid modes are perpendicular. We use an accurate numerical algorithm based on mode coupling [23] to calculate PCE and get a slightly higher value of 99.5%, and the IL is found to be 2.2 dB. Actually, the sum of the two calculated θ defined in Eq. (2) or [8,17] are not exactly 90° for a pair of hybrid modes. Furthermore, the deviation from 90° is observed in plasmonic waveguides. For example, the device in [17] with a metal strip of 120 and 180 nm has a θ of 82.7° and 90.7°, respectively. In this case, we cannot use Eq. (1) to calculate PCE directly. The numerical calculation gives a PCE of 98.1% for the 180 nm metal strip for TE polarization input, which is smaller than the claimed value by Eq. (1). Based on a square cross section silicon waveguide, both additive and subtractive deformations could induce a nonzero θ. The latter can be realized by a corner cut as in [7,8]. For additive deformation, half-cladding with a thin film of silicon oxide (similar to Fig. 1 but no metal) only induce a very small Δn of 0.001, which results in a device length over 700 μm. In the proposed structure (Fig. 1), additional metal claddings greatly improve Δn due to the plasmonic mode property and therefore achieve a compact device. Compared to the design with subtractive deformation or the additive deformation in [17], the present waveguide PR can be easily fabricated by oblique deposition of silicon oxide and metal after etching the silicon waveguide without precise alignment for two-step lithography. Detailed investigation of the structure dimension to the device performance are shown in Fig. 3. Here, only TE polarization input is considered. In Fig. 3(a), LC shows a monotonic decrease with W Si . Actually, at W Si 160 nm, Δn is over 0.33 resulting in a ultracompact device of a length of 2.3 μm. However, the coupling
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Fig. 3. (a) CE and conversion length (LC ), (b) PCE and rotation angle (θ) versus W Si H Si at W SiO2 H SiO2 50 nm and W Ag H Ag 30 nm, 50, 100, and 150 nm, respectively.
efficiency (CE, the efficiency of optical power transferring between PR and silicon input/output waveguide) decreases with the shrinkage of the silicon waveguide, which can be understood as a result of the weak mode confinement of a small waveguide. These variation trends are similar for different W Ag . But for a smaller W Ag , CE is lower and LC is smaller, which may be the result of the stronger plasmonic effect in a thin metal film. We also can see from Fig. 3(b) that the rotation angle θ can be tuned by W Si and W Ag . Around θ 45°, a maximum of PCE can be obtained, which is predicted by Eq. (1). The silicon oxide layer is also important to the device performance. Due to the ohmic loss in metal, an intermediate film of oxide layer between silicon and metal can reduce the mode loss and offer one more free degree in optimization. As shown in Fig. 4, we can see that the propagation loss of the two hybrid modes
Fig. 4. Propagation loss of two hybrid modes and LC versus W SiO2 H SiO2 at W Si H Si 300 nm and W Ag H Ag 50 nm, respectively.
Fig. 5. Transverse electric field distributions in the x–z plane at the center of Si core for (a), (b) TM and (c), (d) TE polarization input. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
decreases with the increasing silicon oxide thickness due to the less overlap of the field with the metal. However, LC increases for a thick silicon oxide layer due to the reduced mode index difference. In order to verify the proposed PR and demonstrate the device performance, 3D-FDTD simulations were carried out for an optimized structure with W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm. The PR length is 9.7 μm. From Figs. 5(a) and 5(b), we can see that the dominant component E y attenuates in the PR but E x appears in the PR and becomes stronger along the devices. As a result, TM polarization is rotated to TE polarization. The similar polarization rotation phenomenon is also observed for TE polarization input. As in [17], we define extinction ratio (ER) for TE polarization input as 10 logP TM ∕P TE .
Fig. 6. Wavelength dependence of the PCE and IL. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
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zation of the polarization modes. The plasmonic mode in the MIS waveguide gives a large mode index difference and a relatively low loss. In an optimized device, we achieve PCE of 99.7% in a compact device of 9.7 μm with an IL of 2.2 dB. Furthermore, this PR can be easily fabricated without fine alignment for the two-step lithography as required in previous design.
Fig. 7. Dependence of PCE on the deviation of the conversion length. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
The calculated PCE, ER and IL, are 99.7%, 26.2, and 2.2 dB, respectively. The spectral responses of PCE and IL are plotted in Fig. 6. The bandwidth is as large as 200 nm for a PCE over 95%. Specifically, for the entire C band PCE is larger than 99% and the ER is over 20 dB. The wide-bandwidth makes the PR available for many applications. Figure 7 shows PCE as a function of LC . The tolerance of LC is approximately 2 μm for PCE over 90%. In addition, for a commercial SOI wafer with a 250 nm thick silicon device layer, an optimized PR has H Si 250 nm, W Si 360 nm, H SiO2 40 nm, W SiO2 50 nm, W Ag H Ag 100 nm. In this case, a PCE of 99.9% can be achieved for TE polarization input at a device length of LC 9.07 μm. The electric and magnetic fields of the two hybrid modes are shown in Fig. 8, where a large overlap and desired mode hybridization are achieved via optimizing the thickness of SiO2 . This can be realized by anisotropic etching. In conclusion, we presented a novel PR based on plasmonic waveguides, where asymmetric claddings of silicon oxide and metal are applied to induce a hybridi-
Fig. 8. Optimized device for the PCE via using different heights and widths of the Si core and SiO2 layer. (a), (b) Electric and (c), (d) magnetic field profiles of hybrid mode 1 (a) and (c), hybrid mode 2 (b) and (d). H Si 250 nm, W Si 360 nm, H SiO2 40 nm, W SiO2 50 nm, W Ag H Ag 100 nm.
This work is supported by the Hundred Talents Program of Chinese Academy of Sciences, the Natural Science Foundation of Jiangsu Province for Youths (No. BK20130365), the Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1302108B), and the Opened Fund of the State Key Laboratory on Integrated Optoelectronics (No. IOSKL2013KF01). References 1. B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quantum Electron. 6, 317 (2000). 2. Y. G. Qin, Y. Yu, J. H. Zou, M. Y. Ye, L. Xiang, and X. L. Zhang, Opt. Express 21, 25727 (2013). 3. H. Keang-Po and J. M. Kahn, J. Lightwave Technol. 32, 614 (2014). 4. T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, Nat. Photonics 1, 57 (2007). 5. D. Dai, L. Liu, S. Gao, D.-X. Xu, and S. He, Laser Photon. Rev. 7, 303 (2013). 6. V. P. Tzolov and M. Fontaine, Opt. Commun. 127, 7 (1996). 7. H. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, J. Lightwave Technol. 23, 432 (2005). 8. Z. C. Wang and D. X. Dai, J. Opt. Soc. Am. B 25, 747 (2008). 9. M. R. Watts and H. A. Haus, Opt. Lett. 30, 138 (2005). 10. J. N. Caspers, M. Z. Alam, and M. Mojahedi, Opt. Lett. 37, 4615 (2012). 11. Y. H. Fei, L. B. Zhang, T. T. Cao, Y. M. Cao, and S. W. Chen, IEEE Photon. Technol. Lett. 25, 879 (2013). 12. R. C. Alferness, Appl. Phys. Lett. 36, 513 (1980). 13. H. Heidrich, P. Albrecht, M. Hamacher, H. P. Nolting, H. Schroeter-Janssen, and C. M. Weinert, IEEE Photon. Technol. Lett. 4, 34 (1992). 14. M. Aamer, A. M. Gutierrez, A. Brimont, D. Vermeulen, G. Roelkens, J. M. Fedeli, A. Hakansson, and P. Sanchis, IEEE Photon. Technol. Lett. 24, 2031 (2012). 15. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, Opt. Express 16, 2628 (2008). 16. G. Chen, L. Chen, W. Ding, F. Sun, and R. Feng, Opt. Lett. 38, 1984 (2013). 17. L. F. Gao, Y. J. Huo, J. S. Harris, and Z. P. Zhou, IEEE Photon. Technol. Lett. 25, 2081 (2013). 18. J. Zhang, S. Y. Zhu, S. Y. Chen, G. Q. Lo, and D. L. Kwong, IEEE Photon. Technol. Lett. 23, 1606 (2011). 19. M. Komatsu, K. Saitoh, and M. Koshiba, IEEE Photon. Technol. Lett. 4, 707 (2012). 20. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008). 21. L. Jin, Q. Chen, and S. C. Song, Opt. Lett. 38, 3078 (2013). 22. D. Correia, J. P. da Silva, and I. T. Lima, IEEE Photon. Technol. Lett. 15, 915 (2003). 23. http://www.lumerical.com. 24. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
OPTICS LETTERS / Vol. 39, No. 9 / May 1, 2014
Mode-coupling polarization rotator based on plasmonic waveguide Lin Jin, Qin Chen,* and Long Wen Key Laboratory of Nanodevices and Applications-CAS & Collaborative Innovation Center of Suzhou Nano Science and Technology, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences (CAS), Suzhou 215123, China *Corresponding author: [email protected] Received January 22, 2014; revised March 14, 2014; accepted April 3, 2014; posted April 3, 2014 (Doc. ID 205228); published April 30, 2014 A novel polarization rotator (PR) based on mode coupling in plasmonic waveguides is demonstrated by simulation. A silicon waveguide with asymmetric claddings of silicon oxide and metal is applied to induce a hybridization of the polarization modes. Operating at the telecommunication wavelength of 1.55 μm, polarization conversion efficiency of 99.7% can be achieved in a device at a length of 9.7 μm with an insertion loss of 2.2 dB. This PR can be easily fabricated by oblique deposition of the claddings after etching the silicon waveguide without precise alignment for two-step lithography as required in a previous design. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5440) Polarization-selective devices; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.39.002798
Photonic integrated circuit (PIC) is a ground-breaking technology for optical fiber communications due to its high bit rate for data processing. Silicon-on-insulator (SOI) technology provides a promising platform for developing PIC because of the compatibility with mature complementary metal-oxide-semiconductor technologies and its high-index-contrast (HIC) for compact microphotonic/nanophotonic devices. However, the considerable difference of propagation constant resulting from the HIC in these devices induces polarization-dependent dispersion and loss, which are severe issues because the polarization state changes randomly in optical fibers [1]. In addition, polarization division multiplexing has attracted much attention recently [2,3]. Therefore, a polarization diversity system with polarization manipulating capability is becoming more and more important for PIC [4,5]. A polarization rotator (PR) is a key component in which the input light in one polarization state is converted to the other polarization state at the output by mode coupling [6–8] or mode evolution [9–11]. The modecoupling-based PRs utilizing the mode beating behavior are more compact [8]. Although active PRs or passive PRs with longitudinally periodic structures have been reported [12,13], single-section passive PRs are preferred for practical applications because there is loss at the junction between the neighboring sections in multisection PRs and the active PRs have more power consumption [6]. Tzolov and Fontaine proposed an asymmetric waveguide PR in which the cross section of the waveguide has a slanted sidewall allowing the generation of two hybrid modes that induce the polarization rotation [6]. In this case, the input light first couples to two hybrid modes in the PR and the two modes have a relative phase shift of π after propagating for a half-beat length. As a result, light coupled to the output waveguide completely changes its polarization state compared to the input one. Wang et al. proposed a waveguide PR with a stair-like cross section instead of the slanted sidewall [8] and the device was experimentally demonstrated by Aamer et al. with a polarization conversion efficiency of −0.85 dB in a 25 μm long device [14]. The PCE is defined as the output power 0146-9592/14/092798-04$15.00/0
ratio of the desired polarization to the sum of both polarizations. For transverse electric (TE) input, PCETE P TM ∕P TE P TM , P TE , and P TM are the output powers of TE and transverse magnetic (TM) polarizations, respectively. Although the stair-like waveguide PRs can be relatively easier for fabrication compared to the slanted waveguide ones, two-step lithography and etch processes are required with precise alignment. Alternative designs for PRs also suffer from the complex waveguide structure that is difficult to fabricate [15,16]. Recently, Gao et al. proposed a plasmonic waveguide PR with a metal film partially covering the silicon waveguide [17]. The asymmetric cross section induces a hybridization of the polarization modes and a large mode index contrast between the two plasmonic waveguide modes was observed. As a result, an ultracompact (3.2 μm) PR shows a PCE of 99.5% in simulation. Because the PCE is sensitive to the width and position of the metal film on the silicon waveguide, the fabrication of this device is still challenging due to the precise alignment in lithography. Some other PRs based on mode evolution in plasmonic waveguides were also reported [18,19]. However, the fabrication is very difficult due to the complex structures. In this Letter, we present a mode-coupling PR based on a silicon waveguide partially cladded by a thin film of silica and metal. Lithography with a large tolerance of alignment and a one-step etch are required to fabricate this device. The asymmetric cross section for mode hybridization can be realized by oblique deposition process. In an optimized structure, sub-10 μm waveguide length is enough to achieve a PCE over 99% for a TE polarization input with a reasonably low insertion loss [IL, −10 logP TM ∕P Input , P Input is the input power]. The present design is shown in Fig. 1, where a thin film of silicon oxide and silver covers the top plane and the right-hand-side sidewall of the silicon waveguide. As well known, this metal/insulator/silicon (MIS) waveguide has excellent propagating properties, such as low loss and strong field confinement [20]. Our previous work on full-cladding silicon plasmonic waveguides shows that this type of waveguide could support mode propagation © 2014 Optical Society of America
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Fig. 1. Schematic cross section of the proposed modecoupling plasmonic waveguide PR.
of both polarizations and have very low difference of propagation constant [21]. When the metal and silicon oxide layers are removed from one sidewall of the silicon waveguide as shown in Fig. 1, hybridization of the two polarization modes occurs and ensures the polarization rotation along the propagation. By controlling the deposition condition, the film thickness on the top plane and the sidewall could be nearly the same. As a result, the whole waveguide has a quasi-45° symmetry due to the strong confinement of the modes inside the silicon oxide layer. The full symmetry could be obtained by depositing additional silicon oxide cladding over the whole structure as [14]. After propagating for a conversion length LC π∕β1 − β2 λ∕2Δn, where β1 and β2 are the propagation constants of the two hybrid modes, Δn is the hybrid mode index difference, λ is the wavelength, the two modes have a relative phase shift of π, which results in a complete polarization conversion. A figure-of-merit of a PR is PCE. As discussed in [7], in a mode-coupling scheme the PCE is related to the hybrid mode optical axis rotation angle θ and LC : 2 2 πL : (1) PCE sin 2θsin 2LC In [3,4], the rotation angle θ is defined by the transverse electric fields. However, the calculation accuracy of the electric fields in the case of a MIS waveguide is very sensitive to the mesh allocation due to the discontinuity of the normal component of the electric field at the interface [22]. Here, we define θ by the transverse magnetic fields: ZZ 2 H x x; ydxdy : (2) tanθ R H 2y x; ydxdy The mode property was investigated by threedimensional FDTD simulation (3D-FDTD, Lumerical Solutions, Inc.) [23]. The refractive indices of silicon and silicon dioxide are 3.48 and 1.44, respectively, the dielectric constant of a silver cladding is assumed to be −86.64 8.74i at 1.55 μm [24]. The calculated electric and magnetic fields of the two hybrid modes are shown in Fig. 2. It is clear that the electric fields are confined in the thin oxide layer. The half-cladding oxide and metal layers provide an asymmetric field profile that is necessary for polarization mode hybridization. The magnetic field profiles indicate a large overlap of the two modes and a near −45° rotation angle, which results in a PCE close to 100% at a device length of LC . For the structure shown in Fig. 2,
Fig. 2. (a), (b) Electric and (c), (d) magnetic field profiles of hybrid mode 1 (a) and (c), hybrid mode 2 (b) and (d). W Si H Si 310 nm, W SiO2 H SiO2 50 nm, W Ag H Ag 80 nm.
the calculated Δn is 0.08 and θ 47.9°. Therefore, we have TE polarization (with a main electric field in the x direction) input. TM polarization (with a main electric field in the y direction) has approximately the same results. Notice that the theoretical result of PCE by Eq. (1) is an approximate result and it is only valid if the optical axes of the two hybrid modes are perpendicular. We use an accurate numerical algorithm based on mode coupling [23] to calculate PCE and get a slightly higher value of 99.5%, and the IL is found to be 2.2 dB. Actually, the sum of the two calculated θ defined in Eq. (2) or [8,17] are not exactly 90° for a pair of hybrid modes. Furthermore, the deviation from 90° is observed in plasmonic waveguides. For example, the device in [17] with a metal strip of 120 and 180 nm has a θ of 82.7° and 90.7°, respectively. In this case, we cannot use Eq. (1) to calculate PCE directly. The numerical calculation gives a PCE of 98.1% for the 180 nm metal strip for TE polarization input, which is smaller than the claimed value by Eq. (1). Based on a square cross section silicon waveguide, both additive and subtractive deformations could induce a nonzero θ. The latter can be realized by a corner cut as in [7,8]. For additive deformation, half-cladding with a thin film of silicon oxide (similar to Fig. 1 but no metal) only induce a very small Δn of 0.001, which results in a device length over 700 μm. In the proposed structure (Fig. 1), additional metal claddings greatly improve Δn due to the plasmonic mode property and therefore achieve a compact device. Compared to the design with subtractive deformation or the additive deformation in [17], the present waveguide PR can be easily fabricated by oblique deposition of silicon oxide and metal after etching the silicon waveguide without precise alignment for two-step lithography. Detailed investigation of the structure dimension to the device performance are shown in Fig. 3. Here, only TE polarization input is considered. In Fig. 3(a), LC shows a monotonic decrease with W Si . Actually, at W Si 160 nm, Δn is over 0.33 resulting in a ultracompact device of a length of 2.3 μm. However, the coupling
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Fig. 3. (a) CE and conversion length (LC ), (b) PCE and rotation angle (θ) versus W Si H Si at W SiO2 H SiO2 50 nm and W Ag H Ag 30 nm, 50, 100, and 150 nm, respectively.
efficiency (CE, the efficiency of optical power transferring between PR and silicon input/output waveguide) decreases with the shrinkage of the silicon waveguide, which can be understood as a result of the weak mode confinement of a small waveguide. These variation trends are similar for different W Ag . But for a smaller W Ag , CE is lower and LC is smaller, which may be the result of the stronger plasmonic effect in a thin metal film. We also can see from Fig. 3(b) that the rotation angle θ can be tuned by W Si and W Ag . Around θ 45°, a maximum of PCE can be obtained, which is predicted by Eq. (1). The silicon oxide layer is also important to the device performance. Due to the ohmic loss in metal, an intermediate film of oxide layer between silicon and metal can reduce the mode loss and offer one more free degree in optimization. As shown in Fig. 4, we can see that the propagation loss of the two hybrid modes
Fig. 4. Propagation loss of two hybrid modes and LC versus W SiO2 H SiO2 at W Si H Si 300 nm and W Ag H Ag 50 nm, respectively.
Fig. 5. Transverse electric field distributions in the x–z plane at the center of Si core for (a), (b) TM and (c), (d) TE polarization input. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
decreases with the increasing silicon oxide thickness due to the less overlap of the field with the metal. However, LC increases for a thick silicon oxide layer due to the reduced mode index difference. In order to verify the proposed PR and demonstrate the device performance, 3D-FDTD simulations were carried out for an optimized structure with W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm. The PR length is 9.7 μm. From Figs. 5(a) and 5(b), we can see that the dominant component E y attenuates in the PR but E x appears in the PR and becomes stronger along the devices. As a result, TM polarization is rotated to TE polarization. The similar polarization rotation phenomenon is also observed for TE polarization input. As in [17], we define extinction ratio (ER) for TE polarization input as 10 logP TM ∕P TE .
Fig. 6. Wavelength dependence of the PCE and IL. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
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zation of the polarization modes. The plasmonic mode in the MIS waveguide gives a large mode index difference and a relatively low loss. In an optimized device, we achieve PCE of 99.7% in a compact device of 9.7 μm with an IL of 2.2 dB. Furthermore, this PR can be easily fabricated without fine alignment for the two-step lithography as required in previous design.
Fig. 7. Dependence of PCE on the deviation of the conversion length. W Si H Si 310 nm, W SiO2 H SiO2 50 nm, and W Ag H Ag 80 nm.
The calculated PCE, ER and IL, are 99.7%, 26.2, and 2.2 dB, respectively. The spectral responses of PCE and IL are plotted in Fig. 6. The bandwidth is as large as 200 nm for a PCE over 95%. Specifically, for the entire C band PCE is larger than 99% and the ER is over 20 dB. The wide-bandwidth makes the PR available for many applications. Figure 7 shows PCE as a function of LC . The tolerance of LC is approximately 2 μm for PCE over 90%. In addition, for a commercial SOI wafer with a 250 nm thick silicon device layer, an optimized PR has H Si 250 nm, W Si 360 nm, H SiO2 40 nm, W SiO2 50 nm, W Ag H Ag 100 nm. In this case, a PCE of 99.9% can be achieved for TE polarization input at a device length of LC 9.07 μm. The electric and magnetic fields of the two hybrid modes are shown in Fig. 8, where a large overlap and desired mode hybridization are achieved via optimizing the thickness of SiO2 . This can be realized by anisotropic etching. In conclusion, we presented a novel PR based on plasmonic waveguides, where asymmetric claddings of silicon oxide and metal are applied to induce a hybridi-
Fig. 8. Optimized device for the PCE via using different heights and widths of the Si core and SiO2 layer. (a), (b) Electric and (c), (d) magnetic field profiles of hybrid mode 1 (a) and (c), hybrid mode 2 (b) and (d). H Si 250 nm, W Si 360 nm, H SiO2 40 nm, W SiO2 50 nm, W Ag H Ag 100 nm.
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