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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 12646–12651
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Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits

Liu Liu, Yunhong Ding, Kresten Yvind, and Jørn M. Hvam  »View Author Affiliations


Optics Express, Vol. 19, Issue 13, pp. 12646-12651 (2011)
http://dx.doi.org/10.1364/OE.19.012646


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Abstract

A compact and efficient polarization splitting and rotating device built on the silicon-on-insulator platform is introduced, which can be readily used for the interface section of a polarization diversity circuit. The device is compact, with a total length of a few tens of microns. It is also simple, consisting of only two parallel silicon-on-insulator wire waveguides with different widths, and thus requiring no additional and nonstandard fabrication steps. A total insertion loss of −0.6dB and an extinction ratio of 12dB have been obtained experimentally in the whole C-band.

© 2011 OSA

1. Introduction

Silicon-on-insulator (SOI) has been considered recently as a promising platform for photonic circuits, largely driven by the CMOS-compatible fabrication technology and the high refractive-index contrast of the waveguide structure [1

1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

,2

2. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]

]. High-density integration and mass production of devices are therefore made possible. On the other hand, this high index contrast also induces a large polarization dependent dispersion or loss for normal components [3

3. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]

], and makes SOI inconvenient to integrate with other polarization insensitive platforms, like optical fiber networks. Instead of pursuing difficult polarization-independent devices on SOI, a polarization diversity scheme could be employed [4

4. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]

6

6. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4872. [CrossRef] [PubMed]

]. In this case, the orthogonal polarization components of the input light are first split into two different waveguides by using a polarization splitter [7

7. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12401. [CrossRef] [PubMed]

]. A polarization rotator is then employed in one of the waveguides to rotate the polarization 90° [8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

15

15. J. Zhang, M. Yu, G. Lo, and D. L. Kwong, “Silicon waveguide based mode-evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

]. Therefore, for the rest of the photonic chip only one polarization has to be processed. At the output, a copy of the polarization rotator and splitter can be implemented in order to combine the two polarizations without interference. We have successfully demonstrated a compact and efficient polarization converter on SOI based on the cross-polarization coupling between two SOI wires waveguide with different widths [8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

]. As compared to other polarization converters [9

9. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23(1), 432–445 (2005). [CrossRef]

15

15. J. Zhang, M. Yu, G. Lo, and D. L. Kwong, “Silicon waveguide based mode-evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

], this structure can be fabricated together with common deeply-etched SOI wire waveguides and devices, and thus requires no additional fabrication steps.

In this paper, we further extend the ability of the polarization converter in [8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

], and show that such a single device structure can be used for polarization splitting and rotating (PSR) simultaneously. Thus, a polarization diversity scheme on SOI can be readily implemented. We theoretically study the transmission properties of the proposed device. The optimized structures are also fabricated and characterized experimentally.

2. Design and simulation

The structure of the present PSR device is sketched in Fig. 1
Fig. 1 Schematic structure and working principle of the proposed polarization splitter and rotator. (a) three-dimensional model; (b) x-y cross-section; (c) x-z cross-section.
. It consists of two parallel SOI photonic wire waveguides coupled to each other. In order to achieve an efficient cross-polarization coupling, air is employed as the top-cladding. The widths (w 1 and w 2) of the two waveguides (waveguide 1 and waveguide 2, respectively) are adjusted so that the effective index of the fundamental transverse-magnetic (TM) mode in waveguide 1 is equal to that of the fundamental transverse-electric (TE) mode in waveguide 2, i.e., neff1,TM=neff2,TE, which is usually called the phase matching condition. In this case, an efficient coupling between these two modes can be achieved [8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

]. The effective index of a single SOI wire waveguide with air top-cladding at different widths is shown in Fig. 2
Fig. 2 Effective indices of the fundamental TE and TM modes of an air-cladded SOI wire waveguide with different widths w. The model is shown in the inset. h = 250 nm.
. Here, we choose w 1 = 600 nm and w 2 = 333 nm. The height h of the silicon waveguide layer is 250 nm, which is also the parameter of the SOI wafer used in the experiments. On the other hand, at the chosen widths the effective index neff1,TE of the TE mode in waveguide 1 is very different from that of any guided mode in waveguide 2 (cf. Figure 2). Therefore, according to the coupling mode theory the TE mode in waveguide 1 is expected to pass freely across the device. In general, such a structure in Fig. 1 exhibits the abilities to couple the TM mode from the input waveguide to the adjacent waveguide and simultaneously convert it into a TE mode, while leave the TE mode untouched in the input waveguide. This is exactly the characteristic of the interface section of a polarization diversity circuit, which is conventionally constructed by cascading an individual polarization splitter and rotator [4

4. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]

6

6. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4872. [CrossRef] [PubMed]

]. A similar structure of two SOI waveguides with the same width was used as a polarization splitter [7

7. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12401. [CrossRef] [PubMed]

]. In the proposed structure, an additional functionality of polarization rotation can be achieved.

In order to model accurately the transmission properties of the proposed device, a mode expansion and matching method [16

16. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com.

] is then employed, which is more suitable to deal with the structure involved here. Figure 4
Fig. 4 Simulated transmission coefficients between differently polarized modes from the input-port to the cross-port (a) and the through-port (b). The models are shown in the insets respectively. Here, w 1 = 600 nm, w 2 = 333 nm, g = 100 nm, h = 250 nm, and l = 36.8 μm. The transmission coefficients which are not presented are well below −35dB.
shows the transmission coefficients Tt(c)i-j when the coupling length l = 36.8 μm. Here, the subscript t or c indicates the response at the through-port or cross-port of the device (cf., Fig. 1), respectively. The superscript i-j, where i, j can be TE or TM, means the transmission from mode i at the input to mode j at the output. Considering the complexity, the simulation model is reduced correspondingly as shown in the insets of Fig. 4, where the bending sections are neglected. For the through-port response shown in Fig. 4(b), TtTE-TE remains close to 1 in the whole wavelength range of simulation. On the other hand, the TM mode from the input port is suppressed at the through port, and a dip is observed in the TtTM-TM curve at 1550 nm wavelength, which corresponds to the position where the phase-matching condition is fulfilled between the fundamental TM mode in waveguide 1 and the fundamental TE mode in waveguide 2. Accordingly, a peak is observed in the TcTM-TE curve shown in Fig. 4(a), which reaches 90%, corresponding to an overall insertion loss of −0.46dB. The unconverted TM mode power remains partly in the through-port (TtTM-TM) and the cross-port (TcTM-TM). They become the main source of cross-talk for the proposed device. Nevertheless, the extinction ratio is still better than 13dB in the whole C-band (1530 nm—1565 nm).

Similar to a common directional coupler on the SOI platform, the proposed PSR device also has a tight tolerance to the variations in device dimensions, e.g., waveguide widths. A slight deviation from the designed value will make the phase-matching condition fail, which will mainly result in a decrease in the efficiency of the cross-polarization coupling at the desired wavelength. We further study the influence of the variation in w 1 on the device performance. Figure 5(a)
Fig. 5 (a) Simulated transmission coefficients. Here, w 2 = 332 nm, 333 nm, 334 nm along the solid arrow direction, and the rest of the parameters are the same as those in Fig. 4. (b) Relation between w 1 and w 2 in order to maintain the phase-matching condition at 1550 nm.
shows the cross-port responses with w 1 = 332 nm, 333 nm, and 334 nm. One finds that the coupling wavelength peaking TcTM-TE shifts with a rate of about 15 nm/nm with respect to the variation of w 1. Figure 5(b) shows the relation between w 1 and w 2 in order to maintain the phase-matching condition at 1550 nm. It is almost a linear curve with a slop of about 12, which implies that the device performance is much less sensitive to the variation of w 2. This sensitivity difference can be explained by the local derivatives of the two curves shown in Fig. 2 at the working point. We also find that employing larger waveguide widths will improve the extinction ratio at the output and decrease the sensitivity to the dimension variations. On the other hand, this will weaken the strength of the cross-polarization coupling and increase the device length. A large waveguide cross-section will also make the effective indices of the high-order modes more close to those of the working fundamental modes (cf., Fig. 2). This will introduce unwanted coupling to those modes.

3. Experiment and measurement

We fabricated the designed devices on a commercial SOI wafer using E-beam lithography (JEOL JBX-9300FS) and dry etching technologies. A picture of a finished device is shown in Fig. 6
Fig. 6 Scanning electron microscope picture of a fabricated device. Arrows indicate propagation directions of the light.
. Adiabatic tapers were used at the input and two output ports for connecting with the standard single-mode SOI waveguide of 450 nm wide in the rest of the circuit [cf., Fig. 1(c)]. The fabricated samples were cleaved for characterization. The waveguides were tapered up to a width of 4 μm at the cleaved facets for better coupling with lensed fibers. The measurement results are illustrated in Fig. 7
Fig. 7 Measured transmission coefficients between different polarized modes from the input-port to the cross-port (a) and the through-port (b).
. We refer to Ref [8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

]. for the detailed measurement setup and calibration procedure. In general, the measured transmission curves are matching well those from the simulations in Fig. 4. The overall insertion loss and extinction ratio in the whole C-band is about −0.6dB and 12dB, respectively, slightly worse than the simulation results. Judged by the period, the fast oscillations observed in, e.g., the TcTM-TM curve is likely due to a slight error in calibrating the measurement setup [7

7. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12401. [CrossRef] [PubMed]

,8

8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

]. The fabrication repeatability of the proposed device was also studied. Figure 8
Fig. 8 Measured transmission coefficient TcTM-TE of two PSR devices with the same parameters on one SOI die.
shows the measured TcTM-TE curves for two PSR devices with the same designed parameters and on the same die. A good consistency can be found. Further investigation on improving the cross-die stability is also undertaken.

4. Conclusion

We have introduced a compact SOI-based PSR device used for the interface section of a polarization diversity circuit. The device is based on the cross-polarization coupling effect between two parallel SOI wire waveguides with air top-cladding, which can be fabricated in one lithography and etching step as needed for making the rest of the SOI circuit. We have demonstrated that such a single device structure can act as an efficient polarization splitter and rotator simultaneously. A total insertion loss of −0.6dB and an extinction ratio of 12dB have been obtained experimentally for a fabricated device.

References and links

1.

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

2.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]

3.

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]

4.

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]

5.

W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-4-1567. [CrossRef] [PubMed]

6.

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4872. [CrossRef] [PubMed]

7.

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12401. [CrossRef] [PubMed]

8.

L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

9.

H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23(1), 432–445 (2005). [CrossRef]

10.

M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]

11.

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Polarization rotator based on silicon wire waveguides,” Opt. Express 16(4), 2628–2635 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2628. [CrossRef] [PubMed]

12.

Y. Yue, L. Zhang, M. Song, R. G. Beausoleil, and A. E. Willner, “Higher-order-mode assisted silicon-on-insulator 90 degree polarization rotator,” Opt. Express 17(23), 20694–20699 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-23-20694. [CrossRef] [PubMed]

13.

Z. Wang and D. Dai, “Ultrasmall Si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B 25(5), 747–753 (2008). [CrossRef]

14.

K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Ultra-compact photonic crystal based polarization rotator,” Opt. Express 17(9), 7145–7158 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-9-7145. [CrossRef] [PubMed]

15.

J. Zhang, M. Yu, G. Lo, and D. L. Kwong, “Silicon waveguide based mode-evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

16.

FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com.

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(130.5440) Integrated optics : Polarization-selective devices

ToC Category:
Integrated Optics

History
Original Manuscript: April 11, 2011
Revised Manuscript: May 18, 2011
Manuscript Accepted: May 30, 2011
Published: June 15, 2011

Citation
Liu Liu, Yunhong Ding, Kresten Yvind, and Jørn M. Hvam, "Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits," Opt. Express 19, 12646-12651 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12646


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References

  1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]
  2. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]
  3. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High density integrated optics,” J. Lightwave Technol. 17(9), 1682–1692 (1999). [CrossRef]
  4. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]
  5. W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-4-1567 . [CrossRef] [PubMed]
  6. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4872 . [CrossRef] [PubMed]
  7. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-12401 . [CrossRef] [PubMed]
  8. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]
  9. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23(1), 432–445 (2005). [CrossRef]
  10. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]
  11. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Polarization rotator based on silicon wire waveguides,” Opt. Express 16(4), 2628–2635 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2628 . [CrossRef] [PubMed]
  12. Y. Yue, L. Zhang, M. Song, R. G. Beausoleil, and A. E. Willner, “Higher-order-mode assisted silicon-on-insulator 90 degree polarization rotator,” Opt. Express 17(23), 20694–20699 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-23-20694 . [CrossRef] [PubMed]
  13. Z. Wang and D. Dai, “Ultrasmall Si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B 25(5), 747–753 (2008). [CrossRef]
  14. K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Ultra-compact photonic crystal based polarization rotator,” Opt. Express 17(9), 7145–7158 (2009), http://www.opticsinfobase.org/abstract.cfm?uri=oe-17-9-7145 . [CrossRef] [PubMed]
  15. J. Zhang, M. Yu, G. Lo, and D. L. Kwong, “Silicon waveguide based mode-evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]
  16. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com .

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