Abstract

There has been a recent trend to reduce the size of photonic waveguide devices to enable high-density integration in silicon photonic integrated circuits. However, this miniaturization tends to result in increased polarization dependency. Particularly challenging is designing devices based on ring waveguides with small radii, which exacerbates the polarization sensitivity. For these microring resonators, a legitimate question is then: Is it possible to simultaneously maintain the conditions of single-mode and structural polarization independence while shrinking the size of both the bend radius and the waveguide cross section, and, if so, how small can the ring resonator be? We demonstrate theoretically the feasibility of achieving this via deeply etched submicrometer silicon-on-insulator rib waveguides, and we show that, for a given cladding and core thickness, the radius of a polarization independent microring resonator can be as small as 3μm, being limited chiefly by the residual birefringence of the resonator cavity and the bend losses.

© 2009 Optical Society of America

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References

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2008 (3)

2007 (3)

2006 (2)

D.-X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett. 18, 343-345 (2006).
[CrossRef]

F. Morichetti, A. Melloni, and M. Martinelli, “Effects of polarization rotation in optical ring-resonator-based devices,” J. Lightwave Technol. 24, 573-585 (2006).
[CrossRef]

2005 (7)

2004 (4)

E. Cassan, L. Vivien, and S. Laval, “Polarization-independent 90° turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths,” Opt. Commun. 235, 83-88 (2004).
[CrossRef]

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

D. Dai and S. He, “Analysis of characteristics of bent rib waveguides,” J. Opt. Soc. Am. A 21, 113-121 (2004).
[CrossRef]

M. K. Chin, C. L. Xu, and W. P. Huang, “Theoretical approach to a polarization insensitive single-mode microring resonator,” Opt. Express 12, 3245-3250 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

2001 (1)

2000 (2)

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

A. Yariv, “Universal relations for coupling of optical power between micro-resonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
[CrossRef]

1998 (1)

1994 (1)

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

1993 (1)

M. K. Smit, E. C. M. Pennings, and H. Blok, “A normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Absil, A. P.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Ang, Y. L.

Aydinli, A.

I. Kiyat, A. Aydinli, and N. Dagli, “Polarization characteristics of compact SOI rib waveguide racetrack resonators,” IEEE Photon. Technol. Lett. 17, 2098-2100 (2005).
[CrossRef]

Bachmann, M.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

Baehr-Jones, T.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

Baets, R.

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, 1567-1578 (2007).
[CrossRef] [PubMed]

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Beausoleil, R. G.

Besse, P. A.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

Blok, H.

M. K. Smit, E. C. M. Pennings, and H. Blok, “A normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Bogaerts, W.

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, 1567-1578 (2007).
[CrossRef] [PubMed]

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Brooks, C.

Brouckaert, J.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Cassan, E.

E. Cassan, L. Vivien, and S. Laval, “Polarization-independent 90° turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths,” Opt. Commun. 235, 83-88 (2004).
[CrossRef]

Chan, S. P.

Cheben, P.

D.-X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett. 18, 343-345 (2006).
[CrossRef]

W. Ye, D. X. Xu, S. Janz, P. Cheben, M. J. Picard, B. Lamontagne, and N. G. Tarr, “Birefringence control using stress engineering in silicon-on-insulator (SOI) waveguides,” J. Lightwave Technol. 23, 1308-1318 (2005).
[CrossRef]

Chin, M. K.

Cho, S.-Y.

Christiaens, I.

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

Chu, S. T.

Y. Yanagase, S. Suzuki, Y. Kokubun, and S. T. Chu, “Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter,” J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Dagli, N.

I. Kiyat, A. Aydinli, and N. Dagli, “Polarization characteristics of compact SOI rib waveguide racetrack resonators,” IEEE Photon. Technol. Lett. 17, 2098-2100 (2005).
[CrossRef]

Dai, D.

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwiched nanowires,” IEEE Photon. Technol. Lett. 19, 759-761 (2007).
[CrossRef]

D. Dai and S. He, “Analysis of characteristics of bent rib waveguides,” J. Opt. Soc. Am. A 21, 113-121 (2004).
[CrossRef]

Dapkus, P. D.

Deng, H.

Dumon, P.

Fukuda, H.

Galarza, M.

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

Gill, D.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

He, S.

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwiched nanowires,” IEEE Photon. Technol. Lett. 19, 759-761 (2007).
[CrossRef]

D. Dai and S. He, “Analysis of characteristics of bent rib waveguides,” J. Opt. Soc. Am. A 21, 113-121 (2004).
[CrossRef]

Headley, W. R.

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

W. R. Headley III, “Optical ring resonators in silicon-on-insulator,” Ph.D. dissertation (University of Surrey, 2005).

Ho, S. T.

Hochberg, M.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

Howe, S.

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Hryniewicz, J. V.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Huang, W. P.

Itabashi, S.

Janz, S.

D.-X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett. 18, 343-345 (2006).
[CrossRef]

W. Ye, D. X. Xu, S. Janz, P. Cheben, M. J. Picard, B. Lamontagne, and N. G. Tarr, “Birefringence control using stress engineering in silicon-on-insulator (SOI) waveguides,” J. Lightwave Technol. 23, 1308-1318 (2005).
[CrossRef]

Jessop, P. E.

Johnson, F. G.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Kimerling, L. C.

King, O.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Kiyat, I.

I. Kiyat, A. Aydinli, and N. Dagli, “Polarization characteristics of compact SOI rib waveguide racetrack resonators,” IEEE Photon. Technol. Lett. 17, 2098-2100 (2005).
[CrossRef]

Kokubun, Y.

Lamontagne, B.

Laval, S.

E. Cassan, L. Vivien, and S. Laval, “Polarization-independent 90° turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths,” Opt. Commun. 235, 83-88 (2004).
[CrossRef]

Lee, K. K.

Li, Y.

Lim, D. R.

Lim, S. T.

Little, B. E.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Liu, A.

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Liu, L.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Lopez-Amo, M.

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Martinelli, M.

Melchior, H.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

Melloni, A.

Moreno, J.

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

Morichetti, F.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

Ong, Y. A.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Elsevier, 1998), p. 548.

Paniccia, M.

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Passaro, V. M. N.

Pennings, E. C. M.

M. K. Smit, E. C. M. Pennings, and H. Blok, “A normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Picard, M. J.

Pluk, E.

Png, C. E.

Reed, G. T.

S. P. Chan, C. E. Png, S. T. Lim, V. M. N. Passaro, and G. T. Reed, “Single mode and polarization independent SOI waveguides with small cross section,” J. Lightwave Technol. 23, 2103-2111 (2005).
[CrossRef]

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Roelkens, G.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Rostami, A.

Rostami, G.

Scherer, A.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

Seiferth, F.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Selvaraja, S.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Shanton, J.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Shinojima, H.

Smit, M. K.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

M. K. Smit, E. C. M. Pennings, and H. Blok, “A normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Soldano, L. B.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

Song, M.

Soref, R.

Suzuki, S.

Taillaert, D.

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, 1567-1578 (2007).
[CrossRef] [PubMed]

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Tarr, N. G.

Trakalo, M.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Tsuchizawa, T.

Van, V.

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

Van Thourhout, D.

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, 1567-1578 (2007).
[CrossRef] [PubMed]

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Vermeulen, D.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

Vivien, L.

E. Cassan, L. Vivien, and S. Laval, “Polarization-independent 90° turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths,” Opt. Commun. 235, 83-88 (2004).
[CrossRef]

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T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005).
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Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwiched nanowires,” IEEE Photon. Technol. Lett. 19, 759-761 (2007).
[CrossRef]

Watanabe, T.

Willner, A. E.

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Xu, D.-X.

D.-X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett. 18, 343-345 (2006).
[CrossRef]

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Appl. Phys. B (1)

M. Galarza, J. Moreno, M. Lopez-Amo, I. Christiaens, D. Van Thourhout, and R. Baets, “Simple low-loss waveguide bends using ARROW effect,” Appl. Phys. B 80, 745-748(2005).
[CrossRef]

Appl. Phys. Lett. (2)

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

W. R. Headley, G. T. Reed, A. Liu, M. Paniccia, and S. Howe, “Polarization-independent optical racetrack resonators using rib waveguide on silicon-on-insulator,” Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between micro-resonators and dielectric waveguides,” Electron. Lett. 36, 321-322 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

I. Kiyat, A. Aydinli, and N. Dagli, “Polarization characteristics of compact SOI rib waveguide racetrack resonators,” IEEE Photon. Technol. Lett. 17, 2098-2100 (2005).
[CrossRef]

D.-X. Xu, S. Janz, and P. Cheben, “Design of polarization-insensitive ring resonators in silicon-on-insulator using MMI couplers and cladding stress engineering,” IEEE Photon. Technol. Lett. 18, 343-345 (2006).
[CrossRef]

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwiched nanowires,” IEEE Photon. Technol. Lett. 19, 759-761 (2007).
[CrossRef]

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

J. Lightwave Technol. (9)

M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16, 1433-1446 (1998).
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M. K. Smit, E. C. M. Pennings, and H. Blok, “A normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Y. Yanagase, S. Suzuki, Y. Kokubun, and S. T. Chu, “Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter,” J. Lightwave Technol. 20, 1525-1529 (2002).
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H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23, 432-445 (2005).
[CrossRef]

A. Rostami and G. Rostami, “All-optical implementation of tunable low-pass, high-pass, and bandpass optical filters using ring resonators,” J. Lightwave Technol. 23, 446-460 (2005).
[CrossRef]

W. Ye, D. X. Xu, S. Janz, P. Cheben, M. J. Picard, B. Lamontagne, and N. G. Tarr, “Birefringence control using stress engineering in silicon-on-insulator (SOI) waveguides,” J. Lightwave Technol. 23, 1308-1318 (2005).
[CrossRef]

S. P. Chan, C. E. Png, S. T. Lim, V. M. N. Passaro, and G. T. Reed, “Single mode and polarization independent SOI waveguides with small cross section,” J. Lightwave Technol. 23, 2103-2111 (2005).
[CrossRef]

F. Morichetti, A. Melloni, and M. Martinelli, “Effects of polarization rotation in optical ring-resonator-based devices,” J. Lightwave Technol. 24, 573-585 (2006).
[CrossRef]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

E. Cassan, L. Vivien, and S. Laval, “Polarization-independent 90° turns in single-mode micro-waveguides on silicon-on-insulator wafers for telecommunication wavelengths,” Opt. Commun. 235, 83-88 (2004).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Other (8)

E. D. Palik, Handbook of Optical Constants of Solids (Elsevier, 1998), p. 548.

W. Bogaerts, L. Liu, S. Selvaraja, J. Brouckaert, D. Taillaert, D. Vermeulen, G. Roelkens, D. Van Thourhout, and R. Baets, “Silicon nanophotonic waveguides and their applications,” presented at Asia-Pacific Optical Communications Conference (APOC), Hangzhou, China, 26-30 October 2008 (invited).

S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, A. P. Absil, F. G. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact full C-band tunable filters for 50 GHz channel spacing based on high order microring resonators,” Conference on Lasers and Electro-Optics (IEEE, 2004), paper PDP9

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

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W. R. Headley III, “Optical ring resonators in silicon-on-insulator,” Ph.D. dissertation (University of Surrey, 2005).

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Figures (15)

Fig. 1
Fig. 1

Cross sectional area of submicrometer rib structure, with width W, height H, and etch depth D.

Fig. 2
Fig. 2

Boundary lines for SMC cutoff dimensions of a submicrometer rib for λ 0 = 1.55 μm at H = 0.4 μm . The area where only TE 00 and TM 00 exist marks the TE and TM SM region. The PI locus that falls into the SM region signifies dimensions that allow both SM and PI operation.

Fig. 3
Fig. 3

Calculated effective indices for quasi-TE and quasi-TM waveguide modes as a function of waveguide width for an etch depth of 0.37 μm for a straight waveguide. The inset shows the close to circular PI modal profile at critical width.

Fig. 4
Fig. 4

Birefringence-free waveguide dimensions of fundamental modes for waveguide height H = 0.4 μm at a wavelength of 1.55 μm . As the rib transforms to a channel WG, PI and SM conditions cannot be fulfilled simultaneously.

Fig. 5
Fig. 5

Calculated effective indices for the quasi-TE and quasi-TM modes as a function of width for straight and curved WGs at bend radii (R) 2 and 4 μm , all at etch depth of 0.37 μm . The dotted line points to the various critical widths W c for each R. Bend W c decreases and tends to that of the straight WG (marked by a thick dotted line to extreme left) with increasing R.

Fig. 6
Fig. 6

Plot of effective index of 90 ° bend as a function of bend radius R at a fixed cross section that is based on the PI dimension ( D = 0.37 μm and W c ( straight ) = 0.39 μm ) of the straight WG, whose effective index is also plotted for comparison. Using the PI dimension ( D = 0.37 μm and W c ( straight ) = 0.39 μm ), the straight WG is ZBC, but the bend is birefringent. The bend birefringence reduces and approaches zero as R increases.

Fig. 7
Fig. 7

Loci of PI critical widths W c at varying bend radius for different etch depths for a fixed silicon height of 0.4 μm at a wavelength of 1.55 μm . The inset shows the transformation of the radial mode into a WGM as the width is increased while keeping the bend radius fixed at 2 μm and the etch depth at 0.37 μm .

Fig. 8
Fig. 8

Two basic architectures of a ring resonator with submicrometer dimensions: (a) directional-coupled racetrack resonator; (b) point-coupled circular microring resonator.

Fig. 9
Fig. 9

Birefringence of straight WGs as a function of the bend radius for various etch depth. The straight WG is designed using the dimensions of the PI bend for each bend radius, resulting in birefringence in the straight WG. The minimum bend radius (determined solely by birefringence) that can be used is about 3 μm .

Fig. 10
Fig. 10

Total bend losses in a 90 ° bend as a function of bend radius for fundamental mode at wavelength of 1.55 μm ( D = 0.37 μm and W c ( bend ) = 0.394 μm ).

Fig. 11
Fig. 11

Plot of MBR LOSS as a function of the etch depth. At each etch depth, the bend width W c ( bend ) for PI operation at R = 3 μm is used to compute this plot.

Fig. 12
Fig. 12

(a) Proposed submicrometer PI ring resonator coupled with one bus WG via a 2 × 2 type I MMI coupler. (b) Type I MMI coupler used for the racetrack resonator design showing the various parameters and the ports’ labeling. (c) Type I, and (d) type II MMI.

Fig. 13
Fig. 13

Effective index as a function of wavelength, for straight WG and bend of R = 3 μm , both with D = 0.37 μm and W = W c ( bend ) = 0.394 μm . At wavelength 1.55 μm , the bend is PI, while residual birefringence exists in the straight WG. However, the geometric dispersion (gradient of graph) is polarization dependent for both bend and straight WG.

Fig. 14
Fig. 14

Simulated transmittance ( T ) spectra of the proposed single-port racetrack resonator design, showing the near to polarization-insensitive performance. The inset shows the proposed submicrometer racetrack ring resonator coupled to a 2 × 2 type I MMI.

Fig. 15
Fig. 15

Birefringence of the fundamental modes of the straight WG as a function of width for various etch depths, at fixed H = 400 nm .

Tables (1)

Tables Icon

Table 1 Coupling Length, Losses, and Birefringence for Type I and Type II Multimode Interferometer Couplers

Equations (10)

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[ P x x P y x P x y P y y ] [ E x E y ] = β 2 [ E x E y ] ,
L rt n eff ( TE , TM ) = m λ R ( TE , TM ) ,
L B [ dB / 90 ° ] = 20 log 10 ( exp [ n i ( bend ) k o R π / 2 ] ) ,
L T [ dB ] = 10 10 | + + E 0 N ( x , y ) E 0 R * ( x , y ) d x d y | 2 | + + E 0 N ( x , y ) E 0 N * ( x , y ) d x d y | | + + E 0 R ( x , y ) E 0 R * ( x , y ) d x d y | ,
L π = π β TE β TM = λ 2 ( n eff , TE n eff , TM ) .
L π = 4 3 n r w eq 2 λ 0 ,
L 3 dB , t ypeI L 3 dB , t ypeII = 3 ( d + W ) 2 ( 3 d ) 2 .
P t = α mmi 2 ( α r 2 + t 2 2 α r t cos θ 1 + α r 2 t 2 2 α r t cos θ ) ,
θ = 2 π / λ ( n eff ( bend ) L bends + n eff ( straight ) L straight WG + n eff ( mmi ) L mmi ) ,
θ = 2 π / λ ( N g ( bend ) L bends + N g ( straight ) L straight WG + N g ( mmi ) L mmi ) .

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