Abstract

We propose and simulate the characteristics of optical filters based on subwavelength gratings. In particular, we demonstrate through numerical simulations the feasibility of implementing SWG Bragg gratings in silicon-on-insulator (SOI). We also propose SWG ring resonators in SOI and verify their operation using numerical simulations and experiments. The fabricated devices exhibit an extinction ratio as large as 30 dB and a Q-factor as high as ~20,000. These fundamental SWG filters can serve as building blocks for more complex devices.

© 2014 Optical Society of America

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2014 (1)

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

2012 (6)

A. V. Velasco, M. L. Calvo, P. Cheben, A. Ortega-Moñux, J. H. Schmid, C. A. Ramos, Í. M. Fernandez, J. Lapointe, M. Vachon, S. Janz, and D. X. Xu, “Ultracompact polarization converter with a dual subwavelength trench built in a silicon-on-insulator waveguide,” Opt. Lett.37(3), 365–367 (2012).
[CrossRef] [PubMed]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

J. Y. Lee and P. M. Fauchet, “Slow-light dispersion in periodically patterned silicon microring resonators,” Opt. Lett.37(1), 58–60 (2012).
[CrossRef] [PubMed]

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

2011 (1)

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

2010 (4)

2009 (3)

2008 (2)

Q. F. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express16(6), 4309–4315 (2008).
[CrossRef] [PubMed]

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (1)

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

2001 (1)

1998 (1)

1997 (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov Phys Jetp-Ussr2, 466–475 (1956).

Aers, G. C.

Alonso-Ramos, C.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

Ams, M.

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Beausoleil, R. G.

Bedard, D.

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Bock, P. J.

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Bruns, J.

Calvo, M. L.

Cardenas, J.

Cartwright, N. A.

Cheben, P.

A. V. Velasco, M. L. Calvo, P. Cheben, A. Ortega-Moñux, J. H. Schmid, C. A. Ramos, Í. M. Fernandez, J. Lapointe, M. Vachon, S. Janz, and D. X. Xu, “Ultracompact polarization converter with a dual subwavelength trench built in a silicon-on-insulator waveguide,” Opt. Lett.37(3), 365–367 (2012).
[CrossRef] [PubMed]

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express18(19), 20251–20262 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express18(15), 16146–16155 (2010).
[CrossRef] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett.35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, “Sub-wavelength grating mode transformers in silicon slab waveguides,” Opt. Express17(21), 19120–19133 (2009).
[CrossRef] [PubMed]

Cheung, K. C.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Chrostowski, L.

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Delâge, A.

Densmore, A.

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Fattal, D.

Fauchet, P. M.

Fernandez, Í. M.

Flueckiger, J.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Foster, M. A.

Gaeta, A. L.

Gajda, A.

Giuntoni, I.

Grist, S.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

Halir, R.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett.35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

Hall, T. J.

Hastings, J. T.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

Hugonin, J. P.

Jaeger, N. A. F.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

Janz, S.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

A. V. Velasco, M. L. Calvo, P. Cheben, A. Ortega-Moñux, J. H. Schmid, C. A. Ramos, Í. M. Fernandez, J. Lapointe, M. Vachon, S. Janz, and D. X. Xu, “Ultracompact polarization converter with a dual subwavelength trench built in a silicon-on-insulator waveguide,” Opt. Lett.37(3), 365–367 (2012).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express18(15), 16146–16155 (2010).
[CrossRef] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett.35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express18(19), 20251–20262 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, “Sub-wavelength grating mode transformers in silicon slab waveguides,” Opt. Express17(21), 19120–19133 (2009).
[CrossRef] [PubMed]

Khan, M. H.

Khurgin, J. B.

Krause, M.

Lalanne, P.

Lapointe, J.

Lee, J. Y.

Li, Q.

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

Liang, Z.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Lipson, M.

J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express18(25), 26525–26534 (2010).
[CrossRef] [PubMed]

M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett.45, 575–577 (2009).

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Lira, H. L. R.

Liu, F. F.

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

Ma, R.

Maese-Novo, A.

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

Marshall, G. D.

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

Molina-Fernandez, I.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

Molina-Fernández, I.

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett.35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

Morton, P.

Murphy, T. E.

Nie, B.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Ortega-Monux, A.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

Ortega-Moñux, A.

Ouellet, E.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Oughstun, K. E.

Petermann, K.

Poitras, C. B.

Poon, J. K. S.

Pradhan, S.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
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Qi, M. H.

Qiu, M.

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

Ramos, C. A.

Ratner, D. M.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov Phys Jetp-Ussr2, 466–475 (1956).

Scheuer, J.

Schmid, J.

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

Schmid, J. H.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

A. V. Velasco, M. L. Calvo, P. Cheben, A. Ortega-Moñux, J. H. Schmid, C. A. Ramos, Í. M. Fernandez, J. Lapointe, M. Vachon, S. Janz, and D. X. Xu, “Ultracompact polarization converter with a dual subwavelength trench built in a silicon-on-insulator waveguide,” Opt. Lett.37(3), 365–367 (2012).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express18(19), 20251–20262 (2010).
[CrossRef] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett.35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express18(15), 16146–16155 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, “Sub-wavelength grating mode transformers in silicon slab waveguides,” Opt. Express17(21), 19120–19133 (2009).
[CrossRef] [PubMed]

Schmidt, B.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Schmidt, S. A.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
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Sherwood-Droz, N.

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X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
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L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Smith, H. I.

Steingrüber, R.

Su, Y. K.

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

Vachon, M.

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Velasco, A. V.

Wang, X.

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Wanguemert-Perez, J.

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

Wanguemert-Perez, J. G.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

Webb, M.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Withford, M. J.

Xiao, S. J.

Xu, D. X.

Xu, D.-X.

Xu, Q. F.

Q. F. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express16(6), 4309–4315 (2008).
[CrossRef] [PubMed]

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Xu, Y.

Yariv, A.

Yun, H.

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

Zavargo-Peche, L.

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

Zhang, B. B.

Zhang, Z. Y.

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

Electron. Lett. (1)

M. Lipson, “Silicon photonics: the optical spice rack,” Electron. Lett.45, 575–577 (2009).

IEEE J Sel Top Quant (1)

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D. X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J Sel Top Quant20(4) 8201313 (2014).

F. F. Liu, Q. Li, Z. Y. Zhang, M. Qiu, and Y. K. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” Ieee J Sel Top Quant14(3), 706–712 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo, I. Molina-Fernández, R. Halir, J. Wanguemert-Perez, P. Cheben, and J. Schmid, “High-performance multimode interference coupler in silicon waveguides with subwavelength structures,” IEEE Photon. Technol. Lett.23(19), 1406–1408 (2011).
[CrossRef]

J. Lightwave Technol. (2)

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

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

Laser Photon Rev (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon Rev6(1), 47–73 (2012).
[CrossRef]

Nature (1)

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Opt. Express (9)

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express17(21), 18518–18524 (2009).
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J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express18(25), 26525–26534 (2010).
[CrossRef] [PubMed]

S. J. Xiao, M. H. Khan, H. Shen, and M. H. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express15(22), 14765–14771 (2007).
[CrossRef] [PubMed]

Q. F. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express16(6), 4309–4315 (2008).
[CrossRef] [PubMed]

X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,” Opt. Express20(14), 15547–15558 (2012).
[CrossRef] [PubMed]

K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express11(13), 1541–1546 (2003).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express18(15), 16146–16155 (2010).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, “Sub-wavelength grating mode transformers in silicon slab waveguides,” Opt. Express17(21), 19120–19133 (2009).
[CrossRef] [PubMed]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express18(19), 20251–20262 (2010).
[CrossRef] [PubMed]

Opt. Lett. (4)

Proc. SPIE (1)

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proc. SPIE8236, 823620 (2012).
[CrossRef]

Prog. Electromagnetics Res. (1)

L. Zavargo-Peche, A. Ortega-Monux, J. G. Wanguemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res.123, 447–465 (2012).
[CrossRef]

Sov Phys Jetp-Ussr (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov Phys Jetp-Ussr2, 466–475 (1956).

Other (4)

R. Kashyap, Fiber Bragg Gratings (Academic Press, 1999).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

D. J. Lockwood and L. Pavesi, Silicon Photonics: Components and Integration, Vol. II (Springer, 2011).

L. Chrostowski, and M. Hochberg, Silicon Photonics Design (Lulu, 2013).

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Figures (10)

Fig. 1
Fig. 1

SWG waveguide in SOI and top view of the SWG taper.

Fig. 2
Fig. 2

Schematic of an SWG Bragg grating.

Fig. 3
Fig. 3

Transmission and reflection spectra of SWG Bragg gratings for (a) f 1 =50% , and f 2 =40% , (b) f 1 =50% , and f 2 =46.67% , (c) f 1 =50% , and f 2 =53.33% , and (d) f 1 =50% , and f 2 =60% .

Fig. 4
Fig. 4

Schematic of the SWG ring resonator. VGC: vertical grating coupler.

Fig. 5
Fig. 5

Top view of the E-field propagating in the SWG ring resonator.

Fig. 6
Fig. 6

Spectral response of an SWG ring resonator with (a) 10 µm radius, (b) 15 µm radius.

Fig. 7
Fig. 7

Measured transmission spectra (10 pm resolution) of SWG ring resonators with a ring radius of (a) 10 µm, (b) 15 µm, and (c) 20 µm. The insets show a zoom of a single resonance measured with 1 pm resolution.

Fig. 8
Fig. 8

Schematic of an SWG race-track ring resonator.

Fig. 9
Fig. 9

Spectral responses of SWG race-track ring resonator with (a) 10 µm radius, and (b) 15 µm radius.

Fig. 10
Fig. 10

Cross-over length versus gap of the coupler at a wavelength of 1550 nm: (a) SWG (b) directional coupler in Si [29].

Tables (3)

Tables Icon

Table 1 Bragg wavelength for different values of duty cycle f2

Tables Icon

Table 2 Effective indices of Bloch modes for different duty cycles

Tables Icon

Table 3 Reflection bandwidth (3 dB) for SWG Bragg gratings with different number of segments

Metrics