Abstract

Over the last two decades, many filters requiring custom spectral responses were obtained from photo-inscribed fiber Bragg gratings because of the flexibility inherent to this technology. However, Bragg gratings in silicon waveguides have the potential to provide faster and more efficient tuning capabilities when compared to optical fiber devices. One drawback is that Bragg gratings filters with elaborate spectral amplitude and phase responses often require a long interaction length, which is not compatible with current integration trends in CMOS compatible photonic circuits. In this paper, we propose to make Bragg gratings in spiral-shaped waveguides in order to increase their lengths while making them more compact. The approach preserves the flexibility of regular straight grating structures. More specifically, we demonstrate 2-mm long gratings wrapped in an area of 200 µm x 190 µm without any spectral degradation due to waveguide curvature. Furthermore, we interleave three spiral waveguides with integrated gratings thereby tripling the density and demonstrate good phase compensation for each of them. Finally, we show that this approach is compatible with phase-apodization of the grating coupling coefficient.

© 2013 OSA

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2012 (2)

2011 (1)

2010 (2)

2008 (2)

2007 (3)

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

2006 (2)

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express14(23), 11128–11141 (2006).
[CrossRef] [PubMed]

2005 (1)

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Full vectorial finite element modal solution of curved optical waveguides,” Laser Phys. Lett.2(3), 131–136 (2005).
[CrossRef]

2003 (1)

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

1998 (1)

1975 (1)

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Sel. Top. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

Adam, K.

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Ayache, M.

Ayazi, A.

Ayotte, N.

Baehr-Jones, T.

T. Baehr-Jones, R. Ding, Y. Liu, A. Ayazi, T. Pinguet, N. C. Harris, M. Streshinsky, P. Lee, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “Ultralow drive voltage silicon traveling-wave modulator,” Opt. Express20(11), 12014–12020 (2012).
[CrossRef] [PubMed]

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Baets, R.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Baets, R. G.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Beckx, S.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Bedard, S.

Belhadj, N.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

Bogaerts, W.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Chrostowski, L.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Claes, T.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Ding, R.

Dumon, P.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Edura, T.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Fainman, Y.

S. Zamek, D. T. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, and Y. Fainman, “Compact chip-scale filter based on curved waveguide Bragg gratings,” Opt. Lett.35(20), 3477–3479 (2010).
[CrossRef] [PubMed]

K. Ikeda, M. Nezhad, and Y. Fainman, “Wavelength selective coupler with vertical gratings on silicon chip,” Appl. Phys. Lett.92(20), 201111 (2008).
[CrossRef]

Freude, W.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Grattan, K. T. V.

B. M. A. Rahman, D. M. H. Leung, S. S. A. Obayya, and K. T. V. Grattan, “Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling,” Appl. Opt.47(16), 2961–2970 (2008).
[CrossRef] [PubMed]

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Full vectorial finite element modal solution of curved optical waveguides,” Laser Phys. Lett.2(3), 131–136 (2005).
[CrossRef]

Harris, J.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Sel. Top. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

Harris, N. C.

Heiblum, M.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Sel. Top. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

Hirono, T.

Hochberg, M.

T. Baehr-Jones, R. Ding, Y. Liu, A. Ayazi, T. Pinguet, N. C. Harris, M. Streshinsky, P. Lee, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “Ultralow drive voltage silicon traveling-wave modulator,” Opt. Express20(11), 12014–12020 (2012).
[CrossRef] [PubMed]

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Honda, S.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

Huang, W.-P.

Ikeda, K.

K. Ikeda, M. Nezhad, and Y. Fainman, “Wavelength selective coupler with vertical gratings on silicon chip,” Appl. Phys. Lett.92(20), 201111 (2008).
[CrossRef]

Jacome, L.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Jaeger, N. A. F.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Jaenen, P.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Kakihara, K.

Khajavikhan, M.

Kono, N.

Koos, C.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Koshiba, M.

LaRochelle, S.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

A. D. Simard, N. Ayotte, Y. Painchaud, S. Bedard, and S. LaRochelle, “Impact of sidewall roughness on integrated Bragg gratings,” J. Lightwave Technol.29(24), 3693–3704 (2011).
[CrossRef]

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Characterization of integrated Bragg grating profiles,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides paper (2012).

Lee, P.

Leung, D. M. H.

Leuthold, J.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Lim, A. E.-J.

Lin, C.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Liow, T.-Y.

Liu, Y.

T. Baehr-Jones, R. Ding, Y. Liu, A. Ayazi, T. Pinguet, N. C. Harris, M. Streshinsky, P. Lee, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo, G.-Q. Lo, and M. Hochberg, “Ultralow drive voltage silicon traveling-wave modulator,” Opt. Express20(11), 12014–12020 (2012).
[CrossRef] [PubMed]

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Lo, G.-Q.

Lui, W. W.

Matsui, J.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Nezhad, M.

K. Ikeda, M. Nezhad, and Y. Fainman, “Wavelength selective coupler with vertical gratings on silicon chip,” Appl. Phys. Lett.92(20), 201111 (2008).
[CrossRef]

Nezhad, M. P.

O’Faolain, L.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Obayya, S. S. A.

B. M. A. Rahman, D. M. H. Leung, S. S. A. Obayya, and K. T. V. Grattan, “Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling,” Appl. Opt.47(16), 2961–2970 (2008).
[CrossRef] [PubMed]

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Full vectorial finite element modal solution of curved optical waveguides,” Laser Phys. Lett.2(3), 131–136 (2005).
[CrossRef]

Painchaud, Y.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

A. D. Simard, N. Ayotte, Y. Painchaud, S. Bedard, and S. LaRochelle, “Impact of sidewall roughness on integrated Bragg gratings,” J. Lightwave Technol.29(24), 3693–3704 (2011).
[CrossRef]

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Characterization of integrated Bragg grating profiles,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides paper (2012).

Pinguet, T.

Poulton, C. G.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Rahman, B. M. A.

B. M. A. Rahman, D. M. H. Leung, S. S. A. Obayya, and K. T. V. Grattan, “Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling,” Appl. Opt.47(16), 2961–2970 (2008).
[CrossRef] [PubMed]

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Full vectorial finite element modal solution of curved optical waveguides,” Laser Phys. Lett.2(3), 131–136 (2005).
[CrossRef]

Rosenthal, A.

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

Saitoh, K.

Scheerlinck, S.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Schelew, E.

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Schrauwen, J.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Shi, W.

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Simard, A. D.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

A. D. Simard, N. Ayotte, Y. Painchaud, S. Bedard, and S. LaRochelle, “Impact of sidewall roughness on integrated Bragg gratings,” J. Lightwave Technol.29(24), 3693–3704 (2011).
[CrossRef]

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Characterization of integrated Bragg grating profiles,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides paper (2012).

Streshinsky, M.

Taillaert, D.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Tan, D. T.

Teo, S. H.-G.

Thourhout, D. V.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Tokuda, M.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Trotter, D. C.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express18(23), 23598–23607 (2010).
[CrossRef] [PubMed]

W. A. Zortman, M. R. Watts, and D. C. Trotter, “Determination of wafer and process induced resonant frequency variation in silicon microdisk-resonators,” in Integrated Photonics and Nanophotonics Research and Applications (2009).

Tsutsui, K.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Utaka, K.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Van Laere, F.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Van Thourhout, D.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

Wada, Y.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Wang, X.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Watts, M. R.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express18(23), 23598–23607 (2010).
[CrossRef] [PubMed]

W. A. Zortman, M. R. Watts, and D. C. Trotter, “Determination of wafer and process induced resonant frequency variation in silicon microdisk-resonators,” in Integrated Photonics and Nanophotonics Research and Applications (2009).

Wiaux, V.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Wouters, J.

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

Wu, Z.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

Xu, C.-L.

Yokoyama, K.

Young, J. F.

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

Yun, H.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

Zamek, S.

Zhang, Y.

Zimmermann, L.

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

Zortman, W. A.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express18(23), 23598–23607 (2010).
[CrossRef] [PubMed]

W. A. Zortman, M. R. Watts, and D. C. Trotter, “Determination of wafer and process induced resonant frequency variation in silicon microdisk-resonators,” in Integrated Photonics and Nanophotonics Research and Applications (2009).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Ikeda, M. Nezhad, and Y. Fainman, “Wavelength selective coupler with vertical gratings on silicon chip,” Appl. Phys. Lett.92(20), 201111 (2008).
[CrossRef]

Electron. Lett. (1)

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett.43(11), 630–631 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Rosenthal and M. Horowitz, “Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings,” IEEE J. Quantum Electron.39(8), 1018–1026 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Sel. Top. Quantum Electron.11(2), 75–83 (1975).
[CrossRef]

W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron.12(6), 1394–1401 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. Koos, C. G. Poulton, L. Zimmermann, L. Jacome, J. Leuthold, and W. Freude, “Ideal bend contour trajectories for single-mode operation of low-loss overmoded waveguides,” IEEE Photon. Technol. Lett.19(11), 819–821 (2007).
[CrossRef]

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photon. Technol. Lett.24(12), 1033–1035 (2012).
[CrossRef]

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett.19(23), 1919–1921 (2007).
[CrossRef]

J. Lightwave Technol. (2)

Laser Phys. Lett. (1)

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Full vectorial finite element modal solution of curved optical waveguides,” Laser Phys. Lett.2(3), 131–136 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (8)

X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F. Jaeger, and L. Chrostowski, “Lithography simulation for the fabrication of silicon photonic devices with deep-ultraviolet lithography,” in 2012 IEEE 9th International Conference on Group IV Photonics (GFP), 288–290 (2012).
[CrossRef]

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Integrated Bragg gratings in curved waveguides,” in the 23rd Annual Meeting of the Photonics Society Denver, USA, paper ThU3 (2010).
[CrossRef]

T. E. Murphy, “Integrated optical grating-based matched filters for fiber-optic communications,” Massachusetts Institute of Technology (1996).

A. D. Simard, Y. Painchaud, and S. LaRochelle, “Characterization of integrated Bragg grating profiles,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides paper (2012).

Y. Painchaud, M. Poulin, C. Latrasse, N. Ayotte, M.-J. Picard, and M. Morin, “Bragg grating notch filters in silicon-on-insulator waveguides,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides paper BW2E.3, Optical Society of America (2012).

S. Spector, M. W. Geis, D. Lennon, R. C. Williamson, and T. M. Lyszczarz, “Hybrid multi-mode/single-mode waveguides for low loss,” in Integrated Photonics Research, Optical Society of America (2004).

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters in phase-shifted contra-directional couplers,” in 2012 9th International Conference on Group IV Photonics (GFP)78–80 (2012).
[CrossRef]

W. A. Zortman, M. R. Watts, and D. C. Trotter, “Determination of wafer and process induced resonant frequency variation in silicon microdisk-resonators,” in Integrated Photonics and Nanophotonics Research and Applications (2009).

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Figures (6)

Fig. 1
Fig. 1

(a) Three different schematic of spiral gratings; (b) CAD mask of the spiral IBGs used in this paper; (c) Optical microscope image of the first spiral-IBG row.

Fig. 2
Fig. 2

(a) Radius of curvature of the spirals shown in Fig. 1(a); (b) Variation of the effective index of a 1200 nm x 220 nm passivated silicon waveguide as function of its radius of curvature; (c) Phase function that must be incorporated in the grating structure to compensate the effective index variation caused by the curvature of the spirals shown in Fig. 1(a). (d) The resulting grating period. The dotted black line is the uncorrected grating period.

Fig. 3
Fig. 3

(a) Comparison of the experimental reflection spectrum of an uncompensated spiral IBG (in red) with the reconstructed reflection spectrum (in black) and the designed uniform grating response (blue curve). Retrieved (b) λB and (c) Δn profiles, which are used to calculate the black curve of (a).

Fig. 4
Fig. 4

(a) Comparison of the experimental reflection spectrum of a phase compensated spiral IBG (in red) with the reconstructed reflection spectrum (in black) and the designed uniform grating response (blue curve). Retrieved (b) λB and (c) Δn profiles, which are used to calculate the black curve of (a).

Fig. 5
Fig. 5

(a) Interleaved spiral having R0 = 59 µm, Δw = 15 µm and α = 0.671 and a minimal radius of curvature of 20 µm for the blue and red waveguides and 25 µm for the black (central) waveguide. (b) Radius of curvature of a typical interleaved spiral as function of the position on the spiral waveguide. (c) Phase function that must be incorporated in the grating structure to compensate the effective index variation caused by the curvature. (d) Comparison of the experimental reflection spectrum of a compensated interleaved spiral IBG (in red) with the reconstructed reflection spectrum (in black) and the designed uniform grating response (blue curve). Retrieved (e) λB and (f) Δn profiles, which are used to calculate the black curve of (d).

Fig. 6
Fig. 6

(a) Comparison of the experimental reflection spectrum of a compensated Gaussian-apodized CBG (in red) with the reconstructed reflection spectrum (in black). The blue curve is the spectrum obtained with the ideal Gaussian apodization profile shown in (c) and an ideal Bragg wavelength while the green curve is the spectrum calculated with the noisy apodization profile but without phase noise (ideal Bragg wavelength). Retrieved (b) λB and (c) Δn profiles, which are used to calculate the black curve of (a).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

S=R(ρ) e i| ρ | Δx
R(ρ)= R 0 sgn(ρ)+ Δwρ /π
Δx= R 0 sgn(ρ) e | ρ |/α
n(z)=n(λ)+δn( R(z) )+Δncos( 2π Λ z+θ(z)+Ω(z) )
Ω(z)= 2π nΛ L/2 z dz'δn( R(z') ) .
Λ( z )= Λ [ 1+ Λ 2π θ(z) z + Λ 2π Ω(z) z ]
Δncos( 2π Λ z+θ(z)+Ω(z)+ϕ(z)sin( 2π Λ M z ) ).

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