Abstract

We show by theory and experiment that silicon-dioxide-cladding gratings for Fabry-Pérot cavities on silicon-on-insulator channel (“wire”) waveguides provide a low-refractive-index perturbation, which is required for several important integrated photonics components. The underlying refractive index perturbation of these gratings is significantly weaker than that of analogous silicon gratings, leading to finer control of the coupling coefficient κ. Our Fabry-Pérot cavities are designed using the transfer-matrix method (TMM) in conjunction with the finite element method (FEM) for calculating the effective index of each waveguide section. Device parameters such as coupling coefficient, κ, Bragg mirror stop band, Bragg mirror reflectivity, and quality factor Q are examined via TMM modeling. Devices are fabricated with representative values of distributed Bragg reflector lengths, cavity lengths, and propagation losses. The measured transmission spectra show excellent agreement with the FEM/TMM calculations.

© 2011 OSA

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2011 (2)

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

2010 (1)

2009 (6)

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34, 1357–1359 (2009).
[CrossRef] [PubMed]

M. Gnan, W. C. L. Hopman, G. Bellanca, R. M. de Ridder, R. M. De La Rue, and P. Bassi, “Closure of the stop-band in photonic wire Bragg gratings,” Opt. Express 17, 8830–8842 (2009).
[CrossRef] [PubMed]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
[CrossRef]

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

M. Hammer and O. V. Ivanova , “Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment,” Opt. Quantum Electron.,  41, 267–283 (2009).
[CrossRef]

2008 (3)

J. Mu, H. Zhang, and W. Huang, “Design of waveguide Bragg gratings with strong index corrugations,” J. Light-wave Technol. 26, 1596–1601 (2008).
[CrossRef]

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12084–12089 (2008).
[CrossRef]

2007 (6)

2006 (1)

M. Gnan, H. Bellanca, H. M. H. Chong, P. Bassi, and R. M. De La Rue, “Modelling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38, 133148 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (3)

2002 (3)

A. Melloni, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

2001 (1)

1997 (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

1996 (2)

M. Y. Liu and S. Y. Chou, “High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflectors,” Appl. Phys. Lett. 68, 170–172 (1996).
[CrossRef]

P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017–2019 (1996).
[CrossRef] [PubMed]

Abrams, D. S.

Ahmad, R. U.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

Barrios, C. A.

Bassi, P.

M. Gnan, W. C. L. Hopman, G. Bellanca, R. M. de Ridder, R. M. De La Rue, and P. Bassi, “Closure of the stop-band in photonic wire Bragg gratings,” Opt. Express 17, 8830–8842 (2009).
[CrossRef] [PubMed]

M. Gnan, H. Bellanca, H. M. H. Chong, P. Bassi, and R. M. De La Rue, “Modelling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38, 133148 (2006).
[CrossRef]

Bauer, J.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

Baus, M.

P. Muellner, R. Bruck, M. Karl, M. Baus, T. Wahlbrink, and R. Hainberger, “Silicon photonic wire Bragg grating for on-chip wavelength (de)multiplexing employing ring resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMF4.

Bazin, A.

Bellanca, G.

Bellanca, H.

M. Gnan, H. Bellanca, H. M. H. Chong, P. Bassi, and R. M. De La Rue, “Modelling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38, 133148 (2006).
[CrossRef]

Bowers, J. E.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

Bruck, R.

P. Muellner, R. Bruck, M. Karl, M. Baus, T. Wahlbrink, and R. Hainberger, “Silicon photonic wire Bragg grating for on-chip wavelength (de)multiplexing employing ring resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMF4.

Bruns, J.

I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
[CrossRef]

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

Camarda, G. S.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

Charvolin, T.

Chen, R.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Chong, H. M. H.

M. Gnan, H. Bellanca, H. M. H. Chong, P. Bassi, and R. M. De La Rue, “Modelling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38, 133148 (2006).
[CrossRef]

Chou, S. Y.

M. Y. Liu and S. Y. Chou, “High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflectors,” Appl. Phys. Lett. 68, 170–172 (1996).
[CrossRef]

Chrostowski, L.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Dadap, J. I.

De Almeida, V. R.

De La Rue, R. M.

de Ridder, R. M.

Denault, S.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Espinola, R. L.

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Raman amplication in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004).
[CrossRef] [PubMed]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

Fainman, Y.

Fan, S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017–2019 (1996).
[CrossRef] [PubMed]

Fang, A. W.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

Ferraro, M. S.

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Floridi, M.

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Frank, I. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Gajda, A.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
[CrossRef]

Gan, F.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

Geis, M. W.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

Giuntoni, I.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
[CrossRef]

Gnan, M.

M. Gnan, W. C. L. Hopman, G. Bellanca, R. M. de Ridder, R. M. De La Rue, and P. Bassi, “Closure of the stop-band in photonic wire Bragg gratings,” Opt. Express 17, 8830–8842 (2009).
[CrossRef] [PubMed]

M. Gnan, H. Bellanca, H. M. H. Chong, P. Bassi, and R. M. De La Rue, “Modelling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38, 133148 (2006).
[CrossRef]

Goodberlet, J. G.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

Grein, M. E.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

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Hainberger, R.

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M. Hammer and O. V. Ivanova , “Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment,” Opt. Quantum Electron.,  41, 267–283 (2009).
[CrossRef]

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J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguide,” J. Lightwave Technol. 19, 1938–1942 (2001).
[CrossRef]

Hopman, W. C. L.

Huang, W.

J. Mu, H. Zhang, and W. Huang, “Design of waveguide Bragg gratings with strong index corrugations,” J. Light-wave Technol. 26, 1596–1601 (2008).
[CrossRef]

Hugonin, J. P.

C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, “Modal-reflectivity enhancement by geometry tuning in photonic crystal microcavities,” Opt. Express 13, 245–255 (2005).
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P. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high-Q, small-V microcavities,” IEEE J. Quantum Electron. 39, 1430–1438, (2003).
[CrossRef]

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Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Ivanova, O. V.

M. Hammer and O. V. Ivanova , “Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment,” Opt. Quantum Electron.,  41, 267–283 (2009).
[CrossRef]

Jaeger, N. A. F.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Jiang, G.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Jiang, X.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Joannopoulos, J. D.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017–2019 (1996).
[CrossRef] [PubMed]

Johnson, N. P.

Jones, R.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

Karl, M.

P. Muellner, R. Bruck, M. Karl, M. Baus, T. Wahlbrink, and R. Hainberger, “Silicon photonic wire Bragg grating for on-chip wavelength (de)multiplexing employing ring resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMF4.

Karle, T. J.

Kärtner, F. X.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

Khan, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
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Kim, H. C.

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Koch, B. R.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

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Kuo, Y.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

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Lecamp, G.

Lennon, D. M.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

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A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

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J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

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Liu, M. Y.

M. Y. Liu and S. Y. Chou, “High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflectors,” Appl. Phys. Lett. 68, 170–172 (1996).
[CrossRef]

Lively, E.

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

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P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Lyszczarz, T. M.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

Marschmeyer, S.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
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McCutcheon, M. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

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Md Zain, A. R.

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J. Mu, H. Zhang, and W. Huang, “Design of waveguide Bragg gratings with strong index corrugations,” J. Light-wave Technol. 26, 1596–1601 (2008).
[CrossRef]

Muellner, P.

P. Muellner, R. Bruck, M. Karl, M. Baus, T. Wahlbrink, and R. Hainberger, “Silicon photonic wire Bragg grating for on-chip wavelength (de)multiplexing employing ring resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMF4.

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Osgood, R. M.

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Raman amplication in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004).
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R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

Palmacci, S. T.

Petermann, K.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
[CrossRef]

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Picard, E.

Pizzuto, F.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

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Rabinovich, W. S.

Raineri, F.

Raj, R.

Rao, H.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

Richter, H.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
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M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

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X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Smith, H. I.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguide,” J. Lightwave Technol. 19, 1938–1942 (2001).
[CrossRef]

Smith, Henry I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Spector, S. J.

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15, 16886–16895 (2007).
[CrossRef] [PubMed]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
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Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Stolarek, D.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
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Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, 1991).
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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Tillack, B.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
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Vafaei, R.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Van Thourhout, D.

Velha, P.

Villeneuve, P. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017–2019 (1996).
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Wahlbrink, T.

P. Muellner, R. Bruck, M. Karl, M. Baus, T. Wahlbrink, and R. Hainberger, “Silicon photonic wire Bragg grating for on-chip wavelength (de)multiplexing employing ring resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMF4.

Wang, M.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Wang, X.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Wynn, C. M.

Yang, J.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

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M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
[CrossRef]

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Zhang, H.

J. Mu, H. Zhang, and W. Huang, “Design of waveguide Bragg gratings with strong index corrugations,” J. Light-wave Technol. 26, 1596–1601 (2008).
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G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Zimmermann, L.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

M. Y. Liu and S. Y. Chou, “High-modulation-depth and short-cavity-length silicon Fabry-Perot modulator with two grating Bragg reflectors,” Appl. Phys. Lett. 68, 170–172 (1996).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high-Q, small-V microcavities,” IEEE J. Quantum Electron. 39, 1430–1438, (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y. Kuo, and J. E. Bowers, “A distributed Bragg reflector silicon evanescent laser,” IEEE Photon. Technol. Lett. 20, 1667–1669 (2008).
[CrossRef]

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI Rib Waveguides,” IEEE Photon. Technol. Lett. 24, 1894–1896 (2009).
[CrossRef]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, “Ultracompact corner-mirrors and T-Branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14, 65–67 (2002).
[CrossRef]

M. W. Geis, S. J. Spector, M. E. Grein, R. T. Schulein, J. U. Yoo, D. M. Lennon, S. Denault, F. Gan, F. X. Kärtner, and T. M. Lyszczarz, “CMOS-compatible all-Si high-speed waveguide photodiodes with responsivity in near-infrared communication band,” IEEE Photon. Technol. Lett. 19, 152–154 (2007).
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J. Light-wave Technol. (1)

J. Mu, H. Zhang, and W. Huang, “Design of waveguide Bragg gratings with strong index corrugations,” J. Light-wave Technol. 26, 1596–1601 (2008).
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J. Lightwave Technol. (3)

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

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

J. Vac. Sci. Technol. B (1)

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B 20, 2753–2757 (2002).
[CrossRef]

Nature (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Opt. Express (8)

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I. Giuntoni, A. Gajda, M. Krause, R. Steingrber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express 17, 18518–18524 (2009).
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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the SiWG FP cavity (b) Tilted side view SEM image of a SiWG FP with Lc = 2a. (c) Comparison of κ for a SiO2-cladding grating and a Si etched grating with increasing h, plotted on a logarithmic scale. For a Si etched grating with h > 20 nm the fundamental quasi-TM (QTM) mode is no longer supported, thus κ is not calculated for this polarization. (inset) Cross-sectional schematic of a SiO2-cladding grating and a Si waveguide etched grating.

Fig. 2
Fig. 2

Modal profiles at λ = 1.55 μm for (a) QTE mode with cladding, (b) QTE mode without cladding, (c) QTM mode with cladding and (d) QTM mode without cladding, where Δneff,QTE = 0.015, Δneff,QTM = 0.035. (e) Δneff (λ) with h = 90 nm for both QTE and QTM modes.

Fig. 3
Fig. 3

(a) DBR reflectivity for the QTE and QTM modes as a function of number of grating periods N1 = N2 = N, with h = 90 nm, λ0 = 1.55 μm, and α = 3 dB/cm, (b) Spectral width of the DBR stop band Δλgap as a function of h, calculated with TMM and with the analytical expression (8), (inset) SEM micrograph of a fabricated DBR.

Fig. 4
Fig. 4

Experimentally measured transmission spectra with TMM calculated curve fits for (a) Case 1: Lc = 2a, α = 3 dB/cm, N1 = N2 = 50, (b) Case 2: Lc = 2a, α = 3 dB/cm, N1 = N2 = 90, (c) Case 3: Lc = 2a, α = 100 dB/cm, N1 = N2 = 52, (d) Case 4: Lc = 123a, α = 100 dB/cm, N1 = N2 = 52.

Tables (2)

Tables Icon

Table 1 Device parameters for fabricated devices. Effective indices of each quarter-wave stack section are adjusted to fit TMM transmission calculations to the experimentally measured data, given as Δneff,a and Δneff,b.

Tables Icon

Table 2 Comparison of measured and theoretical device characteristics. Experimental data is fit with a cubic spline interpolation, TMM calculations are performed with neff,a and neff,b adjusted such that the calculated transmission spectrum fits the experimental data in the least squares sense.

Equations (8)

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κ = ω 4 1 | Δ ɛ ( x , y ) | 2 = ω 8 ɛ 0 ( n perturb 2 n air 2 ) h w E 1 * E 2 d x d y ,
[ U in ( + ) U in ( ) ] = M [ U out ( + ) U out ( ) ] ,
M t = [ A B C D ] N 1 [ e i k am L c 0 0 e i k am L c ] [ A B C D ] N 2 .
A 0 = e i k a 0 a [ cos ( k b 0 b ) + i 2 ( k b 0 k a 0 + k a 0 k b 0 ) sin ( k b 0 b ) ]
B 0 = e i k a 0 a [ i 2 ( k b 0 k a 0 k a 0 k b 0 ) sin ( k b 0 b ) ]
A 1 = e i k a 1 a [ cos ( k b 1 b ) + i 2 ( n eff , b 2 k a 1 n eff , a 2 k b 1 + n eff , a 2 k b 1 n eff , b 2 k a 1 ) sin ( k b 1 b ) ]
B 1 = e i k a 1 a [ i 2 ( n eff , b 2 k a 1 n eff , a 2 k b 1 n eff , a 2 k b 1 n eff , b 2 k a 1 ) sin ( k b 1 b ) ] .
Δ λ gap = 4 π λ 0 [ n eff , a n eff , b n eff , a + n eff , b ] .

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