Abstract

Properties of reflection and transmission spectral filters based on Bragg gratings in subwavelength grating (SWG) metamaterial waveguides on silicon-on-insulator platform have been analyzed using proprietary 2D and 3D simulation tools based on Fourier modal method and the coupled-mode theory. We also demonstrate that the coupled Bloch mode theory can be advantageously applied to design of Bragg gratings in SWG waveguides. By combining different techniques, including judiciously positioning silicon loading segments within the evanescent field of the SWG waveguide and making use of its dispersion properties, it is possible to attain sub-nanometer spectral bandwidths for both reflection and transmission filters in the wavelength range of 1550 nm while keeping minimum structural features of the filters as large as 100 nm. Numerical simulations have also shown that a few nanometer jitter in the size and position of Si segments is well tolerated in our filter designs.

© 2018 Optical Society of America

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2017 (3)

2016 (10)

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
[Crossref] [PubMed]

H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. Jaeger, “Broadband 2 × 2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Opt. Lett. 41(13), 3041–3044 (2016).
[Crossref] [PubMed]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016).
[Crossref] [PubMed]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
[Crossref] [PubMed]

J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
[Crossref] [PubMed]

L. Liu, Q. Deng, and Z. Zhou, “Manipulation of beat length and wavelength dependence of a polarization beam splitter using a subwavelength grating,” Opt. Lett. 41(21), 5126–5129 (2016).
[Crossref] [PubMed]

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

Y. Xu and J. Xiao, “Ultracompact and high efficient silicon-based polarization splitter-rotator using a partially-etched subwavelength grating coupler,” Sci. Rep. 6(1), 27949 (2016).
[Crossref] [PubMed]

2015 (4)

D. Pérez-Galacho, D. Marris-Morini, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and L. Vivien, “Add/drop mode-division multiplexer based on a Mach-Zehnder interferometer and periodic waveguides,” IEEE Photonics J. 7(4), 7800907 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

2014 (7)

W. Shi, V. Veerasubramanian, D. Patel, and D. V. Plant, “Tunable nanophotonic delay lines using linearly chirped contradirectional couplers with uniform Bragg gratings,” Opt. Lett. 39(3), 701–703 (2014).
[Crossref] [PubMed]

M. Verbist, W. Bogaerts, and D. Van Thourhout, “Design of weak 1-D Bragg grating filters in SOI waveguides using volume holography techniques,” J. Lightwave Technol. 32(10), 1915–1920 (2014).
[Crossref]

J. Wang, I. Glesk, and L. R. Chen, “Subwavelength grating filtering devices,” Opt. Express 22(13), 15335–15345 (2014).
[Crossref] [PubMed]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond, N. A. F. Jaeger, and L. Chrostowski, “Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings,” Opt. Lett. 39(19), 5519–5522 (2014).
[Crossref] [PubMed]

Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
[Crossref] [PubMed]

F. De Leonardis, C. E. Campanella, B. Troia, A. G. Perri, and V. M. N. Passaro, “Performance of SOI Bragg Grating Ring Resonator for Nonlinear Sensing Applications,” Sensors (Basel) 14(9), 16017–16034 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

2011 (2)

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 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 Photonics Technol. Lett. 23(5), 290–292 (2011).

2010 (2)

2009 (3)

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34(9), 1357–1359 (2009).
[Crossref] [PubMed]

W.-P. Huang and J. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17(21), 19134–19152 (2009).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

2008 (1)

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

2007 (1)

S. P. Chan, V. M. N. Passaro, G. Z. Mashanovich, G. Ensell, and G. T. Reed, “Third order Bragg grating filters in small SOI waveguides,” J. Eur. Opt. Soc. 2, 07029 (2007).
[Crossref]

2006 (1)

2001 (1)

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1284 (1997).
[Crossref]

1994 (1)

1993 (1)

V. Mizrahi and J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11(10), 1513–1517 (1993).
[Crossref]

1976 (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55(1), 109–126 (1976).
[Crossref]

1974 (1)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

Adams, R.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

Alonso-Ramos, C.

D. Pérez-Galacho, C. Alonso-Ramos, F. Mazeas, X. Le Roux, D. Oser, W. Zhang, D. Marris-Morini, L. Labonté, S. Tanzilli, É. Cassan, and L. Vivien, “Optical pump-rejection filter based on silicon sub-wavelength engineered photonic structures,” Opt. Lett. 42(8), 1468–1471 (2017).
[Crossref] [PubMed]

J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
[Crossref] [PubMed]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

Alonso-Ramos, C. A.

Ashrafi, R.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

Ayache, M.

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Benedikovic, D.

Bock, P. J.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

Bogaerts, W.

Bojko, R.

Bruns, J.

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Burger, S.

Campanella, C. E.

F. De Leonardis, C. E. Campanella, B. Troia, A. G. Perri, and V. M. N. Passaro, “Performance of SOI Bragg Grating Ring Resonator for Nonlinear Sensing Applications,” Sensors (Basel) 14(9), 16017–16034 (2014).
[Crossref] [PubMed]

Capmany, J.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

Cassan, É.

Chae, C. J.

C. J. Chae, E. Skafidas, and D. Y. Choi, “Compact Bragg grating reflectors in silicon waveguides and their application to resonator filters,” 2014 Optical Fiber Communications Conference and Exhibition (2014).
[Crossref]

Chan, S. P.

S. P. Chan, V. M. N. Passaro, G. Z. Mashanovich, G. Ensell, and G. T. Reed, “Third order Bragg grating filters in small SOI waveguides,” J. Eur. Opt. Soc. 2, 07029 (2007).
[Crossref]

Cheben, P.

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25(11), 12222–12236 (2017).
[Crossref] [PubMed]

A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
[Crossref] [PubMed]

J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
[Crossref] [PubMed]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
[Crossref] [PubMed]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Chen, L. R.

L. R. Chen, “Subwavelength grating waveguide devices in silicon-on-insulators for integrated microwave photonics (Invited Paper),” Chin. Opt. Lett. 15(1), 010004 (2017).
[Crossref]

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

J. Wang, I. Glesk, and L. R. Chen, “Subwavelength grating filtering devices,” Opt. Express 22(13), 15335–15345 (2014).
[Crossref] [PubMed]

M. Ma and L. R. Chen, 41M. Ma and L. R. Chen, “Towards an integrated SPM-based 2R regenerator in SOI with waveguides incorporating Bragg gratings,” 2014 IEEE Photonics Society Summer Topical Meeting Series, 210–211 (2014).
[Crossref]

M. Ma and L. R. Chen, 41M. Ma and L. R. Chen, “Towards an integrated SPM-based 2R regenerator in SOI with waveguides incorporating Bragg gratings,” 2014 IEEE Photonics Society Summer Topical Meeting Series, 210–211 (2014).
[Crossref]

Chen, R. Y.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Cheung, K. C.

Choi, D. Y.

C. J. Chae, E. Skafidas, and D. Y. Choi, “Compact Bragg grating reflectors in silicon waveguides and their application to resonator filters,” 2014 Optical Fiber Communications Conference and Exhibition (2014).
[Crossref]

Chrostowski, L.

H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. Jaeger, “Broadband 2 × 2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Opt. Lett. 41(13), 3041–3044 (2016).
[Crossref] [PubMed]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016).
[Crossref] [PubMed]

X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond, N. A. F. Jaeger, and L. Chrostowski, “Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings,” Opt. Lett. 39(19), 5519–5522 (2014).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 23(5), 290–292 (2011).

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

Ctyroký, J.

D’Amico, G.

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Dado, M.

De Leonardis, F.

F. De Leonardis, C. E. Campanella, B. Troia, A. G. Perri, and V. M. N. Passaro, “Performance of SOI Bragg Grating Ring Resonator for Nonlinear Sensing Applications,” Sensors (Basel) 14(9), 16017–16034 (2014).
[Crossref] [PubMed]

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

de Sterke, C. M.

Delâge, A.

Deng, Q.

Densmore, A.

Donzella, V.

Durán-Valdeiglesias, E.

Ensell, G.

S. P. Chan, V. M. N. Passaro, G. Z. Mashanovich, G. Ensell, and G. T. Reed, “Third order Bragg grating filters in small SOI waveguides,” J. Eur. Opt. Soc. 2, 07029 (2007).
[Crossref]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1284 (1997).
[Crossref]

Fainman, Y.

Fédéli, J. M.

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
[Crossref]

Flueckiger, J.

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Gasulla, I.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

Giuntoni, I.

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Glesk, I.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

J. Wang, I. Glesk, and L. R. Chen, “Subwavelength grating filtering devices,” Opt. Express 22(13), 15335–15345 (2014).
[Crossref] [PubMed]

Gonzalo Wangüemert-Pérez, J.

Grist, S.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

Halir, R.

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25(11), 12222–12236 (2017).
[Crossref] [PubMed]

A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
[Crossref] [PubMed]

J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
[Crossref] [PubMed]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

Hall, T. J.

Hastings, J. T.

Huang, W.-P.

Ikeda, K.

Jaeger, N. A.

Jaeger, N. A. F.

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X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
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P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
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G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

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P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
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V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
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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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
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R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
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J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
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L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and I. Molina-Fernández, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
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A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
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D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
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J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
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J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
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D. Pérez-Galacho, D. Marris-Morini, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and L. Vivien, “Add/drop mode-division multiplexer based on a Mach-Zehnder interferometer and periodic waveguides,” IEEE Photonics J. 7(4), 7800907 (2015).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
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R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
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J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
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L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and I. Molina-Fernández, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
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S. P. Chan, V. M. N. Passaro, G. Z. Mashanovich, G. Ensell, and G. T. Reed, “Third order Bragg grating filters in small SOI waveguides,” J. Eur. Opt. Soc. 2, 07029 (2007).
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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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
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Sánchez-Postigo, A.

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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
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J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
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Schmid, J. H.

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25(11), 12222–12236 (2017).
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A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
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D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
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Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
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Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
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Schmidt, S.

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, and C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24(4), 194–196 (1974).
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X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
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X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
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Smith, H. I.

Stolarek, D.

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Tan, D. T. H.

Tanzilli, S.

Tillack, B.

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
[Crossref]

Troia, B.

F. De Leonardis, C. E. Campanella, B. Troia, A. G. Perri, and V. M. N. Passaro, “Performance of SOI Bragg Grating Ring Resonator for Nonlinear Sensing Applications,” Sensors (Basel) 14(9), 16017–16034 (2014).
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Vachon, M.

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 Photonics Technol. Lett. 23(5), 290–292 (2011).

Van Thourhout, D.

Veerasubramanian, V.

Verbist, M.

Vivien, L.

Wang, J.

J. Wang, R. Ashrafi, R. Adams, I. Glesk, I. Gasulla, J. Capmany, and L. R. Chen, “Subwavelength grating enabled on-chip ultra-compact optical true time delay line,” Sci. Rep. 6(1), 30235 (2016).
[Crossref] [PubMed]

J. Wang, I. Glesk, and L. R. Chen, “Subwavelength grating filtering devices,” Opt. Express 22(13), 15335–15345 (2014).
[Crossref] [PubMed]

Wang, M. H.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Wang, S.

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25(11), 12222–12236 (2017).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

Wang, X.

X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond, N. A. F. Jaeger, and L. Chrostowski, “Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings,” Opt. Lett. 39(19), 5519–5522 (2014).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 23(5), 290–292 (2011).

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

Wang, Y.

Wanguemert-Pérez, J. G.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Wangüemert-Pérez, J. G.

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
[Crossref] [PubMed]

J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
[Crossref] [PubMed]

D. Pérez-Galacho, D. Marris-Morini, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and L. Vivien, “Add/drop mode-division multiplexer based on a Mach-Zehnder interferometer and periodic waveguides,” IEEE Photonics J. 7(4), 7800907 (2015).
[Crossref]

Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
[Crossref] [PubMed]

L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and I. Molina-Fernández, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
[Crossref]

Xiao, J.

Y. Xu and J. Xiao, “Ultracompact and high efficient silicon-based polarization splitter-rotator using a partially-etched subwavelength grating coupler,” Sci. Rep. 6(1), 27949 (2016).
[Crossref] [PubMed]

Xiong, Y.

Xu, D. X.

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
[Crossref]

J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

Xu, D.-X.

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Xu, Y.

Y. Xu and J. Xiao, “Ultracompact and high efficient silicon-based polarization splitter-rotator using a partially-etched subwavelength grating coupler,” Sci. Rep. 6(1), 27949 (2016).
[Crossref] [PubMed]

Yang, J. Y.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Ye, W. N.

Yun, H.

H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. Jaeger, “Broadband 2 × 2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Opt. Lett. 41(13), 3041–3044 (2016).
[Crossref] [PubMed]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, 35X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” 2011 IEEE Photonics Conference, 869–870 (2011).
[Crossref]

Zamek, S.

Zavargo-Peche, L.

L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and I. Molina-Fernández, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
[Crossref]

Zhang, F.

Zhang, W.

Zhou, Q. A.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Zhou, Z.

Zimmermann, L.

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
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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 Photonics Technol. Lett. 21(24), 1894–1896 (2009).
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G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 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 Photonics Technol. Lett. 23(5), 290–292 (2011).

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V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D. X. Xu, S. Wang, A. Ortega-Moñux, and I. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photonics Rev. 10(6), 1039–1046 (2016).
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R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
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Opt. Express (11)

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
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B. Maes, J. Petráček, S. Burger, P. Kwiecien, J. Luksch, and I. Richter, “Simulations of high-Q optical nanocavities with a gradual 1D bandgap,” Opt. Express 21(6), 6794–6806 (2013).
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W.-P. Huang and J. Mu, “Complex coupled-mode theory for optical waveguides,” Opt. Express 17(21), 19134–19152 (2009).
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J. Wang, I. Glesk, and L. R. Chen, “Subwavelength grating filtering devices,” Opt. Express 22(13), 15335–15345 (2014).
[Crossref] [PubMed]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015).
[Crossref] [PubMed]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012).
[Crossref] [PubMed]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25(11), 12222–12236 (2017).
[Crossref] [PubMed]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016).
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J. S. Penades, A. Ortega-Moñux, M. Nedeljkovic, J. G. Wangüemert-Pérez, R. Halir, A. Z. Khokhar, C. Alonso-Ramos, Z. Qu, I. Molina-Fernández, P. Cheben, and G. Z. Mashanovich, “Suspended silicon mid-infrared waveguide devices with subwavelength grating metamaterial cladding,” Opt. Express 24(20), 22908–22916 (2016).
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Opt. Lett. (12)

L. Liu, Q. Deng, and Z. Zhou, “Manipulation of beat length and wavelength dependence of a polarization beam splitter using a subwavelength grating,” Opt. Lett. 41(21), 5126–5129 (2016).
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J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J. M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, “Controlling leakage losses in subwavelength grating silicon metamaterial waveguides,” Opt. Lett. 41(15), 3443–3446 (2016).
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D. Pérez-Galacho, C. Alonso-Ramos, F. Mazeas, X. Le Roux, D. Oser, W. Zhang, D. Marris-Morini, L. Labonté, S. Tanzilli, É. Cassan, and L. Vivien, “Optical pump-rejection filter based on silicon sub-wavelength engineered photonic structures,” Opt. Lett. 42(8), 1468–1471 (2017).
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A. Sánchez-Postigo, J. Gonzalo Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, “Broadband fiber-chip zero-order surface grating coupler with 0.4 dB efficiency,” Opt. Lett. 41(13), 3013–3016 (2016).
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H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. Jaeger, “Broadband 2 × 2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Opt. Lett. 41(13), 3041–3044 (2016).
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J. Gonzalo Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D. X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39(15), 4442–4445 (2014).
[Crossref] [PubMed]

X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond, N. A. F. Jaeger, and L. Chrostowski, “Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings,” Opt. Lett. 39(19), 5519–5522 (2014).
[Crossref] [PubMed]

Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
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S. Zamek, D. T. H. 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).
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Prog. Electromagnetics Res. (1)

L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Pérez, and I. Molina-Fernández, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
[Crossref]

Sci. Rep. (2)

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Figures (14)

Fig. 1
Fig. 1 Bragg grating in a SWG waveguide proposed in [47]. Λ is the period of the SWG input and output waveguides, ΛB = 2Λ is the period of the Bragg grating. The lengths of even and odd segments, L1 and L2, are different.
Fig. 2
Fig. 2 SWG metamaterial waveguide considered in this paper: (a) top view of the structure, (b) and (c) dominant magnetic and electric field components of the fundamental TE Bloch mode, respectively, (d) detail view of four periods of electric field distribution.
Fig. 3
Fig. 3 Considered designs of Bragg gratings in SWG waveguides. Two periods of Bragg gratings ΛB are shown. Central rectangles (blue) form the SWG waveguide, loading segments (beige) form the Bragg grating.
Fig. 4
Fig. 4 (a) Spectral dependence of Bragg reflectance for various numbers of periods. Nominal design, separation s=250 nm; (b) Reflectance maxima for various numbers of periods (i.e., grating lengths); red line – the best fit to Eq. (3) with κ=0.0205 µm 1 .
Fig. 5
Fig. 5 (a) Dependence of the wavelength of maximum reflectance and (b) of the coupling coefficients κ and κ (dots) on the separation s of loading segments from the edge of SWG waveguide (nominal design), with the corresponding exponential fits (dashed lines).
Fig. 6
Fig. 6 (a) Dependence of the coupling coefficient κof the Bragg grating on the longitudinal shift Δz of loading segments in the modified nominal design for three values of separation s: 150, 250 and 350 nm; (b) dependence of the maximum reflectance wavelength on Δz.
Fig. 7
Fig. 7 (a) BWFN dependence on the length of the Bragg grating on SWG waveguide (nominal design) calculated for various separations s of loading segments; the inset shows the same dependence for larger grating lengths; (b) spectral reflectance of the Bragg grating with separation s = 1000 nm and 65536 Bragg periods.
Fig. 8
Fig. 8 Performance of the Bragg grating with linear apodization obtained by varying the longitudinal shift Δz with s=450 nm. (a) Longitudinal profile of the shift Δz; (b) longitudinal dependence of coupling coefficients κ (blue line) and κ (red line); (c) spectral dependence of reflectance of the apodized Bragg grating (solid red line) and of the uniform (non-apodized) Bragg grating with s=514 nm(dashed blue line).
Fig. 9
Fig. 9 Calculated performance of the apodized SWG Bragg filters. (a) longitudinal profile of s for the s-apodized grating; (b) longitudinal dependence of coupling coefficients κ (blue line) and κ (red line); (c) spectral dependence of reflectance of the Bragg gratings apodized by varying s (dashed blue line) and by varying Δz (solid red line).
Fig. 10
Fig. 10 Schematic configuration of a FP resonator with DBR mirrors in a SWG waveguide.
Fig. 11
Fig. 11 (a) Reflectance and transmittance of SWG DBR; (b) transmittance of the FP resonator with DBR mirrors and SWG waveguide.
Fig. 12
Fig. 12 Schematic of a FP resonator with broadband DBR mirrors in a SWG waveguide.
Fig. 13
Fig. 13 (a) Reflectance spectra of broadband DBR mirrors with different number of periods, ∞ sign denotes reflectance from the semi-infinite grating; (b) transmittance spectrum of the FP resonator with 7 Bragg mirror periods and 2048 SWG waveguide periods.
Fig. 14
Fig. 14 (a) Effect of jitter in silicon segment length on the reflectance of the narrowband SWG Bragg grating; (b) jitter influence on the transmittance of the FP resonator with DBR mirrors. Solid blue lines–ideal devices, dashed red lines–devices with jitter. σ L =4 nm is the standard deviation of segment length fluctuations.

Equations (8)

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d dz ( a(z) b(z) )=j( Δβ κ κ Δβ )( a(z) b(z) ).
R= | b(0) a(0) | 2 = κ 2 sin h 2 (σL) σ 2 + κ 2 sin h 2 (σL) ,
R max =tan h 2 (κL).
BWFN= λ max 2 N g L 1+ ( κL π ) 2 ,
κ =π(1/ Λ B 2 N eff / λ max ),
κ=0.1171exp(6.94s), κ =0.2155exp(6.95s),
κ(Δz)=κ(0)cos( πΔz/ Λ B ).
s(z) ln[ ( κ 0 / 0.1171 )cos( πΔz(z)/ Λ B ) ]/ 6.94 ,

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