Abstract

The availability of low-loss optical interfaces to couple light between standard optical fibers and high-index-contrast silicon waveguides is essential for the development of chip-integrated nanophotonics. Input and output couplers based on diffraction gratings are attractive coupling solutions. Advanced grating coupler designs, with Bragg or metal mirror underneath, low- and high-index overlays, and multi-level or multi-layer layouts, have proven less useful due to customized or complex fabrication, however. In this work, we propose a rather simpler in design of efficient off-chip fiber couplers that provide a simulated efficiency up to 95% (−0.25 dB) at a wavelength of 1.55 µm. These grating couplers are formed with an L-shaped waveguide profile and synthesized subwavelength grating metamaterials. This concept jointly provides sufficient degrees of freedom to simultaneously control the grating directionality and out-radiated field profile of the grating mode. The proposed chip-to-fiber couplers promote robust sub-decibel coupling of light, yet contain device dimensions (> 120 nm) compatible with standard lithographic technologies presently available in silicon nanophotonic foundries. Fabrication imperfections are also investigated. Dimensional offsets of ± 15 nm in shallow-etch depth and ± 10 nm in linewidth’s and mask misalignments are tolerated for a 1-dB loss penalty. The proposed concept is meant to be universal, which is an essential prerequisite for developing reliable and low-cost optical couplers. We foresee that the work on L-shaped grating couplers with sub-decibel coupling efficiencies could also be a valuable direction for silicon chip interfacing in integrated nanophotonics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (5)

W. Zhou, Z. Cheng, X. Chen, K. Xu, X. Sun, and H. K. Tsang, “Subwavelength engineering in silicon photonic devices,” IEEE J. Sel. Top. Quantum Electron. 25(3), 2900113 (2019).
[Crossref]

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photon. Res. 7(2), 201–239 (2019).
[Crossref]

T. Barwicz, B. Peng, R. Leidy, A. Janta-Polczynski, T. Houghton, M. Hhater, S. Kamlapurkar, S. Engelman, P. Fortier, N. Boyer, and W. M. J. Green, “Integrated Metamaterial Interfaces for Self-Aligned Fiber-to-Chip Coupling in Volume Manufacturing,” IEEE J. Sel. Top. Quantum Electron. 25(3), 4700313 (2019).
[Crossref]

D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quantum Electron. 25(3), 8200205 (2019).
[Crossref]

N. Purwaha, A. Atieh, and W. N. Ye, “Broadband and polarization flexible SOI grating coupler based on sub-wavelength gratings with low back reflections,” OSA Continuum 2(4), 1350–1357 (2019).
[Crossref]

2018 (12)

W. Zhou, Z. Cheng, X. Sun, and H. K. Tsang, “Tailorable dual-wavelength-band coupling in a transverse-electric-mode focusing subwavelength grating coupler,” Opt. Lett. 43(12), 2985–2988 (2018).
[Crossref] [PubMed]

Y. Tong, W. Zhou, and H. K. Tsang, “Efficient perfectly vertical grating coupler for multi-core fibers fabricated with 193 nm DUV lithography,” Opt. Lett. 43(23), 5709–5712 (2018).
[Crossref] [PubMed]

G. Son, S. Han, J. Park, K. Kwon, and K. Yu, “High-efficiency broadband light coupling between optical fibers and photonic integrated circuits,” Nanophotonics 7(12), 1845–1864 (2018).
[Crossref]

D. Vermeulen and C. V. Poulton, “Optical Interfaces for Silicon Photonic Circuits,” Proc. IEEE 106(12), 2270–2280 (2018).
[Crossref]

C. Doerr and L. Chen, “Silicon Photonics in Optical Coherent Systems,” Proc. IEEE 106(12), 2291–2301 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref] [PubMed]

A. Rahim, T. Spuesens, R. Baets, and W. Bogaerts, “Open-Access Silicon Photonics: Current Status and Emerging Initiatives,” Proc. IEEE 106(12), 2313–2330 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-Grating Metamaterial Structures for Silicon Photonic Devices,” Proc. IEEE 106(12), 2144–2157 (2018).
[Crossref]

W. S. Sacher, J. C. Mikkelsen, Y. Huang, J. C. C. Mak, Z. Yong, X. Luo, Y. Li, P. Dumais, J. Jiang, D. Goodwill, E. Bernier, P. G.-Q. Lo, and J. K. S. Poon, “Monolithically Integrated Multilayer Silicon Nitride-on-Silicon Waveguide Platforms for 3-D Photonic Circuits and Devices,” Proc. IEEE 106(12), 2232–2245 (2018).
[Crossref]

L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023–4034 (2018).
[Crossref] [PubMed]

A. Michaels and E. Yablonovitch, “Inverse design of near unity efficiency perfectly vertical grating couplers,” Opt. Express 26(4), 4766–4779 (2018).
[Crossref] [PubMed]

D. Oser, D. Pérez-Galacho, C. Alonso-Ramos, X. Le Roux, S. Tanzilli, L. Vivien, L. Labonté, and É. Cassan, “Subwavelength engineering and asymmetry: two efficient tools for sub-nanometer-bandwidth silicon Bragg filters,” Opt. Lett. 43(14), 3208–3211 (2018).
[Crossref] [PubMed]

2017 (7)

Y. Chen, T. Domínguez Bucio, A. Z. Khokhar, M. Banakar, K. Grabska, F. Y. Gardes, R. Halir, Í. Molina-Fernández, P. Cheben, and J.-J. He, “Experimental demonstration of an apodized-imaging chip-fiber grating coupler for Si3N4 waveguides,” Opt. Lett. 42(18), 3566–3569 (2017).
[Crossref] [PubMed]

X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25(15), 17864–17871 (2017).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, D. Pérez-Galacho, S. Guerber, V. Vakarin, G. Marcaud, X. Le Roux, E. Cassan, D. Marris-Morini, P. Cheben, F. Boeuf, C. Baudot, and L. Vivien, “L-shaped fiber-chip grating couplers with high directionality and low reflectivity fabricated with deep-UV lithography,” Opt. Lett. 42(17), 3439–3442 (2017).
[Crossref] [PubMed]

T. Watanabe, M. Ayata, U. Koch, Y. Fedoryshyn, and J. Leuthold, “Perpendicular Grating Coupler Based on a Blazed Antiback-Reflection Structure,” IEEE J. Light. Technol. 35(21), 4663–4669 (2017).
[Crossref]

M. Passoni, D. Gerace, L. Carroll, and L. C. Andreani, “Grating couplers in silicon-on-insulator: The role of photonic guided resonances on lineshape and bandwidth,” Appl. Phys. Lett. 110(4), 041107 (2017).
[Crossref]

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2016 (4)

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F. Boeuf, S. Crémer, E. Temporiti, M. Feré, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, “Silicon Photonics R&D and Manufacturing on 300-mm Wafer Platform,” IEEE J. Light. Technol. 34(2), 286–295 (2016).
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M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
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2015 (5)

2014 (8)

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2012 (2)

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2006 (2)

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R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J.-G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
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Koch, U.

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Kwon, K.

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Lacava, C.

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Lapointe, J.

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[Crossref] [PubMed]

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[Crossref]

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

L. Carroll, J.-S. Lee, C. Scarcella, K. Gradkowski, M. Duperron, H. Lu, Y. Zhao, C. Eason, P. Morrissey, M. Rensing, S. Collins, H. Y. Hwang, and P. O’Brien, “Photonic Packaging: Transforming Silicon Photonic Integrated Circuits into Photonic Devices,” Appl. Sci. (Basel) 6(12), 426 (2016).
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T. Barwicz, B. Peng, R. Leidy, A. Janta-Polczynski, T. Houghton, M. Hhater, S. Kamlapurkar, S. Engelman, P. Fortier, N. Boyer, and W. M. J. Green, “Integrated Metamaterial Interfaces for Self-Aligned Fiber-to-Chip Coupling in Volume Manufacturing,” IEEE J. Sel. Top. Quantum Electron. 25(3), 4700313 (2019).
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Letzkus, F.

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T. Watanabe, M. Ayata, U. Koch, Y. Fedoryshyn, and J. Leuthold, “Perpendicular Grating Coupler Based on a Blazed Antiback-Reflection Structure,” IEEE J. Light. Technol. 35(21), 4663–4669 (2017).
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D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, D. De Messel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
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Z. Wang, Y. Tang, L. Wosinski, and S. He, “Experimental demonstration of a high-efficiency polarization splitter based on a one-dimensional grating with a Bragg reflector underneath,” IEEE Photonics Technol. Lett. 22(21), 1568–1570 (2010).
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W. Zhou, Z. Cheng, X. Chen, K. Xu, X. Sun, and H. K. Tsang, “Subwavelength engineering in silicon photonic devices,” IEEE J. Sel. Top. Quantum Electron. 25(3), 2900113 (2019).
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W. Zhou, Z. Cheng, X. Sun, and H. K. Tsang, “Tailorable dual-wavelength-band coupling in a transverse-electric-mode focusing subwavelength grating coupler,” Opt. Lett. 43(12), 2985–2988 (2018).
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Y. Tong, W. Zhou, and H. K. Tsang, “Efficient perfectly vertical grating coupler for multi-core fibers fabricated with 193 nm DUV lithography,” Opt. Lett. 43(23), 5709–5712 (2018).
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C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95,” Opt. Lett. 39(18), 5351–5354 (2014).
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R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
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R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J.-G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
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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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Xu, K.

W. Zhou, Z. Cheng, X. Chen, K. Xu, X. Sun, and H. K. Tsang, “Subwavelength engineering in silicon photonic devices,” IEEE J. Sel. Top. Quantum Electron. 25(3), 2900113 (2019).
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Yvind, K.

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R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fédéli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12–13), 521–526 (2012).
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L. Zavargo-Peche, A. Ortega-Moñux, J. G. Wangüemert-Perez, and I. Molina-Fernandez, “Fourier based combined techniques to design novel sub-wavelength optical integrated devices,” Prog. Electromagnetics Res. 123, 447–465 (2012).
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Appl. Opt. (1)

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IEEE J. Light. Technol. (2)

F. Boeuf, S. Crémer, E. Temporiti, M. Feré, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, “Silicon Photonics R&D and Manufacturing on 300-mm Wafer Platform,” IEEE J. Light. Technol. 34(2), 286–295 (2016).
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IEEE J. Quantum Electron. (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, D. De Messel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
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IEEE J. Sel. Top. Quantum Electron. (5)

T. Barwicz, B. Peng, R. Leidy, A. Janta-Polczynski, T. Houghton, M. Hhater, S. Kamlapurkar, S. Engelman, P. Fortier, N. Boyer, and W. M. J. Green, “Integrated Metamaterial Interfaces for Self-Aligned Fiber-to-Chip Coupling in Volume Manufacturing,” IEEE J. Sel. Top. Quantum Electron. 25(3), 4700313 (2019).
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IEEE Photonics J. (1)

X. Chen and H. K. Tsang, “Nanoholes grating couplers for coupling between silicon-on-insulator waveguides and optical fibers,” IEEE Photonics J. 1(3), 184–190 (2009).
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Z. Wang, Y. Tang, L. Wosinski, and S. He, “Experimental demonstration of a high-efficiency polarization splitter based on a one-dimensional grating with a Bragg reflector underneath,” IEEE Photonics Technol. Lett. 22(21), 1568–1570 (2010).
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Nanophotonics (2)

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Opt. Express (16)

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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G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express 14(24), 11622–11630 (2006).
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D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18(17), 18278–18283 (2010).
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P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
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W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Opt. Express 22(2), 1277–1286 (2014).
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L. Carroll, D. Gerace, I. Cristiani, and L. C. Andreani, “Optimizing polarization-diversity couplers for Si-photonics: reaching the -1dB coupling efficiency threshold,” Opt. Express 22(12), 14769–14781 (2014).
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C. Li, K. S. Chee, J. Tao, H. Zhang, M. Yu, and G. Q. Lo, “Silicon photonics packaging with lateral fiber coupling to apodized grating coupler embedded circuit,” Opt. Express 22(20), 24235–24240 (2014).
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S. Yang, Y. Zhang, T. Baehr-Jones, and M. Hochberg, “High efficiency germanium-assisted grating coupler,” Opt. Express 22(25), 30607–30612 (2014).
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M. Dai, L. Ma, Y. Xu, M. Lu, X. Liu, and Y. Chen, “Highly efficient and perfectly vertical chip-to-fiber dual-layer grating coupler,” Opt. Express 23(2), 1691–1698 (2015).
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A. Bozzola, L. Carroll, D. Gerace, I. Cristiani, and L. C. Andreani, “Optimising apodized grating couplers in a pure SOI platform to -0.5 dB coupling efficiency,” Opt. Express 23(12), 16289–16304 (2015).
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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).
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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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M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
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X. Chen, D. J. Thomson, L. Crudginton, A. Z. Khokhar, and G. T. Reed, “Dual-etch apodised grating couplers for efficient fibre-chip coupling near 1310 nm wavelength,” Opt. Express 25(15), 17864–17871 (2017).
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L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023–4034 (2018).
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A. Michaels and E. Yablonovitch, “Inverse design of near unity efficiency perfectly vertical grating couplers,” Opt. Express 26(4), 4766–4779 (2018).
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Opt. Lett. (13)

W. Zhou, Z. Cheng, X. Sun, and H. K. Tsang, “Tailorable dual-wavelength-band coupling in a transverse-electric-mode focusing subwavelength grating coupler,” Opt. Lett. 43(12), 2985–2988 (2018).
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D. Oser, D. Pérez-Galacho, C. Alonso-Ramos, X. Le Roux, S. Tanzilli, L. Vivien, L. Labonté, and É. Cassan, “Subwavelength engineering and asymmetry: two efficient tools for sub-nanometer-bandwidth silicon Bragg filters,” Opt. Lett. 43(14), 3208–3211 (2018).
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Y. Tong, W. Zhou, and H. K. Tsang, “Efficient perfectly vertical grating coupler for multi-core fibers fabricated with 193 nm DUV lithography,” Opt. Lett. 43(23), 5709–5712 (2018).
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D. Benedikovic, C. Alonso-Ramos, D. Pérez-Galacho, S. Guerber, V. Vakarin, G. Marcaud, X. Le Roux, E. Cassan, D. Marris-Morini, P. Cheben, F. Boeuf, C. Baudot, and L. Vivien, “L-shaped fiber-chip grating couplers with high directionality and low reflectivity fabricated with deep-UV lithography,” Opt. Lett. 42(17), 3439–3442 (2017).
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Y. Chen, T. Domínguez Bucio, A. Z. Khokhar, M. Banakar, K. Grabska, F. Y. Gardes, R. Halir, Í. Molina-Fernández, P. Cheben, and J.-J. He, “Experimental demonstration of an apodized-imaging chip-fiber grating coupler for Si3N4 waveguides,” Opt. Lett. 42(18), 3566–3569 (2017).
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Y. Chen, R. Halir, Í. Molina-Fernández, P. Cheben, and J.-J. He, “High-efficiency apodized-imaging chip-fiber grating coupler for silicon nitride waveguides,” Opt. Lett. 41(21), 5059–5062 (2016).
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D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, J. Lapointe, S. Janz, R. Halir, A. Ortega-Moñux, J. G. Wangüemert-Pérez, I. Molina-Fernández, J.-M. Fédéli, L. Vivien, and M. Dado, “High-directionality fiber-chip grating coupler with interleaved trenches and subwavelength index-matching structure,” Opt. Lett. 40(18), 4190–4193 (2015).
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Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with -0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
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C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95,” Opt. Lett. 39(18), 5351–5354 (2014).
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R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
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R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J.-G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
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V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
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Figures (7)

Fig. 1
Fig. 1 (a) Three-dimensional (3-D) and de-coupled two-dimensional (2-D) (b) side and (c) top view schematics of the proposed fiber-to-chip grating coupler with an L-shaped waveguide profile and engineered subwavelength grating (SWG) metamaterials embedded within the etched trenches.
Fig. 2
Fig. 2 2-D mapping of the grating directionality as a function of the unetched Si slabs and the shallow-etch trenches for different lengths of the deep-etch trenches: (a) ld = 50 nm and (b) ld = 150 nm. (c) Grating directionality / grating reflectivity and (d) coupling strength as a function of the width of the etched lateral SWG holes. Inset of (c) synthesis of SWG metamaterials.
Fig. 3
Fig. 3 Relation between the transversal and the longitudinal parameters of the proposed L-shaped grating couplers with index-engineered SWG metamaterials.
Fig. 4
Fig. 4 (a) 2-D mapping of the fiber-to-chip coupling loss as a function of the number of apodized grating periods and the width of the etched SWG hole. Coupling loss versus the width of the etched SWG hole for different number of apodized grating periods: (b) NPa = 5, (c) NPa = 10, (d) NPa = 15, and (e) NPa = 20. In panels (b) to (e), the horizontal line (solid black) represents a 1-dB loss threshold in fiber-to-chip coupling, while two vertical lines (solid red and blue) denote minimum feature size that can be fabricated by using state-of-the-art patterning technologies (immersion {A} and deep-ultraviolet {B} optical lithography’s) used in Si nanophotonic foundries.
Fig. 5
Fig. 5 Grating reflectivity as a function of the width of the etched SWG hole for different number of apodized grating periods. Two vertical lines (solid red and blue) denote minimum feature criteria for immersion {A} and deep-ultraviolet {B} lithographies.
Fig. 6
Fig. 6 Coupling loss as a function of the wavelength for different critical dimensions and various number of apodized grating periods: (a) NPa = 5, (b) NPa = 10, and (c) NPa = 15. (d) Summarized 3-dB coupling bandwidth of the apodized L-shaped fiber-to-chip grating couplers as a function of the number of apodized periods and various minimum feature sizes.
Fig. 7
Fig. 7 Tolerance analysis: Coupling loss as a function of a wavelength for grating coupler designs. (a) Etch depth variation and (b) in-plane dimensional variation. Insets: Coupling loss as a function of fabrication errors at a design wavelength of 1.55 µm.

Equations (4)

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l gc = i=1 N P a Λ a,i +N P u Λ u
η[dB]=10 log 10 ( ( 1R )( D )( FM ) )
l n,i = kλ n bf,i n c sin( Θ i ) ( l d + l s )
h e = h e,0 + δ err { h e } l d = l d,0 + δ err { l d } l s = l s,0 + δ err { l s } l n = l n,0 δ err { l n } δ err { m } w e = w e,0 δ err { w e }

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