Abstract

A grating coupling scheme from free-space light into silicon waveguide with a remarkable property of wide flat-top angular efficiency is proposed and theoretically investigated. The coupling structure is composed of two cascaded gratings with a proper distance between their peak angular efficiencies. A quantitative semi-analytical theory based on coupled-mode models is developed for performance prediction and validated with the fully vectorial aperiodic Fourier modal method (a-FMM). With the theory, wide flat-top angular response is achieved and the conditions are pointed out. Proof-of-principle demonstrations show that the −1 dB angular width, a figure of merit to evaluate the flat-top performance, is broadened to almost 3 to 4 times, and meanwhile the −3 dB angular width, i.e., angular-full-width-half-maximum (AFWHM), is widened to nearly more than twice, compared with the reference gratings composed of the same number of periodic defects. We believe this work will find applications in biological or chemical sensing and novel optical devices.

© 2012 Optical Society of America

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  1. T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
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    [Crossref]
  21. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
    [Crossref]
  22. L. Dong, S. Iyer, S. Popov, and A. Friberg, “3D fabrication of waveguide and grating coupler in SU-8 by optimized gray scale electron beam lithography,” in Proceedings of ACP (2010).
  23. A. Sure, T. Dillon, J. Murakowski, C. Lin, D. Pustai, and D. W. Prather, “Fabrication and characterization of three-dimensional silicon tapers,” Opt. Express 11, 3555–3561 (2003).
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  24. S. Lardenois, D. Pascal, L. Vivien, E. Cassan, S. Laval, R. Orobtchouk, M. Heitzmann, N. Bouzaida, and L. Mollard, “Low-loss submicrometer silicon-on-insulator rib waveguides and corner mirrors,” Opt. Lett. 28, 1150–1152 (2003).
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  25. G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
    [Crossref]
  26. G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010).
    [Crossref] [PubMed]

2011 (2)

J. Wu, G. Zheng, Z. Li, and C. Yang, “Focal plane tuning in wide-field-of-view microscope with Talbot pattern illumination,” Opt. Lett. 36, 2179–2181 (2011).
[Crossref] [PubMed]

G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
[Crossref]

2010 (4)

2008 (4)

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
[Crossref]

E. D. Tommasi, L. D. Stefano, I. Rea, V. D. Sarno, L. Rotiroti, P. Arcari, A. Lamberti, C. Sanges, and I. Rendina, “Porous silicon based resonant mirrors for biochemical sensing,” Sensors 8, 6549–6556 (2008).
[Crossref]

G. Maire, L. Vivien, G. Sattler, A. Kazmierczak, B. Sanchez, K. B. Gylfason, A. Griol, D. Marris-Morini, E. Cassan, D. Giannone, H. Sohlström, and D. Hill, “High efficiency silicon nitride surface grating couplers,” Opt. Express 16, 328–333 (2008).
[Crossref] [PubMed]

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[Crossref]

2007 (6)

A. B. Greenwell, S. Boonruang, and M. G. Moharam, “Multiple wavelength resonant grating filters at oblique incidence with broad angular acceptance,” Opt. Express 15, 8626–8638 (2007).
[Crossref] [PubMed]

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

K. L. Lee, C. W. Lee, W. S. Wang, and P. K. Wei, “Sensitive biosensor array using surface plasmon resonance on metallic nanoslits,” J. Biomed. Opt. 12, 044023 (2007).
[Crossref] [PubMed]

F. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, M. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Light-wave Technol. 25, 151–156 (2007).
[Crossref]

S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. V. Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625–9630 (2007).
[Crossref] [PubMed]

G. Roelkens, D. V. Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32, 1495–1497 (2007).
[Crossref] [PubMed]

2006 (3)

L. Vivien, D. Pascal, S. Lardenois, D. Marris-Morini, E. Cassan, F. Grillot, S. Laval, J. M. Fédéli, and L. E. Melhaoui, “Light injection in SOI microwaveguides using high-efficiency grating couplers,” J. Lightwave Technol. 24, 3810–3815 (2006).
[Crossref]

J. Ho, A. V. Parwani, D. M. Jukic, Y. Yagi, L. Anthony, and J. R. Gilbertson, “Use of whole slide imaging in surgical pathology quality assurance: design and pilot validation studies,” Hum. Pathol. 37, 322–331 (2006).
[Crossref] [PubMed]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[Crossref]

2005 (1)

2003 (2)

2002 (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
[Crossref]

2000 (1)

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
[Crossref]

Absil, P.

Alameh, K.

G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
[Crossref]

Ang, T. W.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
[Crossref]

Anthony, L.

J. Ho, A. V. Parwani, D. M. Jukic, Y. Yagi, L. Anthony, and J. R. Gilbertson, “Use of whole slide imaging in surgical pathology quality assurance: design and pilot validation studies,” Hum. Pathol. 37, 322–331 (2006).
[Crossref] [PubMed]

Arcari, P.

E. D. Tommasi, L. D. Stefano, I. Rea, V. D. Sarno, L. Rotiroti, P. Arcari, A. Lamberti, C. Sanges, and I. Rendina, “Porous silicon based resonant mirrors for biochemical sensing,” Sensors 8, 6549–6556 (2008).
[Crossref]

Ayre, M.

F. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, M. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Light-wave Technol. 25, 151–156 (2007).
[Crossref]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[Crossref]

Baets, R.

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
[Crossref]

F. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, M. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Light-wave Technol. 25, 151–156 (2007).
[Crossref]

G. Roelkens, D. V. Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32, 1495–1497 (2007).
[Crossref] [PubMed]

S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. V. Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625–9630 (2007).
[Crossref] [PubMed]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
[Crossref]

Balis, U. J.

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

Basha, M. A.

Bell, D. W.

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

Bienstman, P.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
[Crossref]

Bogaerts, W.

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. V. Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
[Crossref] [PubMed]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
[Crossref]

Boonruang, S.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Bouzaida, N.

Brision, S.

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
[Crossref]

Cai, L.

G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
[Crossref]

G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010).
[Crossref] [PubMed]

Cassan, E.

Chaudhuri, S.

Coskun, A. F.

Daele, P. V.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
[Crossref]

Digumarthy, S.

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

Dillon, T.

Dong, L.

L. Dong, S. Iyer, S. Popov, and A. Friberg, “3D fabrication of waveguide and grating coupler in SU-8 by optimized gray scale electron beam lithography,” in Proceedings of ACP (2010).

Evans, A. G. R.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
[Crossref]

Fédéli, J. M.

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
[Crossref]

L. Vivien, D. Pascal, S. Lardenois, D. Marris-Morini, E. Cassan, F. Grillot, S. Laval, J. M. Fédéli, and L. E. Melhaoui, “Light injection in SOI microwaveguides using high-efficiency grating couplers,” J. Lightwave Technol. 24, 3810–3815 (2006).
[Crossref]

Fehrembach, A.

Friberg, A.

L. Dong, S. Iyer, S. Popov, and A. Friberg, “3D fabrication of waveguide and grating coupler in SU-8 by optimized gray scale electron beam lithography,” in Proceedings of ACP (2010).

Gautier, P.

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
[Crossref]

Giannone, D.

Gilbertson, J. R.

J. Ho, A. V. Parwani, D. M. Jukic, Y. Yagi, L. Anthony, and J. R. Gilbertson, “Use of whole slide imaging in surgical pathology quality assurance: design and pilot validation studies,” Hum. Pathol. 37, 322–331 (2006).
[Crossref] [PubMed]

Greenwell, A. B.

Grillot, F.

Griol, A.

Gylfason, K. B.

Haber, D. A.

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

Heitzmann, M.

Hill, D.

Ho, J.

J. Ho, A. V. Parwani, D. M. Jukic, Y. Yagi, L. Anthony, and J. R. Gilbertson, “Use of whole slide imaging in surgical pathology quality assurance: design and pilot validation studies,” Hum. Pathol. 37, 322–331 (2006).
[Crossref] [PubMed]

Hugonin, J. P.

H. Liu, P. Lalanne, X. Yang, and J. P. Hugonin, “Surface plasmon generation by subwavelength isolated objects,” IEEE J. Sel. Top. Quantum Electron. 14, 1522–1529 (2008).
[Crossref]

Irimia, D.

S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
[Crossref] [PubMed]

Iyer, S.

L. Dong, S. Iyer, S. Popov, and A. Friberg, “3D fabrication of waveguide and grating coupler in SU-8 by optimized gray scale electron beam lithography,” in Proceedings of ACP (2010).

Josey, M. R.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
[Crossref]

Jukic, D. M.

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D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
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S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
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F. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, M. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Light-wave Technol. 25, 151–156 (2007).
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S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. V. Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625–9630 (2007).
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Laval, S.

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K. L. Lee, C. W. Lee, W. S. Wang, and P. K. Wei, “Sensitive biosensor array using surface plasmon resonance on metallic nanoslits,” J. Biomed. Opt. 12, 044023 (2007).
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K. L. Lee, C. W. Lee, W. S. Wang, and P. K. Wei, “Sensitive biosensor array using surface plasmon resonance on metallic nanoslits,” J. Biomed. Opt. 12, 044023 (2007).
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G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010).
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Lin, C.

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E. D. Tommasi, L. D. Stefano, I. Rea, V. D. Sarno, L. Rotiroti, P. Arcari, A. Lamberti, C. Sanges, and I. Rendina, “Porous silicon based resonant mirrors for biochemical sensing,” Sensors 8, 6549–6556 (2008).
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Sure, A.

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D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
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D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
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D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. V. Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. V. Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625–9630 (2007).
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S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Balis, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450, 1235–1239 (2007).
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G. Li, L. Cai, F. Xiao, Y. Pei, and A. Xu, “A quantitative theory and the generalized Bragg condition for surface plasmon Bragg reflectors,” Opt. Express 18, 10487–10499 (2010).
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G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
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Appl. Phys. Lett. (1)

G. Roelkens, D. Vermeulen, D. V. Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92, 131101 (2008).
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J. Ho, A. V. Parwani, D. M. Jukic, Y. Yagi, L. Anthony, and J. R. Gilbertson, “Use of whole slide imaging in surgical pathology quality assurance: design and pilot validation studies,” Hum. Pathol. 37, 322–331 (2006).
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IEEE J. Quantum Electron. (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, 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, 949–955 (2002).
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IEEE Photon. Technol. Lett. (1)

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, “Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,” IEEE Photon. Technol. Lett. 12, 59–61 (2000).
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J. Biomed. Opt. (1)

K. L. Lee, C. W. Lee, W. S. Wang, and P. K. Wei, “Sensitive biosensor array using surface plasmon resonance on metallic nanoslits,” J. Biomed. Opt. 12, 044023 (2007).
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F. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, M. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Light-wave Technol. 25, 151–156 (2007).
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G. Li, F. Xiao, L. Cai, K. Alameh, and A. Xu, “Theory of the scattering of light and surface plasmon polaritons by finite-size subwavelength metallic defects vis field decomposition,” New J. Phys. 13, 073045 (2011).
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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Opt. Lett. (3)

Sensors (1)

E. D. Tommasi, L. D. Stefano, I. Rea, V. D. Sarno, L. Rotiroti, P. Arcari, A. Lamberti, C. Sanges, and I. Rendina, “Porous silicon based resonant mirrors for biochemical sensing,” Sensors 8, 6549–6556 (2008).
[Crossref]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

L. Dong, S. Iyer, S. Popov, and A. Friberg, “3D fabrication of waveguide and grating coupler in SU-8 by optimized gray scale electron beam lithography,” in Proceedings of ACP (2010).

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Figures (6)

Fig. 1
Fig. 1 The overlapping diffraction patterns: (a) light waves from two objects are unresolved; (b) Rayleigh criterion; (c) light waves from two objects are resolved.

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Fig. 2
Fig. 2 (a) Schematic of the proposed grating coupler. (b) Schematic of the global model, which treats each array of grating as a ‘black box’. The first (or the second) ‘black box’ is composed of N1 (or N2) periodic defects with period p1 (or p2). The defects in both ‘black boxes’ are of constant height hr and width wr. The structural distance between two ‘black boxes’ is d. (c,d) show the main elementary scattering processes for the ‘black box’ of Nm defects, i.e., the excitation coefficients β N m ±, reflection coefficients r N m ± and transmission coefficient tNm under illumination of plane wave (c) and waveguide modes (d). (e) schematic of the nested model of an isolated ‘black box’. (f,g) show the scattering coefficients of a single defect under illumination of plane wave (f) and waveguide mode (g). The vertical blue-dashed lines in (b,e) indicate the zero phase of the incident plane wave.

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Fig. 3
Fig. 3 Physical interpretations of Eq. (3).

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Fig. 4
Fig. 4 Comparisons among coupling efficiency of the isolated grating η N + with N1 or N2 defects (top row), the reference grating η N 1 + N 2 + with N1 + N2 defects of period p1 (or p2) (middle row), and the cascaded gratings η N 1 N 2 + with N1 defects of period p1, N2 defects of period p2, and ‘box-to-box’ structural distance d (bottom row) by model predictions (green-dashed lines with circles) and a-FMM computational data (red-solid lines). The vertical black-dashed lines indicate the peak angular positions. The calculation of the four columns from left to right by a-FMM are performed for: hr = 250 nm, wr = 520 nm, (a,b,c) p1 = 567 nm, N1 = 8, p2 = 675 nm, N2 = 4, and d = 240 nm; (d,e,f) p1 = 617 nm, N1 = 7, p2 = 740 nm, N2 = 6, and d = 1150 nm; (g,h,i) p1 = 675 nm, N1 = 7, p2 = 811 nm, N2 = 6, and d = 1195 nm. (j,k,l) p1 = 567 nm, N1 = 14, p2 = 675 nm, N2 = 6, and d = 720 nm; Φ is broadened from 6° or 5° to 20° (b,c), from 7° or 5° to 15° (e,f), from 5° or 6° to 16° (h,i), and from 5° or 4° to 24° (k,l), respectively; Θ is widened from 12° or 10° to 27° (b,c), from 11° or 10° to 20° (e,f), from 9° or 10° to 20° (h,i), and from 10° or 7° to 29° (h,i), respectively.

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Fig. 5
Fig. 5 Influential elements on wide-flat top angular efficiency: (a,b) structural distance, (c,d) peak incoupling cross sections, and (e,f) the interval between angular peaks. The vertical black-dashed lines indicate the peak angular positions. The calculation of the three columns from left to right by a-FMM are performed respectively for: hr = 250 nm, wr = 520 nm, (a,b) p1 = 567 nm, p2 = 675 nm, N1 = 8, N2 = 4, and d = 490 nm; (c,d) p1 = 617 nm, p2 = 740 nm, N1 = 6, N2 = 8, and d = 905 nm; (e,f) p1 = 567 nm, p2 = 617 nm, N1 = 9, N2 = 6, and d = 495 nm, respectively.

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Fig. 6
Fig. 6 The calculations are performed for deeply etched rectangular grating with groove depth hr = 100 nm and width wr = 150 nm. (a–d) depict the comparison of the model predictions (blue-dashed line with circles) and the a-FMM computational data (red line) for 10 periodic grooves on (a) |r10|2, (b) arg(r10), (c) |t10|2, and (d) arg(t10) as functions of the period p. (e,f) show the comparison between the reference rectangular grating η N 1 + N 2 + with N1 + N2 defects of period p1 or p2 (e), and the cascaded rectangular grating η N 1 N 2 + with N1 defects of period p1, N2 defects of period p2, and ‘box-to-box’ structural distance d (f). p1 = 809 nm, p2 = 1057 nm, N1 = 6, N2 = 4, and d = 630 nm.

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Equations (17)

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B 1 = β N 1 − + t N 1 u B 2 + r N 1 + u A 0
A 1 = β N 1 + + r N 1 − u B 2 + t N 1 u A 0
B 2 = w β N 2 − + r N 2 + u A 1
A 2 = w β N 2 + + t N 2 u A 1
β N 1 N 2 + = w β N 2 + + t N 2 u r N 1 − u w β N 2 − + β N 1 + 1 − r N 1 − r N 2 + u 2 ,
β N 1 N 2 − = β N 1 − + t N 1 u w β N 2 − + r N 2 + u β N 1 + 1 − r N 1 − r N 2 + u 2 ,
r N 1 N 2 = r N 1 + + r N 2 + t N 1 2 u 2 1 − r N 1 − r N 2 + u 2 ,
t N 1 N 2 = t N 1 t N 2 u 1 − r N 1 − r N 2 + u 2 ,
β N 1 N 2 + ≈ t N 2 u β N 1 + + w β N 2 +
arg ( t N 2 ) + k 0 Re ( n eff ) d ≈ 2 m π
β N + = w N − 1 ( β 1 + + t 1 r N − 1 − u N − 1 2 β 1 − ) 1 − t 1 u N − 1 w N − 1 − 1 ,
r N = r N − 1 + + r 1 + t N − 1 2 u N − 1 2 1 − r 1 + r N − 1 − u N − 1 2 ,
t N = t 1 t N − 1 u N − 1 1 − r 1 + r N − 1 − u N − 1 2 .
β N + = w N − 1 ( β 1 + + t 1 r N − 1 u 2 β 1 − ) 1 − t 1 u w 1 − N
r N = r N − 1 + r 1 t N − 1 2 u 2 ,
t N = t 1 t N − 1 u .
arg ( t 1 ) + k 0 Re ( n eff ) p − k 0 n 0 p sin θ = 2 m π

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