Abstract

We rigorously analyze and compare preferential-order waveguide grating output couplers using the finite-difference time-domain method in the total-field/scattered-field formulation for TE and TM polarizations. Four kinds of preferential-order grating couplers are studied: volume holographic grating couplers, slanted parallelogrammic surface-relief grating couplers, double-corrugated surface-relief grating couplers, and reflecting-stack surface-relief grating couplers. The outcoupling efficiencies and branching ratios of the couplers, revealing their preferentiality, are calculated and compared with the rigorous coupled-wave analysis leaky-mode method. In addition, their performance is examined in terms of the main design parameters and the excitation wavelength.

© 2010 Optical Society of America

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  1. H. Kogelnik and P. Sosnowski, “Holographic thin film couplers,” Bell. Syst. Tech. J. 49, 1602–1608 (1970).
  2. K. Ogawa and W. S. C. Chang, “Analysis of holographic thin film grating coupler,” Appl. Opt. 12, 2167–2171 (1973).
    [CrossRef] [PubMed]
  3. W. Y. Wang and T. J. DiLaura, “Bragg effect waveguide coupler analysis,” Appl. Opt. 16, 3230–3236 (1977).
    [CrossRef] [PubMed]
  4. W. Driemeier and A. Brockmeyer, “High-resolution photorefractive polymer for optical recording of waveguide gratings,” Appl. Opt. 25, 2960–2966 (1986).
    [CrossRef] [PubMed]
  5. W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15, 725–727 (1990).
    [CrossRef] [PubMed]
  6. W. Driemeier, “Coupled-wave analysis of the Bragg effect waveguide coupler,” J. Mod. Opt. 38, 363–377 (1991).
    [CrossRef]
  7. S. M. Schultz and E. N. Glytsis, “Design, fabrication and performance of preferential-order volume waveguide couplers,” Appl. Opt. 39, 1223–1232 (2000).
    [CrossRef]
  8. S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design of a high-efficiency volume grating coupler for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
    [CrossRef]
  9. S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Volume grating preferential-order focusing waveguide coupler,” Opt. Lett. 24, 1708–1710 (1999).
    [CrossRef]
  10. R. A. Villalaz, E. N. Glytsis, and T. K. Gaylord, “Volume grating couplers: polarization and loss effects,” Appl. Opt. 41, 5223–5229 (2002).
    [CrossRef] [PubMed]
  11. S.-D. Wu and E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method,” Appl. Opt. 43, 1009–1023 (2004).
    [CrossRef] [PubMed]
  12. A. D. Papadopoulos and E. N. Glytsis, “Optical waveguide grating couplers: 2nd-order and 4th-order finite-difference time-domain analysis,” Appl. Opt. 48, 5164–5175 (2009).
    [CrossRef] [PubMed]
  13. S. T. Peng and T. Tamir, “Directional blazing of waves guided by asymmetrical dielectric gratings,” Opt. Commun. 11, 405–409 (1974).
    [CrossRef]
  14. W. Streifer, R. D. Burnham, and D. R. Scifres, “Analysis of grating-coupled radiatio in GaAs: GaAlAs lasers and waveguide-II: blazing effects,” IEEE J. Quantum Electron. 12, 494–499 (1976).
    [CrossRef]
  15. T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29, 303–304 (1976).
    [CrossRef]
  16. M. Matsumoto, “Analysis of the blazing effect in second order gratings,” IEEE J. Quantum Electron. 28, 2016–2023(1992).
    [CrossRef]
  17. M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245(1994).
    [CrossRef]
  18. M. Li and S. J. Sheard, “Experimental study of waveguide grating couplers with parallelogramic tooth profiles,” Opt. Eng. 35, 3101–3106 (1996).
    [CrossRef]
  19. T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
    [CrossRef]
  20. T. Liao and S. Sheard, “Integrated-optic array illuminator: a new design for guided-wave optical interconnections,” Appl. Opt. 37, 2729–2734 (1998).
    [CrossRef]
  21. J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambrill, “Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection,” Appl. Opt. 36, 5717–5727 (1997).
    [CrossRef] [PubMed]
  22. I. A. Avrutsky, A. S. Svakhin, and V. A. Sychugov, “Interference phenomena in waveguide with two corrugated boundaries,” J. Mod. Opt. 36, 1303–1320 (1989).
    [CrossRef]
  23. I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett. 15, 1446–1448 (1990).
    [CrossRef] [PubMed]
  24. J. C. Brazas, L. Li, and A. L. McKeon, “High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation,” Appl. Opt. 34, 604–609 (1995).
    [CrossRef] [PubMed]
  25. R. L. Roncone, L. Li, K. A. Bates, J. J. Burke, L. Weisenbach, and B. J. J. Zelinski, “Design and fabrication of single-leakage-channel grating coupler,” Appl. Opt. 32, 4522–4528 (1993).
    [CrossRef] [PubMed]
  26. R. L. Roncone, L. Li, K. A. Bates, and J. C. Brazas, “Single-leakage-channel grating couplers: comparison of theoretical and experimental branching ratios,” Opt. Lett. 18, 1919–1921(1993).
    [CrossRef] [PubMed]
  27. N. Eriksson, M. Hagberg, and A. Larsson, “Highly directional grating outcouplers with tailored radiation characteristics,” IEEE J. Quantum Electron. 32, 1038–1047 (1996).
    [CrossRef]
  28. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).
  29. H. Kogelnik, “Theory of optical waveguides,” in T.Tamir, ed., Guided-Wave Optoelectronics (Springer-Verlag, 1988), pp. 7–88.
  30. L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Microwave Theory Tech. 48, 334–338 (2000).
    [CrossRef]
  31. A. D. Papadopoulos and E. N. Glytsis, “Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings,” Appl. Opt. 47, 1981–1994 (2008).
    [CrossRef] [PubMed]
  32. J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339 (2000).
    [CrossRef]
  33. R. J. Luebbers and F. Hunsberger, “FDTD for Nth-order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301(1992).
    [CrossRef]
  34. M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microwave Guided Wave Lett. 6, 447–449 (1996).
    [CrossRef]
  35. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
    [CrossRef]
  36. T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
    [CrossRef]
  37. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

2009

2008

2007

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

2004

2002

2000

S. M. Schultz and E. N. Glytsis, “Design, fabrication and performance of preferential-order volume waveguide couplers,” Appl. Opt. 39, 1223–1232 (2000).
[CrossRef]

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339 (2000).
[CrossRef]

L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Microwave Theory Tech. 48, 334–338 (2000).
[CrossRef]

1999

1998

1997

J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambrill, “Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection,” Appl. Opt. 36, 5717–5727 (1997).
[CrossRef] [PubMed]

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

1996

M. Li and S. J. Sheard, “Experimental study of waveguide grating couplers with parallelogramic tooth profiles,” Opt. Eng. 35, 3101–3106 (1996).
[CrossRef]

N. Eriksson, M. Hagberg, and A. Larsson, “Highly directional grating outcouplers with tailored radiation characteristics,” IEEE J. Quantum Electron. 32, 1038–1047 (1996).
[CrossRef]

M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microwave Guided Wave Lett. 6, 447–449 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

1995

1994

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245(1994).
[CrossRef]

1993

1992

R. J. Luebbers and F. Hunsberger, “FDTD for Nth-order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301(1992).
[CrossRef]

M. Matsumoto, “Analysis of the blazing effect in second order gratings,” IEEE J. Quantum Electron. 28, 2016–2023(1992).
[CrossRef]

1991

W. Driemeier, “Coupled-wave analysis of the Bragg effect waveguide coupler,” J. Mod. Opt. 38, 363–377 (1991).
[CrossRef]

1990

1989

I. A. Avrutsky, A. S. Svakhin, and V. A. Sychugov, “Interference phenomena in waveguide with two corrugated boundaries,” J. Mod. Opt. 36, 1303–1320 (1989).
[CrossRef]

1986

1977

1976

W. Streifer, R. D. Burnham, and D. R. Scifres, “Analysis of grating-coupled radiatio in GaAs: GaAlAs lasers and waveguide-II: blazing effects,” IEEE J. Quantum Electron. 12, 494–499 (1976).
[CrossRef]

T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29, 303–304 (1976).
[CrossRef]

1974

S. T. Peng and T. Tamir, “Directional blazing of waves guided by asymmetrical dielectric gratings,” Opt. Commun. 11, 405–409 (1974).
[CrossRef]

1973

1970

H. Kogelnik and P. Sosnowski, “Holographic thin film couplers,” Bell. Syst. Tech. J. 49, 1602–1608 (1970).

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

Aoyagi, T.

T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29, 303–304 (1976).
[CrossRef]

Aoyagi, Y.

T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29, 303–304 (1976).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett. 15, 1446–1448 (1990).
[CrossRef] [PubMed]

I. A. Avrutsky, A. S. Svakhin, and V. A. Sychugov, “Interference phenomena in waveguide with two corrugated boundaries,” J. Mod. Opt. 36, 1303–1320 (1989).
[CrossRef]

Baechtold, W.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Bates, K. A.

Beaucoudrey, N.

Brazas, J. C.

Brockmeyer, A.

Burke, J. J.

Burnham, R. D.

W. Streifer, R. D. Burnham, and D. R. Scifres, “Analysis of grating-coupled radiatio in GaAs: GaAlAs lasers and waveguide-II: blazing effects,” IEEE J. Quantum Electron. 12, 494–499 (1976).
[CrossRef]

Cambrill, E.

Chang, W. S. C.

Chavel, P.

DiLaura, T. J.

Driemeier, W.

Eriksson, N.

N. Eriksson, M. Hagberg, and A. Larsson, “Highly directional grating outcouplers with tailored radiation characteristics,” IEEE J. Quantum Electron. 32, 1038–1047 (1996).
[CrossRef]

Erni, D.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Gaylord, T. K.

Gedney, S. D.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339 (2000).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Glytsis, E. N.

Gurel, L.

L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Microwave Theory Tech. 48, 334–338 (2000).
[CrossRef]

Hafner, C. H.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Hagberg, M.

N. Eriksson, M. Hagberg, and A. Larsson, “Highly directional grating outcouplers with tailored radiation characteristics,” IEEE J. Quantum Electron. 32, 1038–1047 (1996).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

Hunsberger, F.

R. J. Luebbers and F. Hunsberger, “FDTD for Nth-order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301(1992).
[CrossRef]

Jalali, T.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Kogelnik, H.

H. Kogelnik and P. Sosnowski, “Holographic thin film couplers,” Bell. Syst. Tech. J. 49, 1602–1608 (1970).

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell. Syst. Tech. J. 48, 2909–2947 (1969).

H. Kogelnik, “Theory of optical waveguides,” in T.Tamir, ed., Guided-Wave Optoelectronics (Springer-Verlag, 1988), pp. 7–88.

Kuzuoglu, M.

M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microwave Guided Wave Lett. 6, 447–449 (1996).
[CrossRef]

Larsson, A.

N. Eriksson, M. Hagberg, and A. Larsson, “Highly directional grating outcouplers with tailored radiation characteristics,” IEEE J. Quantum Electron. 32, 1038–1047 (1996).
[CrossRef]

Li, L.

Li, M.

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

M. Li and S. J. Sheard, “Experimental study of waveguide grating couplers with parallelogramic tooth profiles,” Opt. Eng. 35, 3101–3106 (1996).
[CrossRef]

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245(1994).
[CrossRef]

Liao, T.

T. Liao and S. Sheard, “Integrated-optic array illuminator: a new design for guided-wave optical interconnections,” Appl. Opt. 37, 2729–2734 (1998).
[CrossRef]

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

Luebbers, R. J.

R. J. Luebbers and F. Hunsberger, “FDTD for Nth-order dispersive media,” IEEE Trans. Antennas Propag. 40, 1297–1301(1992).
[CrossRef]

Matsumoto, M.

M. Matsumoto, “Analysis of the blazing effect in second order gratings,” IEEE J. Quantum Electron. 28, 2016–2023(1992).
[CrossRef]

McKeon, A. L.

Miller, J. M.

Mittra, R.

M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microwave Guided Wave Lett. 6, 447–449 (1996).
[CrossRef]

Mohammadi, A.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Namba, S.

T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29, 303–304 (1976).
[CrossRef]

Ogawa, K.

Oguz, U.

L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Microwave Theory Tech. 48, 334–338 (2000).
[CrossRef]

Papadopoulos, A. D.

Parriaux, O.

Peng, S. T.

S. T. Peng and T. Tamir, “Directional blazing of waves guided by asymmetrical dielectric gratings,” Opt. Commun. 11, 405–409 (1974).
[CrossRef]

Prewett, P.

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

Rauscher, K.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Roden, J. A.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–339 (2000).
[CrossRef]

Roncone, R. L.

Schultz, S. M.

Scifres, D. R.

W. Streifer, R. D. Burnham, and D. R. Scifres, “Analysis of grating-coupled radiatio in GaAs: GaAlAs lasers and waveguide-II: blazing effects,” IEEE J. Quantum Electron. 12, 494–499 (1976).
[CrossRef]

Sheard, S.

T. Liao and S. Sheard, “Integrated-optic array illuminator: a new design for guided-wave optical interconnections,” Appl. Opt. 37, 2729–2734 (1998).
[CrossRef]

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

Sheard, S. J.

M. Li and S. J. Sheard, “Experimental study of waveguide grating couplers with parallelogramic tooth profiles,” Opt. Eng. 35, 3101–3106 (1996).
[CrossRef]

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245(1994).
[CrossRef]

Shoushtari, Z. M.

T. Jalali, K. Rauscher, A. Mohammadi, D. Erni, C. H. Hafner, W. Baechtold, and Z. M. Shoushtari, “Efficient effective permittivity treatment for the 2D-FDTD simulation of photonic crystals,” J. Comput. Theor. Nanosci. 4, 644–648 (2007).
[CrossRef]

Sosnowski, P.

H. Kogelnik and P. Sosnowski, “Holographic thin film couplers,” Bell. Syst. Tech. J. 49, 1602–1608 (1970).

Streifer, W.

W. Streifer, R. D. Burnham, and D. R. Scifres, “Analysis of grating-coupled radiatio in GaAs: GaAlAs lasers and waveguide-II: blazing effects,” IEEE J. Quantum Electron. 12, 494–499 (1976).
[CrossRef]

Svakhin, A. S.

I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett. 15, 1446–1448 (1990).
[CrossRef] [PubMed]

I. A. Avrutsky, A. S. Svakhin, and V. A. Sychugov, “Interference phenomena in waveguide with two corrugated boundaries,” J. Mod. Opt. 36, 1303–1320 (1989).
[CrossRef]

Sychugov, V. A.

I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett. 15, 1446–1448 (1990).
[CrossRef] [PubMed]

I. A. Avrutsky, A. S. Svakhin, and V. A. Sychugov, “Interference phenomena in waveguide with two corrugated boundaries,” J. Mod. Opt. 36, 1303–1320 (1989).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

Tamir, T.

S. T. Peng and T. Tamir, “Directional blazing of waves guided by asymmetrical dielectric gratings,” Opt. Commun. 11, 405–409 (1974).
[CrossRef]

Turunen, J.

Villalaz, R. A.

Wang, W. Y.

Weisenbach, L.

Wu, S.-D.

Zelinski, B. J. J.

Zhu, J.

T. Liao, S. Sheard, M. Li, J. Zhu, and P. Prewett, “High-efficiency focusing waveguide grating coupler parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
[CrossRef]

Appl. Opt.

K. Ogawa and W. S. C. Chang, “Analysis of holographic thin film grating coupler,” Appl. Opt. 12, 2167–2171 (1973).
[CrossRef] [PubMed]

W. Y. Wang and T. J. DiLaura, “Bragg effect waveguide coupler analysis,” Appl. Opt. 16, 3230–3236 (1977).
[CrossRef] [PubMed]

W. Driemeier and A. Brockmeyer, “High-resolution photorefractive polymer for optical recording of waveguide gratings,” Appl. Opt. 25, 2960–2966 (1986).
[CrossRef] [PubMed]

S. M. Schultz and E. N. Glytsis, “Design, fabrication and performance of preferential-order volume waveguide couplers,” Appl. Opt. 39, 1223–1232 (2000).
[CrossRef]

S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design of a high-efficiency volume grating coupler for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
[CrossRef]

R. A. Villalaz, E. N. Glytsis, and T. K. Gaylord, “Volume grating couplers: polarization and loss effects,” Appl. Opt. 41, 5223–5229 (2002).
[CrossRef] [PubMed]

S.-D. Wu and E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method,” Appl. Opt. 43, 1009–1023 (2004).
[CrossRef] [PubMed]

A. D. Papadopoulos and E. N. Glytsis, “Optical waveguide grating couplers: 2nd-order and 4th-order finite-difference time-domain analysis,” Appl. Opt. 48, 5164–5175 (2009).
[CrossRef] [PubMed]

T. Liao and S. Sheard, “Integrated-optic array illuminator: a new design for guided-wave optical interconnections,” Appl. Opt. 37, 2729–2734 (1998).
[CrossRef]

J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambrill, “Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection,” Appl. Opt. 36, 5717–5727 (1997).
[CrossRef] [PubMed]

J. C. Brazas, L. Li, and A. L. McKeon, “High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation,” Appl. Opt. 34, 604–609 (1995).
[CrossRef] [PubMed]

R. L. Roncone, L. Li, K. A. Bates, J. J. Burke, L. Weisenbach, and B. J. J. Zelinski, “Design and fabrication of single-leakage-channel grating coupler,” Appl. Opt. 32, 4522–4528 (1993).
[CrossRef] [PubMed]

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Figures (16)

Fig. 1
Fig. 1

Geometric configuration of the waveguide grating coupler and the complete ( actual + CPML ) computational domain used for FDTD analysis.

Fig. 2
Fig. 2

Types of waveguide grating couplers used: (a) VHGC (grating in the cover region), (b) two-level SPSRGC (grating in the film region), (c) DCSRGC, and (d) RSSRGC.

Fig. 3
Fig. 3

CE c 1 for the VHGC for TE polarization as a function of the number of cells, N, per minimum wavelength.

Fig. 4
Fig. 4

Coupling efficiency CE c 1 in the cover region, as a function of the number of grating periods ( L g / Λ y ) for TE polarization.

Fig. 5
Fig. 5

Coupling efficiency CE c 1 in the cover region, as a function of the number of grating periods ( L g / Λ y ) for TM polarization.

Fig. 6
Fig. 6

Branching ratio [for the first diffracted order: BR 1 = P c 1 / ( P c 1 + P s 1 ) ] as a function of the number of grating periods ( L g / Λ y ) for TE polarization.

Fig. 7
Fig. 7

Branching ratio [for the first diffracted order: BR 1 = P c 1 / ( P c 1 + P s 1 ) ] as a function of the number of grating periods ( L g / Λ y ) for TM polarization.

Fig. 8
Fig. 8

Branching ratio ( BR = P c / ( P c + P s ) ) as a function of the number of grating periods ( L g / Λ y ) for TE polarization.

Fig. 9
Fig. 9

Branching ratio [ BR = P c / ( P c + P s ) ] as a function of the number of grating periods ( L g / Λ y ) for TM polarization.

Fig. 10
Fig. 10

Coupling efficiency CE c 1 in the cover region for the VHGC, as a function of slant angle, ϕ (°), for TE-TM polarization.

Fig. 11
Fig. 11

Coupling efficiency CE c 1 in the cover region for the SPSRGC, as a function of the slant angle, ϕ (°), for TE-TM polarization.

Fig. 12
Fig. 12

Coupling efficiency CE c 1 in the cover region for the DCSRGC, as a function of shift s ( μm ) of two-level surface-relief gratings, for TE polarization.

Fig. 13
Fig. 13

Coupling efficiency CE c 1 in the cover region for the DCSRGC, as a function of shift s ( μm ) of two-level surface-relief gratings, for TM polarization.

Fig. 14
Fig. 14

Coupling efficiency CE c 1 in the cover region for the RSSRGC, as a function of the buffer length b ( μm ) , for TE-TM polarization.

Fig. 15
Fig. 15

Coupling efficiency CE c 1 in the cover region, as a function of the wavelength ( μm ), for TE polarization.

Fig. 16
Fig. 16

Coupling efficiency CE c 1 in the cover region, as a function of the wavelength ( μm ), for TM polarization.

Tables (1)

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Table 1 Fabrication Tolerances with Respect to the Main Design Parameters for Each Type of Diffractive Coupler a

Equations (2)

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U inc = z ^ g ( x ) h ( t ) cos ( ω t β y ) ,
ϵ = ϵ avg + p = 1 ϵ p c cos ( p K · r ) + p = 1 ϵ p s sin ( p K · r ) ,

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