Abstract

Output optical waveguide grating couplers are rigorously analyzed using the 2-order and the 4-order finite-difference time-domain (FDTD) method in conjunction with the total field/scattered field (TF-SF) approach and special averaging and regularization techniques for the mitigation of permittivity discontinuities. Volume-holographic and surface-relief grating couplers are analyzed for both TE and TM polarizations. The 2- and 4-order FDTD results are compared in terms of computational efficiency and accuracy. In addition, the FDTD results are compared to the approximate ones obtained by the rigorous coupled-wave analysis in conjunction with the leaky modes.

© 2009 Optical Society of America

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2008 (2)

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

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]

2007 (3)

2006 (2)

E. Kashdan and E. Turkel, “High-order accurate modeling of electromagnetic wave propagation across media-grid conforming bodies,” J. Comput. Phys. 218, 816-835 (2006).
[CrossRef]

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, 4695-4702(2006).
[CrossRef] [PubMed]

2005 (2)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884-1886 (2005).
[CrossRef]

B. Wang, J. Jiang, D. M. Chambers, J. Cai, and G. P. Nordin, “Stratified waveguide grating coupler for normal fiber incidence,” Opt. Lett. 30, 845-847 (2005).
[CrossRef] [PubMed]

2004 (3)

2002 (5)

2001 (6)

K. P. Hwang and A. C. Cangellaris, “Effective permittivities for second-order accurate FDTD equations at dielectric interfaces,” IEEE Microwave Wireless Comp. Lett. 11, 158-160(2001).
[CrossRef]

P. G. Dinesen and J. S. Hesthaven, “Fast and accurate modeling of waveguide grating couplers, II. Three-dimensional vectorial case,” J. Opt. Soc. Am. A 18, 2876-2885(2001).
[CrossRef]

E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865-2875 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
[CrossRef]

2000 (6)

1999 (2)

1998 (1)

1996 (1)

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 (4)

1994 (1)

P. G. Petropoulos, “Phase error control for FD-TD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859-862 (1994).
[CrossRef]

1992 (1)

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

1986 (1)

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

1977 (2)

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235-254 (1977).
[CrossRef]

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

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123 (1975).
[CrossRef]

1973 (2)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150-152 (1973).
[CrossRef]

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

1972 (1)

1970 (1)

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

1969 (1)

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

Anderson, U.

U. Anderson, “Time domain methods for the Maxwell equations,” Ph.D. dissertation (Royal Institute of Technology Sweden, 2001).

Backlund, J.

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
[CrossRef]

Bengtsson, J.

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
[CrossRef]

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123 (1975).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150-152 (1973).
[CrossRef]

Bihari, B.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Borsboone, P.-P.

Britow, J.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Butler, J. K.

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

Cai, J.

Cangellaris, A. C.

K. P. Hwang and A. C. Cangellaris, “Effective permittivities for second-order accurate FDTD equations at dielectric interfaces,” IEEE Microwave Wireless Comp. Lett. 11, 158-160(2001).
[CrossRef]

Cao, Q.

Carlstrom, C.-F.

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
[CrossRef]

Chambers, D. M.

Chang, W. S. C.

Cheben, P.

Chen, R. T.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Choi, C.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Dalgoutte, D. G.

Densmore, A.

DiLaura, T. J.

Dinesen, P. G.

Evans, G. A.

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

Ferguson, W. E.

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

Frankena, H. J.

Gaylord, T. K.

Gedney, S. D.

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.

Goldhar, J.

Gurel, L.

L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Antennas Propag. 48, 585-589 (2000).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite- Difference Time-Domain Method, 2nd and 3rd eds. (Artech House, 2000 and 2005).

Hardy, A.

Harris, J. H.

Herman, W. N.

Hesthaven, J. S.

Hibbs-Brenner, M. K.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Hirono, T.

T. Hirono and Y. Yoshikuni, “Accurate modeling of dielectric interfaces by the effective permittivities for the fourth-order symplectic finite-difference time-domain method,” Appl. Opt. 46, 1514-1524 (2007).
[CrossRef] [PubMed]

T. Hirono, Y. Yoshikuni, and Y. Shibata, “Third-order effective permittivities for the 4th-order FDTD method in the 2-D TM polarization case,” Proc. SPIE 4646, 630-640 (2002).
[CrossRef]

Hishihara, H.

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

Ho, S. H.

Hu, W.

C. Huang, J. Liu, W. Hu, and J. Sun, “FDTD analysis of optical field distribution in waveguide grating coupler,” Proc. SPIE 6783, 67834 (2007).
[CrossRef]

Huang, C.

C. Huang, J. Liu, W. Hu, and J. Sun, “FDTD analysis of optical field distribution in waveguide grating coupler,” Proc. SPIE 6783, 67834 (2007).
[CrossRef]

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

Huang, D.

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

Hugonin, J.-P.

Hwang, K. P.

K. P. Hwang and A. C. Cangellaris, “Effective permittivities for second-order accurate FDTD equations at dielectric interfaces,” IEEE Microwave Wireless Comp. Lett. 11, 158-160(2001).
[CrossRef]

Izhaky, N.

Janz, S.

Jiang, J.

Jones, M. L.

Kang, C.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Kashdan, E.

E. Kashdan and E. Turkel, “High-order accurate modeling of electromagnetic wave propagation across media-grid conforming bodies,” J. Comput. Phys. 218, 816-835 (2006).
[CrossRef]

Kenan, R. P.

Kogelnik, H.

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

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

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

Koyama, J.

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

Kunz, R. E.

Lalanne, P.

Larsson, A.

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
[CrossRef]

Lee, E. H.

Leng, Y.

Lin, L.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Liscidini, M.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Liu, J.

C. Huang, J. Liu, W. Hu, and J. Sun, “FDTD analysis of optical field distribution in waveguide grating coupler,” Proc. SPIE 6783, 67834 (2007).
[CrossRef]

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

Liu, Y. J.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Liu, Y. S.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Lucas, L.

Nishida, R.

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

Nishihara, H.

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

Nordin, G. P.

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. Antennas Propag. 48, 585-589 (2000).
[CrossRef]

Papadopoulos, A. D.

Patrini, M.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Peng, S.

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

Peng, S. T.

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235-254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123 (1975).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150-152 (1973).
[CrossRef]

Petropoulos, P. G.

P. G. Petropoulos, “Phase error control for FD-TD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859-862 (1994).
[CrossRef]

Picor, B.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Retterer, S. T.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Rong, G.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Rosen, A.

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

Schultz, S. M.

Shibata, Y.

T. Hirono, Y. Yoshikuni, and Y. Shibata, “Third-order effective permittivities for the 4th-order FDTD method in the 2-D TM polarization case,” Proc. SPIE 4646, 630-640 (2002).
[CrossRef]

Silberstein, E.

Sipe, J. E.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Sosnowski, T. P.

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

Stabile, P. J.

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

Suhara, T.

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

Sun, J.

C. Huang, J. Liu, W. Hu, and J. Sun, “FDTD analysis of optical field distribution in waveguide grating coupler,” Proc. SPIE 6783, 67834 (2007).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite- Difference Time-Domain Method, 2nd and 3rd eds. (Artech House, 2000 and 2005).

Tamir, T.

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235-254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123 (1975).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150-152 (1973).
[CrossRef]

Tang, S.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Tsiboukis, T. D.

T. T. Zygiridis and T. D. Tsiboukis, “Low-dispersion algorithms based on the higher order (2,4) FDTD method,” IEEE Trans. Microwave Theory Tech. 52, 1321-1327 (2004).
[CrossRef]

Turkel, E.

E. Kashdan and E. Turkel, “High-order accurate modeling of electromagnetic wave propagation across media-grid conforming bodies,” J. Comput. Phys. 218, 816-835 (2006).
[CrossRef]

Ura, S.

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

Verber, C. M.

Villalaz, R. A.

Wang, B.

Wang, W. Y.

Wei, X.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Weiss, S. M.

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

Wickman, R.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Wiki, M.

Winn, R. K.

Wu, L.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Wu, S.-D.

Xu, D.-X.

Yoshikuni, Y.

T. Hirono and Y. Yoshikuni, “Accurate modeling of dielectric interfaces by the effective permittivities for the fourth-order symplectic finite-difference time-domain method,” Appl. Opt. 46, 1514-1524 (2007).
[CrossRef] [PubMed]

T. Hirono, Y. Yoshikuni, and Y. Shibata, “Third-order effective permittivities for the 4th-order FDTD method in the 2-D TM polarization case,” Proc. SPIE 4646, 630-640 (2002).
[CrossRef]

Yuan, X.

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

Yun, V.

Zygiridis, T. T.

T. T. Zygiridis and T. D. Tsiboukis, “Low-dispersion algorithms based on the higher order (2,4) FDTD method,” IEEE Trans. Microwave Theory Tech. 52, 1321-1327 (2004).
[CrossRef]

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[CrossRef] [PubMed]

T. Hirono and Y. Yoshikuni, “Accurate modeling of dielectric interfaces by the effective permittivities for the fourth-order symplectic finite-difference time-domain method,” Appl. Opt. 46, 1514-1524 (2007).
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Appl. Phys. (1)

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235-254 (1977).
[CrossRef]

Bell Syst. Tech. J. (1)

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

Bell. Syst. Tech. J. (1)

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

Electron. Lett. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150-152 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. K. Butler, W. E. Ferguson, Jr., G. A. Evans, P. J. Stabile, and A. Rosen, “A boundary element technique applied to the analysis of waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. 28, 1701-1709 (1992).
[CrossRef]

IEEE Microwave Wireless Comp. Lett. (1)

K. P. Hwang and A. C. Cangellaris, “Effective permittivities for second-order accurate FDTD equations at dielectric interfaces,” IEEE Microwave Wireless Comp. Lett. 11, 158-160(2001).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17, 1884-1886 (2005).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among three vertically integrated waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 133-135 (2001).
[CrossRef]

S. Ura, R. Nishida, T. Suhara, and H. Nishihara, “Wavelength selective coupling among vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678-680 (2001).
[CrossRef]

J. Backlund, J. Bengtsson, C.-F. Carlstrom, and A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815-817 (2001).
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S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
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L. Gurel and U. Oguz, “Signal-processing techniques to reduce the sinusoidal steady-state error in the FDTD method,” IEEE Trans. Antennas Propag. 48, 585-589 (2000).
[CrossRef]

P. G. Petropoulos, “Phase error control for FD-TD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859-862 (1994).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. T. Zygiridis and T. D. Tsiboukis, “Low-dispersion algorithms based on the higher order (2,4) FDTD method,” IEEE Trans. Microwave Theory Tech. 52, 1321-1327 (2004).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123 (1975).
[CrossRef]

J. Appl. Phys. (1)

X. Wei, C. Kang, M. Liscidini, G. Rong, S. T. Retterer, M. Patrini, J. E. Sipe, and S. M. Weiss, “Grating couplers on porous silicon planar waveguides for sensing applications,” J. Appl. Phys. 104, 123113 (2008).
[CrossRef]

J. Comput. Phys. (1)

E. Kashdan and E. Turkel, “High-order accurate modeling of electromagnetic wave propagation across media-grid conforming bodies,” J. Comput. Phys. 218, 816-835 (2006).
[CrossRef]

J. Lightwave Technol. (1)

S. Ura, T. Suhara, H. Hishihara, and J. Koyama, “An integrated-optic disk pickup device,” J. Lightwave Technol. 4, 913-918 (1986).
[CrossRef]

J. Opt. Soc. Am. A (8)

Opt. Express (2)

Opt. Lett. (3)

Proc. IEEE (1)

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, J. Britow, and Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Proc. SPIE (3)

J. Liu, X. Yuan, C. Huang, S. Peng, and D. Huang, “Analysis of light field of waveguide grating couplers using the FDTD method,” Proc. SPIE 4927, 245-248 (2002).
[CrossRef]

C. Huang, J. Liu, W. Hu, and J. Sun, “FDTD analysis of optical field distribution in waveguide grating coupler,” Proc. SPIE 6783, 67834 (2007).
[CrossRef]

T. Hirono, Y. Yoshikuni, and Y. Shibata, “Third-order effective permittivities for the 4th-order FDTD method in the 2-D TM polarization case,” Proc. SPIE 4646, 630-640 (2002).
[CrossRef]

Other (3)

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A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite- Difference Time-Domain Method, 2nd and 3rd eds. (Artech House, 2000 and 2005).

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Figures (11)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Types of waveguide grating couplers used: (a) VHGC (grating in the film region), (b) 2-level SRGC (grating in the cover region).

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 of the VHGC as a function of the number of grating periods ( L g / Λ y ) for TE polarization.

Fig. 5
Fig. 5

Branching ratio (for the first diffracted order) of the VHGC as a function of the number of grating periods ( L g / Λ y ) for TE polarization.

Fig. 6
Fig. 6

Coupling efficiency sum (in %) for the VHGC (TE polarization) and for the 2-level SRGC (TE, TM polarization) as a function of the number of cells per minimum wavelength. The 100% line is also shown for facilitating the convergence observation.

Fig. 7
Fig. 7

CE c 1 for the 2-level SRGC for TE polarization as a function of the number of cells per minimum wavelength.

Fig. 8
Fig. 8

CE c 1 for the 2-level-SRGC for TM polarization as a function of the number of cells per minimum wavelength.

Fig. 9
Fig. 9

CE c 1 for the 2-level SRGC as a function of the number of grating periods ( L g / Λ ) for TE and TM polarizations.

Fig. 10
Fig. 10

Branching ratio ( BR 1 ) of the 2-level SRGC as a function of the number of grating periods ( L g / Λ ) for TE and TM polarizations.

Fig. 11
Fig. 11

Electric field for a ten-period 2-level SRGC at steady state for TE polarization.

Tables (2)

Tables Icon

Table 1 Performance of the VHGC and Comparison of Various Numerical Methods (All Coupling Efficiencies are Expressed in %)

Tables Icon

Table 2 Performance of the 2-level SRGC and Comparison of Various Numerical Methods (All Coupling Efficiencies are Expressed in %)

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

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 ) ,
f w | l n = C w 1 ( f l + 1 / 2 n f l 1 / 2 n ) + C w 2 ( f l + 3 / 2 n f l 3 / 2 n ) Δ w ,
f t | l n = A ( f l n + 1 / 2 f l n 1 / 2 ) Δ t ,
[ 1 J 0 ( k Δ w ) J 0 ( k Δ w ) J 0 ( 2 k Δ w ) J 0 ( k Δ w ) J 0 ( 2 k Δ w ) 1 J 0 ( 3 k Δ w ) ] [ C w 1 C w 2 ] = [ J 1 ( k Δ w 2 ) J 1 ( 3 k Δ w 2 ) ] k Δ w ,
ϵ avg. * = ( 1 2 + d ) ϵ 1 + ( 1 2 d ) ϵ 2 , for     E S ,
1 ϵ avg. * = d ϵ 1 + ( 1 d ) ϵ 2 , for     E S ,
ϵ ˜ ( x ) = 1 2 ( ϵ 1 + ϵ 2 ) + 45 16 ( ϵ 2 ϵ 1 ) ( x δ ) 25 2 ( ϵ 2 ϵ 1 ) ( x δ ) 3 + 21 ( ϵ 2 ϵ 1 ) ( x δ ) 5 ,
F i ( k y m ) = q = 0 M 1 U ˜ ( x = x i , q Δ y ) exp [ i k y m ( q Δ y ) ] ,
P p p , TE = Δ y 2 M m = β ( p + 1 / 2 ) K y β ( p 1 / 2 ) K y | F i ( k y m ) | 2 Re ( k i , x m * η i * k i * ) ,
P i p , TM = Δ y 2 M m = β ( p + 1 / 2 ) K y β ( p 1 / 2 ) K y | F i ( k y m ) | 2 Re ( k i , x m η i k i ) ,
P i = 1 2 Re ( E ˜ ( x , y = y i ) × H ˜ * ( x , y = y i ) d x ) .

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