Abstract

Two configurations of volume holographic grating couplers are rigorously analyzed by means of the finite-difference frequency-domain method (FDFD) for both TE and TM polarizations and for 0- and 45-deg output coupling. The two configurations depend on the position of the grating coupler, which can be placed either in the film or in the cover waveguide region. The FDFD results are compared with those obtained by the rigorous coupled-wave analysis in conjunction with the leaky-mode approach (RCWA–LM). Because the FDFD method is a rigorous solution of the Maxwell equations, it simulates the VHGC configuration and takes into account the waveguide-coupler discontinuity effects as well as the multimode excitation and interference effects, all of which are neglected by the traditional RCWA–LM.

© 2004 Optical Society of America

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2003

2002

2001

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

P. G. Dinesen, 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]

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

S. Ura, R. Nishida, T. Suhara, H. Nishihara, “Wavelength-selective coupling between 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. Carlström, A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815–817 (2001).
[CrossRef]

2000

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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

M. Wiki, R. E. Kunz, “Wavelength-interrogated optical sensors for biochemical applications,” Opt. Lett. 25, 463–465 (2000).
[CrossRef]

P. G. Dinesen, J. S. Hesthaven, “Fast and accurate modeling of waveguide grating couplers,” J. Opt. Soc. Am. A 17, 1565–1572 (2000).
[CrossRef]

P. Lalanne, E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Lett. 25, 1092–1094 (2000).
[CrossRef]

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

1999

1998

1997

Q. Huang, P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36, 1198–1203 (1997).
[CrossRef] [PubMed]

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

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

1996

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

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

1995

1994

S. Nishiwaki, J. Asada, S. Uchida, “Optical head employing a concentric-circular focusing grating coupler,” Appl. Opt. 33, 1819–1827 (1994).
[CrossRef] [PubMed]

S. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
[CrossRef]

M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

1991

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

1990

1988

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

1986

T. Suhara, H. Hishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22, 845–867 (1986).
[CrossRef]

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

1977

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

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

1975

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

1973

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

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

1972

1970

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

Asada, J.

Ashley, P. R.

Backlund, J.

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

Bendickson, J. M.

Bengtsson, J.

J. Backlund, J. Bengtsson, C.-F. Carlström, 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, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

S. T. Peng, T. Tamir, 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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Borsboom, P.-P.

Brazas, J. C.

Bristow, 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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Cao, Q.

Carlström, C.-F.

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

Chang, W. S. C.

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. Bristow, 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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Dalgoutte, D. G.

DiLaura, T. J.

Dinesen, P. G.

Dübendorfer, J.

Eriksson, N.

N. Eriksson, M. Hagberg, A. Larsson, “Highly efficient grating-coupled surface-emitters with single outcoupling elements,” IEEE Photon. Technol. Lett. 7, 1394–1396 (1995).
[CrossRef]

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
[CrossRef]

M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

Frankena, H. J.

Gaylord, T. K.

Glytsis, E. N.

Hagberg, M.

N. Eriksson, M. Hagberg, A. Larsson, “Highly efficient grating-coupled surface-emitters with single outcoupling elements,” IEEE Photon. Technol. Lett. 7, 1394–1396 (1995).
[CrossRef]

M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
[CrossRef]

Hardy, A.

N. Izhaky, A. Hardy, “Analysis of grating-assisted backward coupling employing the unified coupled-mode formalism,” J. Opt. Soc. Am. A 16, 1303–1311 (1999).
[CrossRef]

N. Izhaky, A. Hardy, “Characteristics of grating-assisted couplers,” Appl. Opt. 38, 6987–6993 (1999).
[CrossRef]

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Harris, J. H.

Hashimoto, T.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Hibino, Y.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

Himeno, A.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

Hishihara, H.

T. Suhara, H. Hishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22, 845–867 (1986).
[CrossRef]

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

Ho, S. H.

Huang, Q.

Hugonin, J.-P.

Izhaky, N.

Jannson, T.

Jones, M. L.

Kenna, R. P.

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas. Propag. 43, 1460–1463 (1995).
[CrossRef]

Kjellberg, T.

M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
[CrossRef]

Kogelnik, H.

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

Kowarz, M. W.

Koyama, J.

S. Ura, T. Suhara, H. Hishihara, 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. Carlström, A. Larsson, “Waveguide input grating couplers for wavelength-division multiplexing and wavelength encoding,” IEEE Photon. Technol. Lett. 13, 815–817 (2001).
[CrossRef]

N. Eriksson, M. Hagberg, A. Larsson, “Highly efficient grating-coupled surface-emitters with single outcoupling elements,” IEEE Photon. Technol. Lett. 7, 1394–1396 (1995).
[CrossRef]

Larsson, A. G.

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
[CrossRef]

M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

Lee, E. H.

Lee, J.-F.

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas. Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas. Propag. 43, 1460–1463 (1995).
[CrossRef]

Li, L.

Li, M.

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

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

Liao, T.

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

Lin, F.

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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Liu, W.-C.

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. Bristow, 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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Mckeon, A. L.

Mehuys, D.

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Nishida, R.

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

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

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

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

S. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

Nishiwaki, S.

Oarriaux, O.

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

Ogawa, K.

Oh, M.

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

Parke, R.

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Peng, S. T.

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

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

S. T. Peng, T. Tamir, H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron. Lett. 9, 150–152 (1973).
[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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Prewett, P.

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

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas. Propag. 43, 1460–1463 (1995).
[CrossRef]

Schultz, S. M.

Sheard, S.

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

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

Shinohara, M.

S. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

Silberstein, E.

Sosnowski, T. P.

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

Strzelecki, E. M.

Suhara, T.

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

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

S. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

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

T. Suhara, H. Hishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22, 845–867 (1986).
[CrossRef]

Sunagawa, H.

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

Sychugov, V. A.

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

Takahashi, H.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

Tamir, T.

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

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

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

Tanaka, T.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Tishchenko, A. V.

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

Tohmori, Y.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

Uchida, S.

Ura, S.

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

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

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

S. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

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

Usievich, B. A.

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

Verber, C. M.

Villalaz, R. A.

Waarts, R. G.

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Wang, W. Y.

Welch, D. F.

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[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. Bristow, 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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Wu, S.-D.

Xing, Q.

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

Yamada, Y.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

Zhu, J.

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

Appl. Opt.

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

Appl. Phys.

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

Bell Syst. Tech. J.

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

Electron. Lett.

M. Hagberg, T. Kjellberg, N. Eriksson, A. G. Larsson, “Demonstration of blazing effect in second order gratings under resonant condition,” Electron. Lett. 30, 410–412 (1994).
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M. Hagberg, N. Eriksson, T. Kjellberg, A. G. Larsson, “Demonstration of blazing effect in detuned second order gratings,” Electron. Lett. 30, 570–571 (1994).
[CrossRef]

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

IEEE J. Quantum Electron.

T. Suhara, H. Hishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22, 845–867 (1986).
[CrossRef]

IEEE Photon. Technol. Lett.

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

S. Ura, R. Nishida, T. Suhara, H. Nishihara, “Wavelength-selective coupling between vertically integrated thin-film waveguides via supermode by a pair of grating couplers,” IEEE Photon. Technol. Lett. 13, 678–680 (2001).
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J. Backlund, J. Bengtsson, C.-F. Carlström, 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. Ura, M. Shinohara, T. Suhara, H. Nishihara, “Integrated-optic grating-scale-displacement sensors using linearly focusing grating couplers,” IEEE Photon. Technol. Lett. 6, 239–241 (1994).
[CrossRef]

D. Mehuys, A. Hardy, D. F. Welch, R. G. Waarts, R. Parke, “Analysis of detuned second-order grating output couplers with an integrated superlattice reflectors,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
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N. Eriksson, M. Hagberg, A. Larsson, “Highly efficient grating-coupled surface-emitters with single outcoupling elements,” IEEE Photon. Technol. Lett. 7, 1394–1396 (1995).
[CrossRef]

IEEE Trans. Antennas. Propag.

Z. S. Sacks, D. M. Kingsland, R. Lee, J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas. Propag. 43, 1460–1463 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

IEICE Trans. Electron.

T. Tanaka, H. Takahashi, Y. Hibino, T. Hashimoto, A. Himeno, Y. Yamada, Y. Tohmori, “Hybrid external cavity lasers composed of spot-size converter integrated LDs and UV written Bragg grating in a planar lightwave circuit on Si,” IEICE Trans. Electron. E83-C, 875–883 (2000).

J. Lightwave Technol.

M. Oh, S. Ura, T. Suhara, H. Nishihara, “Integrated-optics focal-spot intensity modulator using electro-optic polymer waveguide,” J. Lightwave Technol. 12, 1569–1576 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1032 (1988).
[CrossRef]

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

T. Liao, S. Sheard, M. Li, J. Zhu, P. Prewett, “High-efficiency focusing waveguide grating couplers with parallelogramic groove profiles,” J. Lightwave Technol. 15, 1142–1148 (1997).
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J. Opt. Soc. Am. B

Opt. Commun.

Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contra-directional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
[CrossRef]

Opt. Eng.

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, O. Oarriaux, “Optimization and control of grating coupling to or from a silicon-based optical waveguide,” Opt. Eng. 35, 3092–3100 (1996).
[CrossRef]

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

Opt. Lett.

Proc. IEEE

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. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Two basic configurations of waveguide couplers composed of a VHGC (a) in the waveguide film region and (b) in the waveguide cover region. The waveguide consists of a cover region with refractive index n c , a film region with refractive index n w , and a substrate region with refractive index n s . The thickness of the waveguide film region is t w . The volume holographic grating coupler has a grating vector |K| = 2π/Λ (Λ is the grating period), a slant angle ϕ, a length L g , and a thickness t g . The average refractive index in the grating region is n g . The designed out-coupling angle in the cover region is θ c . The power of the incident beam is P inc. P u , P d , P t , and P r denote the upward-coupling power, the downward-coupling power, the transmitted power, and the reflected power, respectively.

Fig. 2
Fig. 2

Transverse field profiles of a VHGC in the waveguide film region for (a) TE polarization with 0-deg output coupling, (b) TM polarization with 0-deg output coupling, (c) TE polarization with 45-deg output coupling, and (d) TM polarization with 45-deg output coupling.

Fig. 3
Fig. 3

Two-dimensional field-amplitude and field-phase patterns of a VHGC with L g = 100 μm in the waveguide film region for (a) TE polarization with 0-deg output coupling, (b) TM polarization with 0-deg output coupling, (c) TE polarization with 45-deg output coupling, and (d) TM polarization with 45-deg output coupling.

Fig. 4
Fig. 4

Normalized field intensity at the top surface of the waveguide film layer (i.e., at y = 5.8 μm) of a VHGC with L g = 100 μm in the waveguide film region for TE polarization with 0-deg output coupling.

Fig. 5
Fig. 5

Normalized intensity of the far-field distribution at (a) y o = 2 μm, (b) y o = 100 μm, and (c) y o = 1 mm of a VHGC with L g = 100 μm in the waveguide film region for TE polarization with 0-deg output coupling.

Fig. 6
Fig. 6

Transverse field profiles of a VHGC in the waveguide cover region for (a) TE polarization with 0-deg output coupling, (b) TM polarization with 0-deg output coupling, (c) TE polarization with 45-deg output coupling, and (d) TM polarization with 45-deg output coupling.

Fig. 7
Fig. 7

Two-dimensional field-amplitude and field-phase patterns of a VHGC in the waveguide cover region for (a) TE polarization with 0-deg output coupling, (b) TM polarization with 0-deg output coupling, (c) TE polarization with 45-deg output coupling, and (d) TM polarization with 45-deg output coupling.

Fig. 8
Fig. 8

Two-dimensional field-amplitude and field-phase patterns of a VHGC in the waveguide cover region for TE polarization with 0-deg output coupling.

Fig. 9
Fig. 9

Normalized field intensity at the top surface of the waveguide film layer (i.e., at y = 8.4 μm) of a VHGC with L g = 100 μm and t g = 6.0 μm in the waveguide cover region for TE polarization with 0-deg output coupling.

Fig. 10
Fig. 10

Normalized intensity of far-field distribution at (a) y o = 2 μm, (b) y o = 100 μm, and (c) y o = 1 mm of a VHGC with L g = 100 μm and t g = 6.0 μm in the waveguide cover region for TE polarization with 0-deg output coupling.

Fig. 11
Fig. 11

Nonmonotonical decrease of the normalized intensity of the electric field distribution at y o = 2 μm for the configuration of a VHGC with (a) t g = 6.0 μm and (b) t g = 1.8 μm in the waveguide cover region for TE polarization with 0-deg output coupling. The numerical results are calculated by use of the FDFD method.

Tables (3)

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Table 1 Design Parameters of Volume Holographic Grating Couplers (VHGCs)

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Table 2 Performance of a VHGC in the Waveguide Film Region and Comparison with the RCWA–LM Approach for 0- and 45-deg Output Coupling

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Table 3 Performance of a VHGC in the Waveguide Cover Region and Comparison with the RCWA–LM Approach for 0- and 45-deg Output Coupling

Equations (9)

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=0εx, y=0ε0+p=1 εpccospK · r+p=1 εpssinpK · r,
2Ez+ω2μsEz=0.
2Hz+ω2μsHz-2jω+σjω+σ ·2Hz=0,
A=U=b,
CEi=PiPinc×100,
BR=PuPu+Pd×100.
αl=-12LglnPtPinc.
Uro=-Γ Urkc2j H12kc|ro-r|yo|ro-r|dx,
URCWA-LMx=exp-αlx0xLg0else.

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