Abstract

A finite volume holographic grating coupler (VHGC) normally illuminated with various incident-beam profiles (such as a Gaussian beam, a flat cosine-squared beam, and an exponential-decay beam) with finite beam widths for input coupling is rigorously analyzed by use of the finite-difference frequency-domain method. The effects of the incident-beam width, the incident-beam position, the incident-beam profile, and the incident-beam angle of incidence on the input coupling efficiency are investigated. The optimum conditions for input coupling are determined. Both a VHGC embedded in the waveguide film region and a VHGC placed in the waveguide cover region are investigated. For a given finite VHGC, the input coupling efficiencies are strongly dependent on incident-beam widths, incident-beam positions, and incident-beam angles of incidence, but are only weakly dependent on incident-beam profiles.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  2. Q. Xing, S. Ura, T. Suhara, H. Nishihara, “Contradirectional coupling between stacked waveguides using grating couplers,” Opt. Commun. 144, 180–182 (1997).
    [CrossRef]
  3. 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]
  4. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Design of a high-efficiency volume grating couplers for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
    [CrossRef]
  5. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Volume grating preferential-order focusing waveguide coupler,” Opt. Lett. 24, 1708–1710 (1999).
    [CrossRef]
  6. 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]
  7. 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]
  8. 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).
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    [CrossRef]
  11. R. A. Villalaz, E. N. Glytsis, T. K. Gaylord, “Volume grating couplers: polarization and loss effect,” Appl. Opt. 41, 5223–5229 (2002).
    [CrossRef] [PubMed]
  12. S.-D. Wu, E. N. Glytsis, “Volume holographic grating couplers: rigorous analysis using the finite-difference frequency-domain method,” Appl. Opt. 43, 1009–1023 (2004).
    [CrossRef] [PubMed]
  13. K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
    [CrossRef]
  14. M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
    [CrossRef]
  15. M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
    [CrossRef]
  16. M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
    [CrossRef]
  17. D. G. Dalgoutte, C. D. W. Wilkinson, “Thin grating couplers for integrated optics: an experimental and theoretical study,” Appl. Opt. 14, 2983–2998 (1975).
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    [CrossRef]
  19. L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
    [CrossRef] [PubMed]
  20. M. C. Gupta, L. Li, “Effect of beam defocus on the efficiency of planar waveguide grating couplers,” Appl. Opt. 30, 4402–4405 (1991).
    [CrossRef] [PubMed]
  21. D. Pascal, R. Orobtchouk, A. Layadi, A. Koster, S. Laval, “Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results,” Appl. Opt. 36, 2443–2447 (1997).
    [CrossRef] [PubMed]
  22. R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39, 5773–5777 (2000).
    [CrossRef]
  23. J. C. Brazas, L. Li, “Analysis of input-grating couplers having finite lengths,” Appl. Opt. 34, 3786–3792 (1995).
    [CrossRef] [PubMed]
  24. R. Waldhäusl, B. Schnabel, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Efficient coupling into polymer waveguides by gratings,” Appl. Opt. 36, 9383–9390 (1997).
    [CrossRef]
  25. C.-K. Kwan, G. W. Taylor, “Optimization of the parallelogrammic gating diffraction efficiency for normally incident wave,” Appl. Opt. 37, 7698–7707 (1998).
    [CrossRef]
  26. B. Wang, J. Jiang, G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
    [CrossRef] [PubMed]
  27. K. Ogawa, W. S. C. Chang, “Analysis of holographic thin film grating coupler,” Appl. Opt. 12, 2167–2171 (1973).
    [CrossRef] [PubMed]
  28. S.-D. Wu, E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19, 2018–2029 (2002).
    [CrossRef]
  29. S.-D. Wu, E. N. Glytsis, “Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and the rigorous coupled-wave analysis,” J. Opt. Soc. Am. B 20, 1177–1188 (2003).
    [CrossRef]
  30. S.-D. Wu, E. N. Glytsis, “Characteristics of DuPont photopolymers for slanted holographic grating formations,” J. Opt. Soc. Am. B 21, 1722–1731 (2004).
    [CrossRef]

2004

2003

2002

2000

R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39, 5773–5777 (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]

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).

1999

1998

1997

1995

1991

1990

1985

1975

1973

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

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

1970

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

Ashley, P. R.

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]

Bräuer, A.

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]

Cadilhac, M.

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Chang, W. S. C.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

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

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.

Dannberg, P.

Gaylord, T. K.

Glytsis, E. N.

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

S.-D. Wu, E. N. Glytsis, “Characteristics of DuPont photopolymers for slanted holographic grating formations,” J. Opt. Soc. Am. B 21, 1722–1731 (2004).
[CrossRef]

S.-D. Wu, E. N. Glytsis, “Holographic grating formation in photopolymers: analysis and experimental results based on a nonlocal diffusion model and the rigorous coupled-wave analysis,” J. Opt. Soc. Am. B 20, 1177–1188 (2003).
[CrossRef]

S.-D. Wu, E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19, 2018–2029 (2002).
[CrossRef]

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

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]

S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Volume grating preferential-order focusing waveguide coupler,” Opt. Lett. 24, 1708–1710 (1999).
[CrossRef]

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

Gualous, H.

Gupta, M. C.

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).

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).

Huang, Q.

Jiang, J.

Karthe, W.

Kley, E.-B.

Kogelnik, H.

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

Koster, A.

Kwan, C.-K.

Laval, S.

Layadi, A.

Lee, E. H.

Li, L.

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, 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]

Neviere, M.

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Nishihara, H.

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

Nordin, G. P.

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

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

Orobtchouk, R.

Pascal, D.

Petit, R.

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (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]

Rosenbaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

Schnabel, B.

Schultz, S. M.

Seshadri, S. R.

Song, S. H.

Sopori, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

Sosnowski, T. P.

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

Suhara, T.

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

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]

Taylor, G. W.

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).

Ura, S.

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

Villalaz, R. A.

Vincent, P.

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Waldhäusl, R.

Wang, B.

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]

Wilkinson, C. D. W.

Woldarczyk, M. T.

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, “Contradirectional 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).

Appl. Opt.

S. H. Song, E. H. Lee, “Focusing-grating-coupler arrays for uniform and efficient signal distribution in a backboard optical interconnect,” Appl. Opt. 34, 5913–5919 (1995).
[CrossRef] [PubMed]

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]

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

L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
[CrossRef] [PubMed]

M. C. Gupta, L. Li, “Effect of beam defocus on the efficiency of planar waveguide grating couplers,” Appl. Opt. 30, 4402–4405 (1991).
[CrossRef] [PubMed]

D. Pascal, R. Orobtchouk, A. Layadi, A. Koster, S. Laval, “Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results,” Appl. Opt. 36, 2443–2447 (1997).
[CrossRef] [PubMed]

R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39, 5773–5777 (2000).
[CrossRef]

J. C. Brazas, L. Li, “Analysis of input-grating couplers having finite lengths,” Appl. Opt. 34, 3786–3792 (1995).
[CrossRef] [PubMed]

R. Waldhäusl, B. Schnabel, P. Dannberg, E.-B. Kley, A. Bräuer, W. Karthe, “Efficient coupling into polymer waveguides by gratings,” Appl. Opt. 36, 9383–9390 (1997).
[CrossRef]

C.-K. Kwan, G. W. Taylor, “Optimization of the parallelogrammic gating diffraction efficiency for normally incident wave,” Appl. Opt. 37, 7698–7707 (1998).
[CrossRef]

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

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

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

D. G. Dalgoutte, C. D. W. Wilkinson, “Thin grating couplers for integrated optics: an experimental and theoretical study,” Appl. Opt. 14, 2983–2998 (1975).
[CrossRef] [PubMed]

Bell Syst. Tech. J.

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

IEEE J. Quantum Electron.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. 9, 29–42 (1973).
[CrossRef]

IEICE Trans. Electron.

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