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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  1. 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]
  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).
  9. S. M. Schultz, “High efficiency volume holographic grating coupler,” Ph.D. dissertation (Georgia Institute of Technology, 1999).
  10. H. Kogelnik, T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).
    [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).
    [CrossRef] [PubMed]
  18. M. T. Woldarczyk, S. R. Seshadri, “Analysis of grating couplers in planar waveguides for waves at oblique incidence,” J. Opt. Soc. Am. A 2, 171–185 (1985).
    [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 (3)

2003 (1)

2002 (2)

2000 (4)

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).

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]

1999 (1)

1998 (2)

1997 (4)

1995 (2)

1991 (1)

1990 (1)

1985 (1)

1975 (1)

1973 (5)

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]

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

1970 (1)

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, “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]

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, 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]

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

Orobtchouk, R.

Pascal, D.

Petit, R.

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]

M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide system,” Opt. Commun. 8, 113–117 (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. (15)

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. (1)

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

IEEE J. Quantum Electron. (1)

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. (1)

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. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Commun. (4)

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]

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

Opt. Express (1)

Opt. Lett. (1)

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

Other (1)

S. M. Schultz, “High efficiency volume holographic grating coupler,” Ph.D. dissertation (Georgia Institute of Technology, 1999).

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Figures (12)

Fig. 1
Fig. 1

Two basic configurations of waveguide input couplers comprised 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 nc, a film region with refractive index nw, and a substrate region with refractive index ns. The thickness of the waveguide film region is tw. The volume holographic grating has a grating vector K, a slant angle ϕ, a finite length Lg, and a thickness tg. The average refractive index in the grating region is ng. The incident beam with incident angle θinc and incident-beam position y0 from the cover region is incident upon the grating. The power of the incident beam is Pinc. Pu, Pd, Pt, and Pr denote the upward-coupled power, the downward-coupled power, the transmitted power, and the reflected power, respectively.

Fig. 2
Fig. 2

Three finite-width incident beams: (a) a Gaussian beam with beam width W, (b) a flat cosine-squared beam (i.e., a quasi plane wave) with flat width W, and (c) an exponential-decay beam with decay width W. θinc is the incident angle of the incident beam.

Fig. 3
Fig. 3

Two-dimensional field-amplitude patterns of a finite input VHGC with Lg = 50 μm in the waveguide film region illuminated by a TE-polarized Gaussian beam with a beam width W = 0.5Lg at the incident-beam position of (a) y0 = 0.3Lg, (b) y0 = 0.6Lg, and (c) y0 = 0.9Lg.

Fig. 4
Fig. 4

Field profiles corresponding to Fig. 3 for (a) the transmitted field at x = 8 μm and (b) the input-coupled field at y = 80 μm.

Fig. 5
Fig. 5

Input coupling efficiencies of the TE0 mode in the upward direction as functions of y0/Lg and W/Lg for a finite input VHGC with Lg = 50 μm in the waveguide film region illuminated by (a) a Gaussian beam, (b) a flat cosine-squared beam, and (c) an exponential-decay beam.

Fig. 6
Fig. 6

Angular sensitivities of the TE0 mode for a finite input VHGC in the waveguide film region illuminated by a Gaussian beam with a beam width W = 0.5Lg at its optimum incident-beam position of y0,opt = 0.6Lg.

Fig. 7
Fig. 7

Two-dimensional field-amplitude patterns of a finite input VHGC with Lg = 50 μm in the waveguide cover region illuminated by a TE-polarized Gaussian beam with a beam width W = 0.5Lg at the incident-beam position of (a) y0 = 0.3Lg, (b) y0 = 0.6Lg, and (c) y0 = 0.9Lg.

Fig. 8
Fig. 8

Field profiles corresponding to Fig. 6 for (a) the transmitted field at x = 16 μm and (b) the input-coupled field at y = 80 μm.

Fig. 9
Fig. 9

Input coupling efficiencies of the TE0 mode in the upward direction as functions of y0/Lg and W/Lg for a finite input VHGC with Lg = 50 μm in the waveguide cover region illuminated by (a) a Gaussian beam, (b) a flat cosine-squared beam, and (c) an exponential-decay beam.

Fig. 10
Fig. 10

Input coupling efficiencies of the TE1 mode in the upward direction as functions of y0/Lg and W/Lg for a finite input VHGC with Lg = 50 μm in the waveguide cover region illuminated by (a) a Gaussian beam, (b) a flat cosine-squared beam, and (c) an exponential-decay beam.

Fig. 11
Fig. 11

Angular sensitivities of both TE0 and TE1 modes for a finite input VHGC in the waveguide cover region illuminated by a Gaussian beam with a beam width W = 0.5Lg at its optimum incident-beam position of y0,opt = 0.7Lg.

Fig. 12
Fig. 12

Configuration of a multilayer slab waveguide consisting of a stack of N layers with finite thickness bounded on either side by two semi-infinite media, denoted as a substrate with refractive index ns and a cover with refractive index nc. The thickness and the refractive index of the ith layer are ti and ni, respectively.

Tables (2)

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Table 1 Optimizations for the Coupling of Finite Beams into a Waveguide via a VHGC of Length Lg = 50 μm in a Waveguide Film Region

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Table 2 Optimizations for the Coupling of Finite Beams into a Waveguide via a VHGC of Length Lg = 50 μm in a Waveguide Cover Region

Equations (15)

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= 0 ɛ ( x , y ) = 0 { ɛ 0 + p = 1 ɛ p c cos ( p K · r ) + p = 1 ɛ p s sin ( p K · r ) } ,
g ( y ) = exp [ ( - y W / 2 ) 2 ] ,
g ( y ) = { 1 0 y W 2 cos 2 [ y - W 2 2 ( D - W ) π ] W 2 y D - W 2 , 0 D - W 2 y
g ( y ) = { exp [ - α l ( y - W 2 ) ] 0 y W 2 cos 2 [ y - W 2 2 ( D - W ) π ] W 2 y D - W 2 , 0 D - W 2 y
E inc = g ( y ) exp ( - j k · r ) z ^ ,
2 E z + ω 2 μ s E z = 0 ,
A ¯ ¯ U = b ,
CE i , TE m = P i P inc × 100 % ,
E z ( x ) = m a m E m z ( x ) + β q ( β ) E z ( x , β ) d β ,
E z ( x ) = m a m E m z ( x ) exp ( - j β m y ) + β q ( β ) E z ( x , β ) × exp ( - j β y ) d β ,
E m z ( x ) , E n z ( x ) = β m 2 ω μ 0 - β m E m z ( x ) E n z * ( x ) d x = P TE m δ m , n ,
a m = 1 P TE m E z ( x ) ,     E m z ( x ) = 1 P TE m β m 2 ω μ 0 - E z ( x ) E m z * ( x ) d x ,
q ( β ) = 1 P TE β E z ( x ) ,     E z ( x , β ) = 1 P TE β β 2 ω μ 0 - E z ( x ) E z * ( x , β ) d x .
P TE = m a m 2 P TE m + β q ( β ) 2 P TE β d β .
P TE m = a m 2 P TE m .

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