Abstract

We analyze the polarization-dependent performance and the loss performance of volume grating couplers using a leaky-mode approach in conjunction with rigorous coupled-wave analysis for two configurations: the volume grating in the cover layer and the volume grating in the waveguide. The angular dependence of TE and TM polarization coupling efficiency is studied, and designs for polarization-dependent and polarization-independent couplers are presented for both configurations. Polarization-dependent couplers are obtained with an outcoupling angle close to normal. Polarization-independent couplers are obtained with outcoupling angles away from normal, 46.7 deg in the case of a volume grating in the cover layer and 54.4 deg in the case of a volume grating in the waveguide. The effect of loss on coupler performance is also analyzed. It is found that, for cases of practical importance, the effect of lossy coupler materials is small. The estimated loss for a commercially available material is 5 dB/cm. For TE-polarized light and the volume grating in the waveguide, a loss of this magnitude reduces the coupling efficiency by less than 3%, whereas in the case of the volume grating in the cover layer, it reduces the coupling efficiency by less than 0.3%.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  2. M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparison between optical and electrical interconnects based on power and speed considerations,” Appl. Opt. 27, 1742–1751 (1988).
    [CrossRef] [PubMed]
  3. D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–739 (2000).
    [CrossRef]
  4. R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Pickor, M. K. Hibbs-Brenner, J. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
    [CrossRef]
  5. H. Kogelnik, T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).
    [CrossRef]
  6. W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15, 725–727 (1990).
    [CrossRef] [PubMed]
  7. 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]
  8. M. L. Jones, R. P. Kenan, C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34, 4149–4158 (1995).
    [CrossRef] [PubMed]
  9. V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
    [CrossRef]
  10. J. H. Harris, R. K. Winn, D. G. Dalgoutte, “Theory and design of periodic couplers,” Appl. Opt. 11, 2234–2241 (1972).
    [CrossRef] [PubMed]
  11. R. Ulrich, “Efficiency of optical-grating couplers,” J. Opt. Soc. Am. 63, 1419–1431 (1973).
    [CrossRef]
  12. A. Wuthrich, W. Lukosz, “Holography with guided optical waves: II. Theory of the diffraction efficiencies,” Appl. Phys. 22, 161–170 (1980).
    [CrossRef]
  13. S. T. Peng, T. Tamir, H. L. Bertoni, “Leaky-wave analysis of optical periodic couplers,” Electron Lett. 9, 150–152 (1973).
    [CrossRef]
  14. S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
    [CrossRef]
  15. K. Ogawa, W. S. C. Chang, “Analysis of holographic thin film grating coupler,” Appl. Opt. 12, 2167–2171 (1973).
    [CrossRef] [PubMed]
  16. W. Y. Wang, T. J. Dilaura, “Bragg effect waveguide coupler analysis,” Appl. Opt. 16, 3230–3236 (1977).
    [CrossRef] [PubMed]
  17. W. Driemeier, “Coupled-wave analysis of the Bragg effect waveguide coupler,” J. Mod. Opt. 38, 363–377 (1991).
    [CrossRef]
  18. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  19. L. Solymar, “Power conservation theorem for 2-dimensional volume holograms,” Electron. Lett. 12, 606–607 (1976).
    [CrossRef]
  20. L. Solymar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977).
    [CrossRef]
  21. K. Matsumoto, K. Rokushima, J. Yamakita, “Three-dimensional rigorous analysis of dielectric grating waveguides for general cases of oblique propagation,” J. Opt. Soc. Am. A 10, 269–276 (1993).
    [CrossRef]
  22. R. K. Kostuk, M. Kato, Y. T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
    [CrossRef] [PubMed]
  23. F. Lin, E. M. Strzelecki, T. Jannson, “Optical multiplanar VLSI interconnects based on multiplexed waveguide holograms,” Appl. Opt. 29, 1126–1133 (1990).
    [CrossRef] [PubMed]
  24. F. Lin, E. M. Strzelecki, C. Nguyen, T. Jannson, “Highly parallel single-mode multiplanar holographic interconnects,” Opt. Lett. 16, 183–185 (1991).
    [PubMed]
  25. M. R. Wang, G. J. Sonek, R. T. Chen, T. Jannson, “Large fanout optical interconnects using thick holographic gratings and substrate wave propagation,” Appl. Opt. 31, 236–249 (1992).
    [CrossRef] [PubMed]
  26. J. H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 2993–2998 (1995).
    [CrossRef]
  27. C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
    [CrossRef]
  28. R. K. Kostuk, G. T. Sincerbox, “Polarization sensitivity of noise gratings recorded in silver halide volume holograms,” Appl. Opt. 27, 2993–2998 (1988).
    [CrossRef] [PubMed]
  29. R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
    [CrossRef]
  30. J. H. Yeh, R. K. Kostuk, “Free-space holographic optical interconnects for board-to-board and chip-to-chip interconnections,” Opt. Lett. 21, 1274–1276 (1996).
    [CrossRef] [PubMed]
  31. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Design of a high-efficiency volume grating coupler for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
    [CrossRef]
  32. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Volume grating preferential-order focusing waveguide coupler,” Opt. Lett. 24, 1708–1710 (1999).
    [CrossRef]
  33. S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Design, fabrication, and performance of preferential-order volume grating waveguide couplers,” Appl. Opt. 39, 1223–1231 (2000).
    [CrossRef]
  34. L. D. Dickson, R. D. Rallison, B. H. Yung, “Holographic polarization-separation elements,” Appl. Opt. 33, 5378–5385 (1994).
    [CrossRef] [PubMed]
  35. J. T. Chang, D. C. Su, Y. T. Huang, “A four channel polarization and wavelength separation element using substrate-mode stacked holograms,” Appl. Phys. Lett. 68, 3537–3539 (1996).
    [CrossRef]
  36. M. Kato, H. Ito, T. Yamamoto, F. Yamagishi, T. Nakagami, “Multichannel optical switch that uses holograms,” Opt. Lett. 17, 769–771 (1992).
    [CrossRef] [PubMed]
  37. R. K. Kostuk, T. J. Kim, G. Campbell, C. W. Han, “Diffractive-optic polarization-sensing element for magneto-optic storage heads,” Opt. Lett. 19, 1257–1259 (1994).
    [CrossRef] [PubMed]
  38. Y. T. Huang, “Polarization-selective volume holograms: general design,” Appl. Opt. 33, 2115–2120 (1994).
    [CrossRef] [PubMed]
  39. J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
    [CrossRef]
  40. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  41. M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
    [CrossRef]
  42. matlab, version 5.3, Matlab, Inc., 1112 NC Highway 49 South, Asheboro, N.C. 27205 (2000).
  43. M. L. Jones, “Design of normal-incidence waveguide-inbedded phase gratings for optical interconnects in multi-chip modules,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1995).

2000 (3)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–739 (2000).
[CrossRef]

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Pickor, M. K. Hibbs-Brenner, J. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (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, 1223–1231 (2000).
[CrossRef]

1999 (1)

1998 (3)

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

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

1997 (1)

1996 (2)

J. H. Yeh, R. K. Kostuk, “Free-space holographic optical interconnects for board-to-board and chip-to-chip interconnections,” Opt. Lett. 21, 1274–1276 (1996).
[CrossRef] [PubMed]

J. T. Chang, D. C. Su, Y. T. Huang, “A four channel polarization and wavelength separation element using substrate-mode stacked holograms,” Appl. Phys. Lett. 68, 3537–3539 (1996).
[CrossRef]

1995 (3)

1994 (3)

1993 (2)

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

K. Matsumoto, K. Rokushima, J. Yamakita, “Three-dimensional rigorous analysis of dielectric grating waveguides for general cases of oblique propagation,” J. Opt. Soc. Am. A 10, 269–276 (1993).
[CrossRef]

1992 (2)

1991 (2)

F. Lin, E. M. Strzelecki, C. Nguyen, T. Jannson, “Highly parallel single-mode multiplanar holographic interconnects,” Opt. Lett. 16, 183–185 (1991).
[PubMed]

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

1990 (3)

1988 (2)

1984 (1)

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1980 (1)

A. Wuthrich, W. Lukosz, “Holography with guided optical waves: II. Theory of the diffraction efficiencies,” Appl. Phys. 22, 161–170 (1980).
[CrossRef]

1977 (2)

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

L. Solymar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977).
[CrossRef]

1976 (1)

L. Solymar, “Power conservation theorem for 2-dimensional volume holograms,” Electron. Lett. 12, 606–607 (1976).
[CrossRef]

1975 (1)

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

1973 (3)

1972 (1)

1970 (1)

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

1969 (1)

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

Ashley, P. R.

Athale, R. A.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[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. Pickor, M. K. Hibbs-Brenner, J. Bristow, Y. S. Liu, “Fully embedded board-level guided-wave optoelectronic interconnects,” Proc. IEEE 88, 780–793 (2000).
[CrossRef]

Bristow, J.

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

Butler, J. J.

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

Campbell, G.

Chang, J. T.

J. T. Chang, D. C. Su, Y. T. Huang, “A four channel polarization and wavelength separation element using substrate-mode stacked holograms,” Appl. Phys. Lett. 68, 3537–3539 (1996).
[CrossRef]

Chang, W. S. C.

Chen, R. T

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Chen, R. T.

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

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

M. R. Wang, G. J. Sonek, R. T. Chen, T. Jannson, “Large fanout optical interconnects using thick holographic gratings and substrate wave propagation,” Appl. Opt. 31, 236–249 (1992).
[CrossRef] [PubMed]

Choi, C.

R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Pickor, 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.

Davies, B. M.

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

Dickson, L. D.

Dilaura, T. J.

Driemeier, W.

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

W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15, 725–727 (1990).
[CrossRef] [PubMed]

Esener, S. C.

Feldman, M. R.

Finkelstein, I.

V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
[CrossRef]

Gaylord, T. K.

Gerald, D.

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Grann, E. B.

Guest, C. C.

Han, C. W.

Harris, J. H.

Hibbs-Brenner, M. K.

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

Huang, Q.

Huang, Y. T.

Ito, H.

Jannson, T.

Jones, M. L.

M. L. Jones, R. P. Kenan, C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34, 4149–4158 (1995).
[CrossRef] [PubMed]

M. L. Jones, “Design of normal-incidence waveguide-inbedded phase gratings for optical interconnects in multi-chip modules,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1995).

Kato, M.

Kenan, R. P.

Kim, T. J.

Kogelnik, H.

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

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

Kostuk, R. K.

Kung, S. Y.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lee, S. H.

Leonberger, F. I.

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Li, M. M.

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Lin, F.

Lin, L.

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

Lukosz, W.

A. Wuthrich, W. Lukosz, “Holography with guided optical waves: II. Theory of the diffraction efficiencies,” Appl. Phys. 22, 161–170 (1980).
[CrossRef]

Malcuit, M. S.

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

Matsumoto, K.

Miller, D. A. B.

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–739 (2000).
[CrossRef]

Millul, E.

V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
[CrossRef]

Moharam, M. G.

Nakagami, T.

Natarajan, S.

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Neviere, M.

M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

Nguyen, C.

Ogawa, K.

Peng, S. T.

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]

Pickor, B.

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

Pommet, D. A.

Rallison, R. D.

Rodriguez, M. A.

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

Rokushima, K.

Ruschin, S.

V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
[CrossRef]

Schultz, S. M.

Sincerbox, G. T.

Solymar, L.

L. Solymar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977).
[CrossRef]

L. Solymar, “Power conservation theorem for 2-dimensional volume holograms,” Electron. Lett. 12, 606–607 (1976).
[CrossRef]

Sonek, G. J.

Sosnowski, T. P.

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

Stone, T. W.

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

Strzelecki, E. M.

Su, D. C.

J. T. Chang, D. C. Su, Y. T. Huang, “A four channel polarization and wavelength separation element using substrate-mode stacked holograms,” Appl. Phys. Lett. 68, 3537–3539 (1996).
[CrossRef]

Sutton, S.

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

Tamir, T.

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]

Tang, S.

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

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Ulrich, R.

Verber, C. M.

Wang, M. R.

Wang, W. Y.

Weiss, V.

V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
[CrossRef]

Wickman, R.

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

Winn, R. K.

Wu, L.

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

Wuthrich, A.

A. Wuthrich, W. Lukosz, “Holography with guided optical waves: II. Theory of the diffraction efficiencies,” Appl. Phys. 22, 161–170 (1980).
[CrossRef]

Yamagishi, F.

Yamakita, J.

Yamamoto, T.

Yeh, J. H.

Yung, B. H.

Zhou, C. C.

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

Appl. Opt. (15)

M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparison between optical and electrical interconnects based on power and speed considerations,” Appl. Opt. 27, 1742–1751 (1988).
[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]

M. L. Jones, R. P. Kenan, C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34, 4149–4158 (1995).
[CrossRef] [PubMed]

J. H. Harris, R. K. Winn, D. G. Dalgoutte, “Theory and design of periodic couplers,” Appl. Opt. 11, 2234–2241 (1972).
[CrossRef] [PubMed]

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

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

R. K. Kostuk, M. Kato, Y. T. Huang, “Polarization properties of substrate-mode holographic interconnects,” Appl. Opt. 29, 3848–3854 (1990).
[CrossRef] [PubMed]

F. Lin, E. M. Strzelecki, T. Jannson, “Optical multiplanar VLSI interconnects based on multiplexed waveguide holograms,” Appl. Opt. 29, 1126–1133 (1990).
[CrossRef] [PubMed]

M. R. Wang, G. J. Sonek, R. T. Chen, T. Jannson, “Large fanout optical interconnects using thick holographic gratings and substrate wave propagation,” Appl. Opt. 31, 236–249 (1992).
[CrossRef] [PubMed]

J. H. Yeh, R. K. Kostuk, “Substrate-mode holograms used in optical interconnects: design issues,” Appl. Opt. 34, 2993–2998 (1995).
[CrossRef]

R. K. Kostuk, G. T. Sincerbox, “Polarization sensitivity of noise gratings recorded in silver halide volume holograms,” Appl. Opt. 27, 2993–2998 (1988).
[CrossRef] [PubMed]

S. M. Schultz, E. N. Glytsis, T. K. Gaylord, “Design of a high-efficiency volume grating coupler 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, 1223–1231 (2000).
[CrossRef]

L. D. Dickson, R. D. Rallison, B. H. Yung, “Holographic polarization-separation elements,” Appl. Opt. 33, 5378–5385 (1994).
[CrossRef] [PubMed]

Y. T. Huang, “Polarization-selective volume holograms: general design,” Appl. Opt. 33, 2115–2120 (1994).
[CrossRef] [PubMed]

Appl. Phys. (1)

A. Wuthrich, W. Lukosz, “Holography with guided optical waves: II. Theory of the diffraction efficiencies,” Appl. Phys. 22, 161–170 (1980).
[CrossRef]

Appl. Phys. Lett. (3)

L. Solymar, “A general two-dimensional theory for volume holograms,” Appl. Phys. Lett. 31, 820–822 (1977).
[CrossRef]

J. T. Chang, D. C. Su, Y. T. Huang, “A four channel polarization and wavelength separation element using substrate-mode stacked holograms,” Appl. Phys. Lett. 68, 3537–3539 (1996).
[CrossRef]

R. T Chen, S. Tang, M. M. Li, D. Gerald, S. Natarajan, “1-to-12 surface normal three-dimensional optical interconnects,” Appl. Phys. Lett. 63, 1883–1885 (1993).
[CrossRef]

Bell Syst. Tech. J. (2)

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

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

Electron Lett. (1)

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

Electron. Lett. (1)

L. Solymar, “Power conservation theorem for 2-dimensional volume holograms,” Electron. Lett. 12, 606–607 (1976).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. C. Zhou, S. Sutton, R. T. Chen, B. M. Davies, “Surface-normal 4 × 4 nonblocking wavelength-selective optical crossbar interconnect using polymer-based volume holograms and substrate-guided waves,” IEEE Photon. Technol. Lett. 10, 1581–1583 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

J. J. Butler, M. A. Rodriguez, M. S. Malcuit, T. W. Stone, “Polarization-sensitive holograms formed using DMP—128 photopolymer,” Opt. Commun. 155, 23–27 (1998).
[CrossRef]

Opt. Lett. (6)

Proc. IEEE (3)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–739 (2000).
[CrossRef]

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

J. W. Goodman, F. I. Leonberger, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Other (4)

V. Weiss, I. Finkelstein, E. Millul, S. Ruschin, “Coupling and waveguiding in photopolymers,” in Precision Plastic Optics for Optical Storage, Displays, Imaging, and Communications, W. F. Frank, ed., Proc. SPIE3135, 136–143 (1997).
[CrossRef]

M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
[CrossRef]

matlab, version 5.3, Matlab, Inc., 1112 NC Highway 49 South, Asheboro, N.C. 27205 (2000).

M. L. Jones, “Design of normal-incidence waveguide-inbedded phase gratings for optical interconnects in multi-chip modules,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Diagrams of the two VGC configurations discussed in this paper: (a) volume grating in the cover layer, (b) volume grating in the waveguide. The grating vector K as well as the period Λ and slant angle ϕ are shown. The outcoupling angle is θ f . The thickness of the grating layer is t g , and the thickness of the waveguide layer is t w .

Fig. 2
Fig. 2

Schematic diagram for the analysis of coupler structures with an arbitrary number of layers and gratings.

Fig. 3
Fig. 3

Electric field plot of leaky mode in a VG in the cover layer structure. Note the waves radiating into the superstrate and the substrate.

Fig. 4
Fig. 4

Coupling coefficient versus outcoupling angle for the VG in the cover layer structure. A minimum for TM polarization occurs close to 0 deg. For TE polarization, the coupling coefficient remains fairly constant as the outcoupling angle is varied.

Fig. 5
Fig. 5

Coupling coefficient versus outcoupling angle for the VG in the waveguide structure. A minimum for TM polarization occurs at -12 deg. For TE polarization, the coupling coefficient remains fairly constant as the outcoupling angle is varied.

Fig. 6
Fig. 6

Coupling coefficient versus grating slant angle for vertical coupling for the VG in the cover layer and the VG in the waveguide configurations. The VG in the waveguide curve has a slightly higher peak and a considerably wider FWHM than the VG in the cover layer curve.

Fig. 7
Fig. 7

Coupling efficiency versus outcoupling angle for a 1-mm-long VG in the cover layer structure. Coupling efficiency for TE polarization remains higher for all angles in this range. For TM polarization, coupling efficiency increases with increasing outcoupling angle, reaching parity near θ f = 46.7 deg.

Fig. 8
Fig. 8

Coupling efficiency versus outcoupling angle for a 1-mm-long VG in the waveguide structure. Coupling efficiency for TE polarization remains high for all angles in this range. For TM polarization, coupling efficiency increases with increasing outcoupling angle, reaching parity near θ f = 54.4 deg.

Fig. 9
Fig. 9

Coupling efficiency versus coupler length for couplers designed to be polarization independent in the VG in the cover layer and the VG in the waveguide configurations. The coupling coefficient is larger for TE than for TM polarization in both cases, which explains why the TE coupling efficiencies saturated faster.

Fig. 10
Fig. 10

Coupling efficiency versus coupler length for lossless and lossy VGCs in the VG in the waveguide configuration. The small effect of absorption losses in the coupler material can be seen. Polarization-dependent coupling is also on display because θ f ≈ 0 deg.

Equations (16)

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

Um=ŷUmz, xexp-jβ˜x,
Umz, x=i Sm,izexp-jσm,i · r m=2,  , M+1,
Sm,iz=j Cjmwi,jm expλjmz,
U1=ŷ i Ri exp-jk1,i · r
k1,i=k˜x,ixˆ+k˜1,zizˆ,
k˜1,zi=Ikk02n12-k˜x,i21/2
k˜1,zi=-k02n12-k˜x,i21/2
UM+2=ŷ i Tiexp-jkM+2,i·r-dz,
kM+2,i=k˜x,ixˆ+k˜M+2,zizˆ,
k˜M+2,zi=k02n12-k˜x,i21/2
k˜M+2,zi=-k02n12-k˜x,i21/2
PVsup,i=|Ri|2Re-k1,zi
PVsub,i=|Ti|2RekM+2,zip
ηl,i=PVl,iiPVsup,i+iPVsub,i.
CEl,i=ηl,i1-exp-2αL.
CEl,i=ηl,iαα+αloss1-exp-2α+αlossL.

Metrics