Abstract

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.

© 2002 Optical Society of America

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2001 (3)

2000 (5)

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]

Z. Hegedus, R. Netterfield, “Low sideband guided-mode resonant filter,” Appl. Opt. 39, 1469–1473 (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]

D. A. B. Miller, “Rationale and challenges for optical interconnects to electric chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. 6, 1312–1317 (2000).
[CrossRef]

1999 (3)

1998 (4)

1997 (7)

D. A. B. Miller, “Physical reasons for optical interconnection,” Special Issue on Smart Pixels, Int. J. Optoelectron. 11, 155–168 (1997).

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[CrossRef]

S. Sinzinger, J. Janns, “Integrated micro-optical imaging system with a high interconnection capacity fabricated in planar optics,” Appl. Opt. 36, 4729–4735 (1997).
[CrossRef] [PubMed]

O. Mata-Mendez, J. Sumaya-Martinez, “Scattering of TE-polarized waves by a finite-grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203–2211 (1997).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
[CrossRef]

J. P. Bérenger, “Improved PML for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 45, 466–473 (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 (4)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

J. P. Bérenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 44, 110–117 (1996).
[CrossRef]

G. Pelosi, G. Manara, G. Toso, “Heuristic diffraction coefficient for plane-wave scattering from edges in periodic planar surfaces,” J. Opt. Soc. Am. A 13, 1689–1697 (1996).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

1995 (3)

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]

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]

J. C. Brazas, L. Li, A. L. Mckeon, “High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation,” Appl. Opt. 34, 604–609 (1995).
[CrossRef] [PubMed]

1994 (3)

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]

E. E. Kriezis, P. K. Pandelakis, A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630–636 (1994).
[CrossRef]

1993 (1)

1991 (1)

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

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Baillie, D. A.

Baukens, V.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Bendickson, J. M.

Bérenger, J. P.

J. P. Bérenger, “Improved PML for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 45, 466–473 (1997).
[CrossRef]

J. P. Bérenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 44, 110–117 (1996).
[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]

Borghs, S.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

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]

Buczynski, R.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Buller, G. S.

Chavez-Rivas, F.

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]

Coppée, D.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Danes, J. A. B.

Debaes, C.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Desmulliez, M. P. Y.

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]

Ferrari, R. L.

P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, New York, 1996).

Forbes, M. G.

Gaylord, T. K.

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487–1494 (2001).
[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).
[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]

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]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Genoe, J.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Glytsis, E. N.

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487–1494 (2001).
[CrossRef]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).
[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]

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]

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

Gourlay, J.

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, 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]

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 2000), Chaps. 6 and 7.

Hardy, A.

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

Hegedus, Z.

Hermanne, A.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

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]

Hirayama, K.

Janns, J.

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]

Kok, Y.-L.

Kowarz, M. W.

Kriezis, E. E.

Kufner, M.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Kufner, S.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Larsson, A.

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, 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]

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]

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, 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]

Manara, G.

Mata-Mendez, O.

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 reflector,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, “Rationale and challenges for optical interconnects to electric chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. 6, 1312–1317 (2000).
[CrossRef]

D. A. B. Miller, “Physical reasons for optical interconnection,” Special Issue on Smart Pixels, Int. J. Optoelectron. 11, 155–168 (1997).

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Neilson, D. T.

Netterfield, R.

Ottevaere, H.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Pandelakis, P. K.

Papagiannakis, A. G.

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 reflector,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Pelosi, G.

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]

Pottier, F.

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]

Prince, S. M.

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]

Schenfeld, E.

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]

Sibbett, W.

Silvester, P. P.

P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, New York, 1996).

Sinzinger, S.

Smith, G. R.

Stanley, C. R.

Sumaya-Martinez, J.

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 2000), Chaps. 6 and 7.

Taghizadeh, M. R.

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]

Thienpont, H.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Toso, G.

Tuteleers, P.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Underwood, I.

Veretennicoff, I.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Verschaffelt, G.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Vögele, B.

Vounckx, R.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

Vynck, P.

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[CrossRef]

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 reflector,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[CrossRef]

Waddie, A.

Walker, A. C.

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 reflector,” 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]

Wilkinson, L. C.

Williams, R.

Wilson, D. W.

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, M. C.

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[CrossRef]

Yang, T.-Y.

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. (9)

S. Sinzinger, J. Janns, “Integrated micro-optical imaging system with a high interconnection capacity fabricated in planar optics,” Appl. Opt. 36, 4729–4735 (1997).
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[CrossRef]

D. T. Neilson, E. Schenfeld, “Free-space optical relay for the interconnection of multimode fibers,” Appl. Opt. 38, 2291–2296 (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]

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]

J. C. Brazas, L. Li, A. L. Mckeon, “High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation,” Appl. Opt. 34, 604–609 (1995).
[CrossRef] [PubMed]

Z. Hegedus, R. Netterfield, “Low sideband guided-mode resonant filter,” Appl. Opt. 39, 1469–1473 (2000).
[CrossRef]

Y.-L. Kok, “General solution to the multiple-metallic-grooves scattering problem: the fast-polarization case,” Appl. Opt. 32, 2573–2581 (1993).
[CrossRef] [PubMed]

W.-C. Liu, M. W. Kowarz, “Vector diffraction from subwavelength optical disk structures: two-dimensional modeling of near-field profiles, far-field intensities, and detector signals from DVD,” Appl. Opt. 38, 3787–3797 (1999).
[CrossRef]

Electron. Lett. (2)

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]

IEEE J. Sel. Top. Quantum Electron. (1)

D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. 6, 1312–1317 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

G. Verschaffelt, R. Buczynski, P. Tuteleers, P. Vynck, V. Baukens, H. Ottevaere, C. Debaes, S. Kufner, M. Kufner, A. Hermanne, J. Genoe, D. Coppée, R. Vounckx, S. Borghs, I. Veretennicoff, H. Thienpont, “Demonstration of a monolithic multichannel module for multi-Gb/s intra-MCM optical interconnects,” IEEE Photon. Technol. Lett. 10, 1629–1631 (1998).
[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 reflector,” IEEE Photon. Technol. Lett. 3, 342–344 (1991).
[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]

IEEE Trans. Antennas Propag. (4)

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]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

J. P. Bérenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 44, 110–117 (1996).
[CrossRef]

J. P. Bérenger, “Improved PML for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. 45, 466–473 (1997).
[CrossRef]

Int. J. Optoelectron. (1)

D. A. B. Miller, “Physical reasons for optical interconnection,” Special Issue on Smart Pixels, Int. J. Optoelectron. 11, 155–168 (1997).

J. Lightwave Technol. (1)

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]

J. Opt. Soc. Am. A (9)

J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
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J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods,” J. Opt. Soc. Am. A 18, 1487–1494 (2001).
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O. Mata-Mendez, J. Sumaya-Martinez, “Scattering of TE-polarized waves by a finite-grating: giant resonant enhancement of the electric field within the grooves,” J. Opt. Soc. Am. A 14, 2203–2211 (1997).
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K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
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O. Mata-Mendez, F. Chavez-Rivas, “Diffraction of Gaussian and Hermite–Gaussian beams by finite gratings,” J. Opt. Soc. Am. A 18, 537–545 (2001).
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E. E. Kriezis, P. K. Pandelakis, A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630–636 (1994).
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J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings,” J. Opt. Soc. Am. A 18, 1912–1928 (2001).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (4)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electric chips,” Proc. IEEE 88, 728–749 (2000).
[CrossRef]

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[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. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (2)

A. Taflove, S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 2000), Chaps. 6 and 7.

P. P. Silvester, R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, New York, 1996).

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Figures (12)

Fig. 1
Fig. 1

(a) Geometry used to model the diffraction of a finite-width beam from a FNP holographic grating. The holographic grating has period Λ, slant angle ϕ, width L, and thickness d. The thickness of the absorbing uniaxial perfectly matching layer (UPML) is δ. (b) The beam profile of the finite incident beam has flat width W, total width (2D-W), and incident angle θinc.

Fig. 2
Fig. 2

Forward-diffraction efficiencies of the ±1 diffracted orders as functions of W/Λ and L/Λ for an unslanted FNP holographic grating with Λ=2.5 μm and d=8 μm. The solid curves and dashed curves represent the results for TE polarization and TM polarization, respectively. The RCWA results correspond to an INP grating illuminated by a plane wave (an infinite-width beam).

Fig. 3
Fig. 3

Two-dimensional diffracted field intensity patterns of unslanted FNP holographic gratings with Λ=2.5 μm, d=8 μm, and L=10Λ illuminated by a TE-polarized beam with (a) W=Λ, (b) W=6Λ, and (c) W=12Λ.

Fig. 4
Fig. 4

Forward-diffraction efficiencies of the -1 diffracted order as functions of W/Λy and L/Λy for a slanted FNP holographic transmission grating with Λ=1.92 μm, ϕ=100°, and d=20 μm. The solid curves and dashed curves represent the results of TE polarization and TM polarization, respectively. The RCWA results correspond to an INP grating illuminated by a plane wave (an infinite-width beam).

Fig. 5
Fig. 5

Two-dimensional diffracted field intensity patterns of slanted FNP holographic transmission gratings with Λ=1.92 μm, ϕ=100°, d=20 μm, and L=10Λy illuminated by a TE-polarized beam with (a) W=Λy, (b) W=6Λy, and (c) W=12Λy.

Fig. 6
Fig. 6

Backward-diffraction efficiencies of the -1 diffracted order as functions of W/Λy and L/Λy for a slanted FNP holographic reflection grating with Λ=0.34 μm, ϕ=170°, and d=20 μm. The solid curves and dashed curves represent the results of TE polarization and TM polarization, respectively. The RCWA results correspond to an INP grating illuminated by a plane wave (an infinite-width beam).

Fig. 7
Fig. 7

Two-dimensional diffracted field intensity patterns of slanted FNP holographic reflection gratings with Λ=0.34 μm, ϕ=170°, d=20 μm, and L=10Λy illuminated by a TE-polarized beam with (a) W=Λy, (b) W=6Λy, and (c) W=12Λy.

Fig. 8
Fig. 8

Artificial reflection error from the UPML as functions of the maximum conductivity σmax and the polynomial order m as the dielectric constant of the truncated media is ε=3 and the thickness of the UPML is δ=2.0 μm.

Fig. 9
Fig. 9

Optimal values of maximum conductivities as functions of the dielectric constant ε and the polynomial order m when the thickness of the UPML is δ=2.0 μm.

Fig. 10
Fig. 10

Normalized transmitted and reflected powers as a function of the number of grid points per wavelength (Nx=Ny) for the case of a TE- or TM-polarized, normally incident plane wave on a planar interface between two regions of refractive indices n1=1.0 and n2=1.5.

Fig. 11
Fig. 11

Magnitude and phase of the total electric field, Ez, as a function of x in the case of a TE-polarized normally incident plane wave on a planar interface between two regions of refractive indices n1=1.0 and n2=1.5. The planar interface is located at x=1 μm.

Fig. 12
Fig. 12

Magnitude and phase of the total magnetic field, Hz, as a function of x in the case of a TM-polarized normally incident plane wave on a planar interface between two regions of refractive indices n1=1.0 and n2=1.5. The planar interface is located at x=1 μm.

Tables (2)

Tables Icon

Table 1 Comparison of the Accuracy of the RCWA for Two-Level FNP Surface-Relief Gratings and Unslanted FNP Holographic Gratings

Tables Icon

Table 2 Comparison of the Accuracy of the RCWA for Eight-Level FNP Surface-Relief Gratings and Slanted FNP Holographic Transmission Gratings

Equations (27)

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

=0ε(x, y)=0ε0+p=1εp cos(pK·r),
g(y)=1,0|y|W2cos2|y|-W22(D-W)π,W2|y|D-W20,D-W2|y|,
Einc=g(y)exp(-jk·r)zˆ,
Hinc=g(y)exp(-jk·r)zˆ,
2Ez+ω2μsEz=0.
2Hz+ω2μsHz-2(jω+σ)jω+σ·2Hz=0,
Nx=λ0/nmaxΔx,
Ny=λ0/nmaxΔy,
A¯¯U=b,
A¯¯incUinc=bs,
A¯¯scaUsca=(A¯¯inc-A¯¯sca)Uinc,
Fi(kym)=q=0M-1U(xi, qΔy)exp[jkym(qΔy)],
PiTE=Δy2Mm=0M-1|Fi(kym)|2 Reki,xm*ηi*ki*(i=1, 3).
PiTM=Δy2Mm=0M-1|Fi(kym)|2 Reki,xmηiki(i=1, 3),
Pi,pTE=Δy2Mm=k1, y-(p+1/2)Kyk1, y-(p-1/2)Ky|Fi(kym)|2 Reki,xm*ηi*ki*
(i=1, 3).
Pi,pTM=Δy2Mm=k1, y-(p+1/2)Kyk1, y-(p-1/2)Ky|Fi(kym)|2 Reki,xmηiki
(i=1, 3),
Error%=DEiu,RCWA-DEiu,FNPDEiu,FNP100,
×E=-jωμs˜H,
×H=jωs˜E,
·(s˜E)=0,
·(μs˜H)=0,
s˜=sx-1sysz000sxsy-1sz000sxsysz-1
1sxx1sxEzx+1syy1syEzy+ω2μEz=0.
1sxx1sxHzx+1syy1syHzy+ω2μHz=0.
σi(ri)=σi,maxriδm,fori=x, y, z,

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