Abstract

The optimum profiles of right-angle-face anisotropically etched silicon surface-relief gratings illuminated at normal incidence for substrate-mode optical interconnects are determined for TE, TM, and random linear (RL) polarizations. A simulated annealing algorithm in conjunction with the rigorous coupled-wave analysis is used. The optimum diffraction efficiencies of the -1 forward-diffracted order are 37.3%, 67.1%, and 51.2% for TE-, TM-, and RL-polarization-optimized profiles, respectively. Also, the sensitivities to grating thickness, slant angle, and incident angle of the optimized profiles are presented.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. S.-D. Wu, T. K. Gaylord, E. N. Glytsis, and Y.-M. Wu, "Angular sensitivities of volume gratings for substrate-mode optical interconnects," Appl. Opt. 44, 4447-4453 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005 (3)

2004 (2)

S.-D. Wu and E. N. Glytsis, "Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method," Appl. Opt. 43, 1009-1023 (2004).

D. Taillaert, P. Bienstman, and R. Baets, "Compact efficient broadband grating coupler for silicon-on-insulator waveguides," Opt. Lett. 29, 2749-2751 (2004).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

K. Sakaino and S. Adachi, "Study of Si(1 0 0) surfaces etched in TMAH solution," Sens. Actuators A 88, 71-78 (2001).
[CrossRef]

2000 (3)

1998 (1)

1996 (1)

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

1995 (2)

J.-H. Yeh and R. K. Kostuk, "Substrate-mode holograms used in optical interconnects: design issues," Appl. Opt. 34, 3152-3164 (1995).
[CrossRef] [PubMed]

N. Rajkumar and J. N. McMullin, "V-groove gratings on silicon for infrared beam splitting," Appl. Opt. 34, 2556-2559 (1995).
[CrossRef] [PubMed]

1987 (1)

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

1985 (1)

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

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1978 (1)

K. E. Bean, "Anisotropic etching of silicon," IEEE Trans. Electron Devices 25, 1185-1193 (1978).
[CrossRef]

Adachi, S.

K. Sakaino and S. Adachi, "Study of Si(1 0 0) surfaces etched in TMAH solution," Sens. Actuators A 88, 71-78 (2001).
[CrossRef]

Ang, T. W.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Auslender, M.

Baets, R.

Bean, K. E.

K. E. Bean, "Anisotropic etching of silicon," IEEE Trans. Electron Devices 25, 1185-1193 (1978).
[CrossRef]

Bienstman, P.

Corana, A.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

Evans, A. G. R.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Gaylord, T. K.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Glytsis, E. N.

Gualous, H.

Hava, S.

Josey, M. R.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Koster, A.

Kostuk, R. K.

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

J.-H. Yeh and R. K. Kostuk, "Substrate-mode holograms used in optical interconnects: design issues," Appl. Opt. 34, 3152-3164 (1995).
[CrossRef] [PubMed]

Laval, S.

Layadi, A.

Levy, D.

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

Martini, C.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

McMullin, J. N.

Moharam, M. G.

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

Orobtchouk, R.

Pascal, D.

Rajkumar, N.

Reed, G. T.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Ridella, S.

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

Routley, P. R.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Sakaino, K.

K. Sakaino and S. Adachi, "Study of Si(1 0 0) surfaces etched in TMAH solution," Sens. Actuators A 88, 71-78 (2001).
[CrossRef]

Schultz, S. M.

Taillaert, D.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Villalaz, R. A.

Vonsovici, A.

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

Wu, S.-D.

S.-D. Wu, T. K. Gaylord, E. N. Glytsis, and Y.-M. Wu, "Three-dimensional converging/diverging Gaussian beam diffraction by a volume grating," J. Opt. Soc. Am. A 22, 1293-1303(2005).
[CrossRef]

S.-D. Wu, E. N. Glytsis, and T. K. Gaylord, "Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams," Appl. Opt. 44, 4435-4446(2005).
[CrossRef] [PubMed]

S.-D. Wu, T. K. Gaylord, E. N. Glytsis, and Y.-M. Wu, "Angular sensitivities of volume gratings for substrate-mode optical interconnects," Appl. Opt. 44, 4447-4453 (2005).
[CrossRef] [PubMed]

S.-D. Wu and E. N. Glytsis, "Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method," Appl. Opt. 43, 1009-1023 (2004).

Wu, Y.-M.

Yeh, J.-H.

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

J.-H. Yeh and R. K. Kostuk, "Substrate-mode holograms used in optical interconnects: design issues," Appl. Opt. 34, 3152-3164 (1995).
[CrossRef] [PubMed]

ACM Trans. Math. Software (1)

A. Corana, M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm," ACM Trans. Math. Software 13, 262-280 (1987).
[CrossRef]

Appl. Opt. (2)

J.-H. Yeh and R. K. Kostuk, "Substrate-mode holograms used in optical interconnects: design issues," Appl. Opt. 34, 3152-3164 (1995).
[CrossRef] [PubMed]

S.-D. Wu, E. N. Glytsis, and T. K. Gaylord, "Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams," Appl. Opt. 44, 4435-4446(2005).
[CrossRef] [PubMed]

Appl. Opt. (6)

IEEE Trans. Electron Devices (1)

K. E. Bean, "Anisotropic etching of silicon," IEEE Trans. Electron Devices 25, 1185-1193 (1978).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

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

Opt. Lett. (1)

Proc. IEEE (1)

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

Science (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Sens. Actuators A (1)

K. Sakaino and S. Adachi, "Study of Si(1 0 0) surfaces etched in TMAH solution," Sens. Actuators A 88, 71-78 (2001).
[CrossRef]

Other (2)

T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, P. R. Routley, and M. R. Josey, "Effects of grating heights on highly efficient unibound SOI waveguide grating couplers," IEEE Photon. Technol. Lett. 12, 59-61 (2000).

S.-D. Wu and E. N. Glytsis, "Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method," Appl. Opt. 43, 1009-1023 (2004).

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Figures (10)

Fig. 1
Fig. 1

Configurations of substrate-mode optical interconnects realized by (a) a V-groove Si SRG and (b) a right-angle-face slanted Si SRG illuminated by a normally incident plane wave with free-space wavelength λ 0 = 1.55 μm . The refractive indices of the incident region and Si are taken to be n I = 1.0 (e.g., air) and n I I = 3.475 . The Si SRGs are characterized by grating period Λ (designed to be Λ = 0.6308 μm to provide the 45 deg forward-diffracted angle of the 1 propagation order), grating thickness d, top filling factor F 1 , bottom filling factor F 2 , and slant angle ϕ (taken to be ϕ = 54.736 ° due to anisotropic etching).

Fig. 2
Fig. 2

Optimized profiles of right-angle-face slanted Si SRGs for (a) TE polarization, (b) TM polarization, (c) RL polarization.

Fig. 3
Fig. 3

Diffraction efficiencies of both TE polarization and TM polarization at normal incidence as a function of d and the corresponding F 2 based on the TE-optimized profile (i.e., F 1 = 0.0000 and ϕ = 54.736 ° are constants).

Fig. 4
Fig. 4

Diffraction efficiencies of both TE polarization and TM polarization at normal incidence as a function of ϕ and the corresponding F 2 based on the TE-optimized profile (i.e., d = 0.6910 μm and F 1 = 0.0000 are constants).

Fig. 5
Fig. 5

Diffraction efficiencies as a function of incident angle θ inc for the TE-optimized profile with a TE-polarized incidence.

Fig. 6
Fig. 6

Diffraction efficiencies as a function of incident angle θ inc for the TE-optimized profile with a TM-polarized incidence.

Fig. 7
Fig. 7

Diffraction efficiencies of both TE polarization and TM polarization at normal incidence as a function of d and the corresponding F 1 based on the TM-optimized profile (i.e., F 2 = 0.9649 and ϕ = 54.736 ° are constants).

Fig. 8
Fig. 8

Diffraction efficiencies of both TE polarization and TM polarization at normal incidence as a function of ϕ and the corresponding F 1 based on the TM-optimized profile (i.e., d = 0.5068 μm and F 2 = 0.9649 are constants).

Fig. 9
Fig. 9

Diffraction efficiencies as a function of incident angle θ inc for the TM-optimized profile with a TE-polarized incidence.

Fig. 10
Fig. 10

Diffraction efficiencies as a function of incident angle θ inc for the TM-optimized profile with a TM-polarized incidence.

Tables (2)

Tables Icon

Table 1 Optimization of Right-Angle-Face Slanted Si SRGs

Tables Icon

Table 2 Performance of Optimized Right-Angle-Face Slanted Si SRGs

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