Abstract

The effect of the refractive index of the substrate together with the incident polarization on the optimization of sawtooth surface-relief gratings (SRGs) is investigated. The global optimum diffraction efficiencies of the 1st forward-diffracted order of sawtooth SRGs are 63 .3% occurring at n2=1.47 for TE polarization and 73.8% occurring at n2=2.88 for TM polarization. Incident TE polarization has higher optimum diffraction efficiency than TM polarization for all n2<1.85. In contrast, TM polarization has higher optimum diffraction efficiency than TE polarization for all n2>1.85. A polymer (n2=1.5) optimum sawtooth SRG exhibits 62.6% efficiency for TE polarization. A silicon (n2=3.475) optimum sawtooth SRG exhibits 68.6% efficiency for TM polarization. These sawtooth SRGs are compared to right-angle-face trapezoidal SRGs. It is found that the optimum profiles of right-angle-face trapezoidal SRGs have only very slightly increased efficiencies over sawtooth SRGs (0.04% for TE and 0.55% for TM).

© 2006 Optical Society of America

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  1. S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).
  2. T. Suhara and H. Nishihara, "Integrated optics components and devices using periodic structures," IEEE J. Quantum Electron. 22, 845-867 (1986).
    [CrossRef]
  3. J. Dübendorfer and R. E. Kunz, "Compact integrated optical immunosensor using replicated chirped grating coupler sensor chips," Appl. Opt. 37, 1890-1894 (1998).
  4. M. Wiki and R. E. Kunz, "Wavelength-interrogated optical sensor for biochemical applications," Opt. Lett. 25, 463-465 (2000).
  5. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, "Normal-incidence guided-mode resonant grating filters: design and experimental demonstration," Opt. Lett. 23, 700-702 (1998).
  6. Z. Hegedus and R. Netterfield, "Low sideband guided-mode resonant filter," Appl. Opt. 39, 1469-1473 (2000).
  7. S. Tibuleac and R. Magnusson, "Narrow-linewidth bandpass filters with diffractive thin-film layers," Opt. Lett. 26, 584-586 (2001).
  8. N. Rajkumar and J. N. McMullin, "V-groove gratings on silicon for infrared beam splitting," Appl. Opt. 34, 2556-2559 (1995).
  9. S. Hava and M. Auslender, "Silicon grating-based mirror for 1.3-μm polarized beams: matlab-aided design," Appl. Opt. 34, 1053-1058 (1995).
  10. D. L. Brundrett, T. K. Gaylord, and E. N. Glytsis, "Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication," Appl. Opt. 37, 2534-2541 (1998).
  11. J. M. Miller, N. de Meaucoudrey, P. Chavel, J. Turunen, and E. Cambril, "Design and fabrication of binary trapezoidal surface-relief gratings for a planar optical interconnection," Appl. Opt. 36, 5717-5727 (1997).
  12. R. T. Chen, L. Lin, C. Choi, Y. J. Liu, B. Bihari, L. Wu, S. Tang, R. Wickman, B. Picor, M. K. Hibbs-Brenner, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
    [CrossRef]
  13. Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
    [CrossRef]
  14. M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, "Optimization of diffraction grating profiles in fabrication by electron-beam lithography," Appl. Opt. 43, 5137-5142 (2004).
    [CrossRef]
  15. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am 72, 1385-1392 (1982).
  16. K. Yokomori, "Dielectric surface-relief gratings with high diffraction efficiency," Appl. Opt. 23, 2303-2310 (1984).
  17. M. C. Gupta and S. T. Peng, "Diffraction characteristics of surface-relief gratings," Appl. Opt. 32, 2911-2917 (1993).
  18. H. J. Gerritsena and M. L. Jepsen, "Rectangular surface-relief transmission gratings with a very larger first-order diffraction efficiency (∼95%) for unpolarized light," Appl. Opt. 37, 5823-5829 (1998).
  19. S.-D. Wu, T. K. Gaylord, J. S. Maikisch, and E. N. Glytsis, "Optimization of anisotropically etched silicon surface-relief gratings for substrate-mode optical interconnects," Appl. Opt. 45, 15-21 (2006).
    [CrossRef]
  20. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
  21. 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]

2006 (1)

2004 (1)

2001 (2)

S. Tibuleac and R. Magnusson, "Narrow-linewidth bandpass filters with diffractive thin-film layers," Opt. Lett. 26, 584-586 (2001).

Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
[CrossRef]

2000 (3)

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

M. Wiki and R. E. Kunz, "Wavelength-interrogated optical sensor for biochemical applications," Opt. Lett. 25, 463-465 (2000).

Z. Hegedus and R. Netterfield, "Low sideband guided-mode resonant filter," Appl. Opt. 39, 1469-1473 (2000).

1998 (4)

1997 (1)

1995 (2)

1993 (1)

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]

1986 (2)

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

T. Suhara and H. Nishihara, "Integrated optics components and devices using periodic structures," IEEE J. Quantum Electron. 22, 845-867 (1986).
[CrossRef]

1984 (1)

1983 (1)

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

1982 (1)

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am 72, 1385-1392 (1982).

Auslender, M.

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Bristow, 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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Brundrett, D. L.

Cambril, E.

Chavel, P.

Chen, D.

Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
[CrossRef]

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics 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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

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]

de Meaucoudrey, N.

Dübendorfer, J.

Gaylord, T. K.

Gelatt, C. D.

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

Gerritsena, H. J.

Glytsis, E. N.

Gupta, M. C.

Hava, S.

Hegedus, Z.

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Hirai, Y.

Jepsen, M. L.

Kikuta, H.

Kirkpatrick, S.

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

Koyama, J.

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

Kunz, R. E.

Li, Y.

Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
[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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics 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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics 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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Magnusson, R.

Maikisch, J. S.

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.

Miller, J. M.

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am 72, 1385-1392 (1982).

Netterfield, R.

Nishihara, H.

T. Suhara and H. Nishihara, "Integrated optics components and devices using periodic structures," IEEE J. Quantum Electron. 22, 845-867 (1986).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

Okano, M.

Peng, S. T.

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Rajkumar, N.

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]

Suhara, T.

T. Suhara and H. Nishihara, "Integrated optics components and devices using periodic structures," IEEE J. Quantum Electron. 22, 845-867 (1986).
[CrossRef]

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Tibuleac, S.

Turunen, J.

Ura, S.

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

Vecchi, M. P.

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

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Wiki, M.

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Wu, S.-D.

Yamamoto, K.

Yang, C.

Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
[CrossRef]

Yokomori, K.

Yotsuya, T.

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. (11)

M. C. Gupta and S. T. Peng, "Diffraction characteristics of surface-relief gratings," Appl. Opt. 32, 2911-2917 (1993).

J. Dübendorfer and R. E. Kunz, "Compact integrated optical immunosensor using replicated chirped grating coupler sensor chips," Appl. Opt. 37, 1890-1894 (1998).

D. L. Brundrett, T. K. Gaylord, and E. N. Glytsis, "Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication," Appl. Opt. 37, 2534-2541 (1998).

H. J. Gerritsena and M. L. Jepsen, "Rectangular surface-relief transmission gratings with a very larger first-order diffraction efficiency (∼95%) for unpolarized light," Appl. Opt. 37, 5823-5829 (1998).

Z. Hegedus and R. Netterfield, "Low sideband guided-mode resonant filter," Appl. Opt. 39, 1469-1473 (2000).

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

S. Hava and M. Auslender, "Silicon grating-based mirror for 1.3-μm polarized beams: matlab-aided design," Appl. Opt. 34, 1053-1058 (1995).

J. M. Miller, N. de Meaucoudrey, P. Chavel, J. Turunen, and E. Cambril, "Design and fabrication of binary trapezoidal surface-relief gratings for a planar optical interconnection," Appl. Opt. 36, 5717-5727 (1997).

K. Yokomori, "Dielectric surface-relief gratings with high diffraction efficiency," Appl. Opt. 23, 2303-2310 (1984).

M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, "Optimization of diffraction grating profiles in fabrication by electron-beam lithography," Appl. Opt. 43, 5137-5142 (2004).
[CrossRef]

S.-D. Wu, T. K. Gaylord, J. S. Maikisch, and E. N. Glytsis, "Optimization of anisotropically etched silicon surface-relief gratings for substrate-mode optical interconnects," Appl. Opt. 45, 15-21 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Suhara and H. Nishihara, "Integrated optics components and devices using periodic structures," IEEE J. Quantum Electron. 22, 845-867 (1986).
[CrossRef]

J. Lightwave Technol. (1)

S. Ura, T. Suhara, H. Nishihara, and J. Koyama, "An integrated-optic disk pickup device," J. Lightwave Technol. 4, 913-918 (1986).

J. Opt. Soc. Am (1)

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am 72, 1385-1392 (1982).

Opt. Laser Tech. (1)

Y. Li, D. Chen, and C. Yang, "Sub-microns period grating couplers fabricated by silicon mold," Opt. Laser Tech. 33, 623-626 (2001).
[CrossRef]

Opt. Lett. (3)

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, S. Bristow, and Y. S. Liu, "Fully embedded board-level guided-wave optoelectronics interconnects," Proc. IEEE 88, 780-793 (2000).
[CrossRef]

Science (1)

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

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Figures (4)

Fig. 1
Fig. 1

Configurations of (a) a sawtooth SRG and (b) a right-angle-face trapezoidal SRG illuminated by a normally incident plane wave with free space wavelength λ0 = 1.55 μm. The refractive indices of the incident region and the substrate are n 1 and n 2, respectively. The SRGs are characterized by the grating period Λ (designed for 45-degree forward-diffracted angle of the −1st forward-diffracted order), the groove depth d, the top filling factor F 1, the bottom filling factor F 2, and the slant angle ϕ.

Fig. 2
Fig. 2

Optimum diffraction efficiencies of the −1st forward-diffracted order for both a sawtooth SRG and a VG as a function of n 2 for both TE and TM polarizations. The corresponding optimum diffraction efficiencies of a right-angle-face trapezoidal SRG in a polymer (n 2 = 1.5) and in Si (n 2 = 3.475) for both TE and TM polarizations are denoted by solid circles (●) and solid squares (■), respectively.

Fig. 3
Fig. 3

Normalized optimum thickness of a sawtooth SRG as a function of n 2 for both TE and TM polarizations.

Fig. 4
Fig. 4

Optimum slant angle of a sawtooth SRG as a function of n 2 for both TE and TM polarizations.

Tables (1)

Tables Icon

Table 1 Optimization of both Sawtooth SRGs and Right-Angle-Face Trapezoidal SRGs in Polymers ( n 2 = 1.5) and in Si ( n 2 = 3.475) for TE and TM Polarizations

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