Abstract

Periodic structures, acting as reflectors, filters, and couplers, are a fundamental building block section in many optical devices. In this paper, a three-dimensional simulation of a grating coupler, a well-known periodic structure, is conducted. Guided waves and leakage characteristics of an out-of-plane grating coupler are studied in detail, and its coupling efficiency is examined. Furthermore, a numerical calibration analysis is applied through a commercial software package on the basis of a full-wave finite-element method to calculate the complex propagation constant of the structure and to evaluate the radiation pattern. For experimental evaluation, an optimized grating coupler is fabricated using electron-beam lithography technique and plasma etching. An excellent agreement between simulations and measurements is observed, thereby validating the demonstrated method.

© 2016 Optical Society of America

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References

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  1. S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
    [Crossref]
  2. D. P. Pai and K. A. Awada, “Analysis of dielectric gratings of arbitrary profiles and thicknesses,” J. Opt. Soc. Am. A 8(5), 755–762 (1991).
    [Crossref]
  3. C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
    [Crossref]
  4. N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
    [Crossref]
  5. D. E. Tremain and K. K. Mei, “Application of the unimoment method to scattering from periodic dielectric structures,” J. Opt. Soc. Am. 68(6), 775–783 (1978).
    [Crossref]
  6. T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) 14(3), 235–254 (1977).
    [Crossref]
  7. K. C. Chang, V. Shah, and T. Tamir, “Scattering and guiding of waves by dielectric gratings with arbitrary profiles,” J. Opt. Soc. Am. 70(7), 804–813 (1980).
    [Crossref]
  8. R. Magnusson and T. K. Gaylord, “Equivalence of multiwave coupled-wave theory and modal theory of periodic-media diffraction,” J. Opt. Soc. Am. 68(12), 1777–1779 (1978).
    [Crossref]
  9. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
    [Crossref]
  10. I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
    [Crossref]
  11. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
    [Crossref]
  12. F. Xu and K. Wu, “Numerical multimode calibration technique for extraction of complex propagation constants of substrate integrated waveguide,” in IEEE MTT-S International Microwave Symposium Digest (IEEE, 2004), Vol. 2, pp. 1227–1230 (2004).
  13. S. F. Helfert and R. Pregla, “Efficient analysis of periodic structures,” J. Lightwave Technol. 16(9), 1694–1702 (1998).
    [Crossref]
  14. A. A. Oliner and D. R. Jackson, Antenna Engineering Handbook (New York: McGraw-Hill, 1993).
  15. R. Collin, Field Theory of Guided Waves (McGraw-Hill Book Company Inc., 1960).
  16. ANSYS Academic Research, Release 15.0.
  17. Optiwave, Release 11.0.
  18. C. Palmer and E. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).
  19. E. V. Jull, Aperture antennas and diffraction theory (IET, 1981).
  20. M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antenn. Propag. 41(1), 31–37 (1993).
    [Crossref]
  21. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
    [Crossref]
  22. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
    [Crossref]

2012 (1)

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

2007 (1)

2006 (1)

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

2002 (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

1998 (1)

1997 (1)

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
[Crossref]

1993 (1)

M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antenn. Propag. 41(1), 31–37 (1993).
[Crossref]

1991 (1)

1980 (1)

1978 (2)

1977 (1)

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) 14(3), 235–254 (1977).
[Crossref]

1976 (1)

C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
[Crossref]

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
[Crossref]

1973 (1)

N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
[Crossref]

Awada, K. A.

Ayre, M.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[Crossref]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Baets, R.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[Crossref]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
[Crossref]

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Cadilhac, M.

N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
[Crossref]

Chang, K. C.

Chen, B.-U.

C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
[Crossref]

Chen, X.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Chen, Y. M.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Cheng, Z.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

De Mesel, K.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Demeester, P. M.

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
[Crossref]

Fung, C. K. Y.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Gaylord, T. K.

Ghizoni, C. C.

C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
[Crossref]

Guglielmi, M.

M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antenn. Propag. 41(1), 31–37 (1993).
[Crossref]

Helfert, S. F.

Jackson, D. R.

M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antenn. Propag. 41(1), 31–37 (1993).
[Crossref]

Krauss, T. E.

Krauss, T. F.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Magnusson, R.

Mei, K. K.

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
[Crossref]

Neviere, N.

N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
[Crossref]

Pai, D. P.

Peng, S. T.

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) 14(3), 235–254 (1977).
[Crossref]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
[Crossref]

Petit, R.

N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
[Crossref]

Pregla, R.

Roelkens, G.

Schrauwen, J.

Shah, V.

Taillaert, D.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[Crossref]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Tamir, T.

K. C. Chang, V. Shah, and T. Tamir, “Scattering and guiding of waves by dielectric gratings with arbitrary profiles,” J. Opt. Soc. Am. 70(7), 804–813 (1980).
[Crossref]

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) 14(3), 235–254 (1977).
[Crossref]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
[Crossref]

Tang, C. L.

C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
[Crossref]

Tremain, D. E.

Tsang, H. K.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Van Daele, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Van Daele, P. P.

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
[Crossref]

Van Laere, F.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[Crossref]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Van Thourhout, D.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[Crossref]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Verstuyft, S.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Wong, C. Y.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Xu, K.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

Appl. Phys. (Berl.) (1)

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) 14(3), 235–254 (1977).
[Crossref]

IEEE J. Quantum Electron. (2)

C. C. Ghizoni, B.-U. Chen, and C. L. Tang, “Theory and experiments on grating couplers for thin-film waveguides,” IEEE J. Quantum Electron. 12(2), 69–73 (1976).
[Crossref]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

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

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

M. Guglielmi and D. R. Jackson, “Broadside radiation from periodic leaky-wave antennas,” IEEE Trans. Antenn. Propag. 41(1), 31–37 (1993).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23(1), 123–133 (1975).
[Crossref]

J. IEEE Photon. (1)

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” J. IEEE Photon. 4(1), 104–113 (2012).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (3)

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

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Opt. Commun. (1)

N. Neviere, R. Petit, and M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8(2), 113–117 (1973).
[Crossref]

Other (7)

F. Xu and K. Wu, “Numerical multimode calibration technique for extraction of complex propagation constants of substrate integrated waveguide,” in IEEE MTT-S International Microwave Symposium Digest (IEEE, 2004), Vol. 2, pp. 1227–1230 (2004).

A. A. Oliner and D. R. Jackson, Antenna Engineering Handbook (New York: McGraw-Hill, 1993).

R. Collin, Field Theory of Guided Waves (McGraw-Hill Book Company Inc., 1960).

ANSYS Academic Research, Release 15.0.

Optiwave, Release 11.0.

C. Palmer and E. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

E. V. Jull, Aperture antennas and diffraction theory (IET, 1981).

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Figures (8)

Fig. 1
Fig. 1 Complete three-dimensional model of the SOI grating-waveguide device is considered in this paper in both simulation and fabrication. In the simulation, half of the structure with shorter taper and waveguide length is simulated.
Fig. 2
Fig. 2 3D Simulated structure. Half of the device is simulated using the wave port excitation of the waveguide and the radiated beam is monitored.
Fig. 3
Fig. 3 The simulated radiation pattern of the proposed SOI grating coupler optimized to work at 1550nm wavelength for the different grating periods. SOI wafer (260nm silicon layer and 2µm buried oxide), waveguide width 500nm, grating width 12.5μm, etching depth 70nm, and taper length 650μm. Coupling angle is changed with the grating period.
Fig. 4
Fig. 4 Simulated efficiency versus incident angles for the proposed SOI grating coupler at 1550nm wavelength for the different grating period. SOI wafer (260nm silicon layer and 2µm buried oxide), waveguide width 500nm, grating width 12.5μm, taper length 650μm, and etching depth 70nm.
Fig. 5
Fig. 5 Simulated efficiency versus incident angle for the proposed SOI grating coupler at 1550nm wavelength for different grating etching depth. SOI wafer (260nm silicon layer and 2 µm buried oxide), waveguide width 500nm, grating width 12.5μm, taper length 650μm. a) grating period = 580nm, b) grating period = 600nm.
Fig. 6
Fig. 6 Simulated efficiency versus incident angle for the proposed SOI grating coupler for different wavelengths. SOI wafer (260nm silicon layer and 2 µm buried oxide), waveguide width 500nm, grating width 12.5 μm, taper length 650 μm, grating period 580nm, etching depth 70nm.
Fig. 7
Fig. 7 AFM scan of a grating coupler.
Fig. 8
Fig. 8 Measured efficiency of SOI grating coupler (260nm silicon layer and 2 µm buried oxide, 580nm grating period and 70nm etching depth) at 1550nm wavelength and comparison with the simulation

Equations (11)

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

β n = β 0 + 2nπ d .
n eff λ d <  n air .
2λ d n eff < n substrate .
T= T in T grating T out .
T grating =[ e γL 0 0 e γL ].
T ij T in = T in T grating ij .
e γ i ΔL = λ i .
sin θ m β k 0
Δθ 1 ( L/λ )cos θ m
R( θ )= co s 2 θ ( α k 0 ) 2 + ( β k0 sinθ ) 2
L λ 0 0.18 α/ K 0

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