Abstract

Results of a theoretical and experimental investigation into the variation of coupling efficiency with coupling angle are presented for various beam focusing conditions for an integrated optical grating coupler. This investigation shows that the acceptance angle of the grating coupler can be broadened, within a relatively large range and with a relatively small loss of coupling efficiency, by focusing the incident laser beam.

© 1990 Optical Society of America

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References

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  1. A. Yariv, M. Nakamura, “Periodic Structures for Integrated Optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
    [CrossRef]
  2. T. Suhara, H. Nishihara, “Integrated Optics Components and Devices Using Periodic Structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
    [CrossRef]
  3. K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
    [CrossRef]
  4. D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
    [CrossRef]
  5. M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
    [CrossRef]
  6. M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
    [CrossRef]
  7. M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
    [CrossRef]
  8. M. Neviere, “The Homogeneous Problem,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, Berlin, 1980), pp. 123–157.
    [CrossRef]
  9. M. C. Gupta, T. A. Strasser, “Electron-Beam-Deposited Corning 7059 Glass Thin Films for Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 993, 44–45 (1988).
  10. M. C. Gupta, “Low-Optical-Loss Glass Thin Films,” Appl. Opt. 29, 4310–4314 (1990).
    [CrossRef] [PubMed]
  11. L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

1990 (1)

1988 (1)

M. C. Gupta, T. A. Strasser, “Electron-Beam-Deposited Corning 7059 Glass Thin Films for Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 993, 44–45 (1988).

1987 (1)

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

1986 (1)

T. Suhara, H. Nishihara, “Integrated Optics Components and Devices Using Periodic Structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

1977 (1)

A. Yariv, M. Nakamura, “Periodic Structures for Integrated Optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

1973 (4)

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Cadilhac, M.

M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Chang, W. S. C.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Collin, C. T.

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

Gupta, M. C.

M. C. Gupta, “Low-Optical-Loss Glass Thin Films,” Appl. Opt. 29, 4310–4314 (1990).
[CrossRef] [PubMed]

M. C. Gupta, T. A. Strasser, “Electron-Beam-Deposited Corning 7059 Glass Thin Films for Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 993, 44–45 (1988).

Li, L.

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

Maystre, D.

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
[CrossRef]

Nakamura, M.

A. Yariv, M. Nakamura, “Periodic Structures for Integrated Optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

Neviere, M.

M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

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

Nishihara, H.

T. Suhara, H. Nishihara, “Integrated Optics Components and Devices Using Periodic Structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Petit, R.

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Rosenbaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Sopori, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Stegeman, G. I.

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

Strasser, T. A.

M. C. Gupta, T. A. Strasser, “Electron-Beam-Deposited Corning 7059 Glass Thin Films for Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 993, 44–45 (1988).

Suhara, T.

T. Suhara, H. Nishihara, “Integrated Optics Components and Devices Using Periodic Structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

Vincent, P.

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Xu, M.

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

Yariv, A.

A. Yariv, M. Nakamura, “Periodic Structures for Integrated Optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (3)

A. Yariv, M. Nakamura, “Periodic Structures for Integrated Optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

T. Suhara, H. Nishihara, “Integrated Optics Components and Devices Using Periodic Structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[CrossRef]

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A Theoretical Analysis of Etched Grating Couplers for Integrated Optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Opt. Commun. (3)

M. Neviere, R. Petit, M. Cadilhac, “About the Theory of Optical Grating Coupler-Waveguide Systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Systematic Study of Resonances of Holographic Thin Film Couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, M. Cadilhac, “Determination of the Coupling Coefficient of a Holographic Thin Film Coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

L. Li, M. Xu, G. I. Stegeman, C. T. Collin, “Fabrication of Photoresist Masks for Submicrometer Surface Relief Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 835, 72–82 (1987).

M. C. Gupta, T. A. Strasser, “Electron-Beam-Deposited Corning 7059 Glass Thin Films for Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 993, 44–45 (1988).

Other (2)

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

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Two limiting cases for the overlap integral given by Eq. (3): (a) Δθ ≪ Δθ i and (b) Δθ ≫ Δθ i .

Fig. 2
Fig. 2

Geometric configuration for optical coupling of a Gaussian beam by a grating coupler.

Fig. 3
Fig. 3

Theoretical coupling efficiency vs coupling angle detuning for four different Gaussian beam angular widths.

Fig. 4
Fig. 4

Experimental data of percentage transmission, reflection, and coupling efficiency vs angular detuning for a Gaussian beam of 0.0085° angular width.

Fig. 5
Fig. 5

Experimental data of percentage transmission, reflection, and coupling efficiency vs angular detuning for a Gaussian beam of 0.058° angular width.

Fig. 6
Fig. 6

Experimental data of (a) percentage transmission, reflection, and coupling efficiency, and (b) outcoupled power vs angular detuning for a Gaussian beam of 0.13° angular width.

Fig. 7
Fig. 7

Experimental data of (a) percentage transmission, reflection, and coupling efficiency, and (b) outcoupled power vs angular detuning for a Gaussian beam of 0.48° angular width.

Fig. 8
Fig. 8

Experimental and theoretical acceptance angle (squares and solid line) and coupling efficiency (triangles and long dashed line) vs Gaussian beam angular width.

Equations (4)

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η ( x ) = 1 n C 0 k 0 { ( α + m K ) r ( x ) 2 + Re [ i r ( x ) q * ( x ) ] } C ( y ) v m ( α , y ) 2 d y ,
d r ( x ) d x + i ( α 0 - α p ) r ( x ) = q ( x ) ,
r ( x ) = - i p ( ξ ) 1 ξ + α 0 - α p exp ( i ξ x ) d ξ ,
r ( x ) = q ( x ) H ( x - x ) exp [ i ( α p - α 0 ) ( x - x ) ] d x ,

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