Abstract

Results of theoretical calculations and experimental measurements of variation of grating coupling efficiency with beam-defocus position are presented. Our results indicate that (1) coupling efficiency is not necessarily maximum at the beam waist, (2) coupling efficiency as a function of defocus position shows oscillatory behavior particularly for a tightly focused beam. The effect of beam size alone cannot account for the observed behavior of variation of coupling efficiency with defocus position. The results of measured angular dependence of coupling efficiency for various defocus conditions are also presented.

© 1991 Optical Society of America

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References

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  1. 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]
  2. M. Neviere, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
    [CrossRef]
  3. M. Nevier, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
    [CrossRef]
  4. S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
    [CrossRef]
  5. H. M. Stroll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
    [CrossRef]
  6. T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
    [CrossRef]
  7. L. Li, M. C. Gupta, “Effects of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320–5325 (1990).
    [CrossRef] [PubMed]
  8. M. C. Gupta, L. Li, “Achromatic compensation for integrated optic grating couplers with focused beams,” Appl. Opt. 30, 1461–1463 (1991).
    [CrossRef] [PubMed]
  9. M. C. Gupta, T. A. Strasser, “Electron beam deposited Corning 7059 glass thin films for waveguides,” in Integrated Optical Circuit Engineering VI, A. M. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.993, 44–45 (1988).
  10. M. C. Gupta, “Low optical loss glass thin films,” Appl. Opt. 29, 4310–4313 (1990).
    [CrossRef] [PubMed]
  11. D. Maystre, “Integral methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
    [CrossRef]

1991 (1)

1990 (2)

1977 (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

1975 (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

1973 (4)

H. M. Stroll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[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]

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

M. Nevier, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Bertoni, H. L.

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Cadilhac, M.

M. Nevier, 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]

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]

Gupta, M. C.

Li, L.

Maystre, D.

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

Nevier, M.

M. Nevier, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[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]

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]

Peng, S. T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Petit, R.

M. Nevier, 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]

Strasser, T. A.

M. C. Gupta, T. A. Strasser, “Electron beam deposited Corning 7059 glass thin films for waveguides,” in Integrated Optical Circuit Engineering VI, A. M. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.993, 44–45 (1988).

Stroll, H. M.

H. M. Stroll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

Tamir, T.

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Vincent, P.

M. Nevier, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Yariv, A.

H. M. Stroll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (1)

T. Tamir, S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

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]

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Opt. Commun. (3)

H. M. Stroll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (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. Nevier, P. Vincent, R. Petit, M. Cadilhac, “Determination of the coupling coefficient of a holographic thin film coupler,” Opt. Commun. 9, 240–245 (1973).
[CrossRef]

Other (2)

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

M. C. Gupta, T. A. Strasser, “Electron beam deposited Corning 7059 glass thin films for waveguides,” in Integrated Optical Circuit Engineering VI, A. M. Mentzer, ed., Proc. Soc. Photo-Opt. Instrum. Eng.993, 44–45 (1988).

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Figures (7)

Fig. 1
Fig. 1

Experimental and theoretical variation of coupling efficiency with defocus position for a Gaussian beam of 0.19-mm beam waist (focal length = 133 cm).

Fig. 2
Fig. 2

Experimental and theoretical variation of coupling efficiency with defocus position for a Gaussian beam of 86.4-μm beam waist (focal length = 60 cm).

Fig. 3
Fig. 3

Theoretical variation of coupling efficiency and experimental outcoupled power with defocus position for a Gaussian beam of 23-μm beam waist (focal length = 16 cm).

Fig. 4
Fig. 4

Theoretical variation of coupling efficiency and experimental outcoupled power with defocus position for a Gaussian beam of 11.5-μm beam waist (focal length = 8 cm).

Fig. 5
Fig. 5

Experimental results of variation of coupling efficiency with coupling detuning for defocus values of −30.0, 0.0, +30.0 cm, respectively.

Fig. 6
Fig. 6

Theoretical results of variation of coupling efficiency with coupling angle detuning for defocus values of −30.0, 0.0, +30.0 cm, respectively.

Fig. 7
Fig. 7

Schematic showing the change in intensity distribution expected at the grating when the grating is located before or after the beam-waist position.

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