Abstract

The problem of diffraction of optical beams with arbitrary profiles by a periodically modulated layer is studied for incidence at normal or at the first Bragg angle. It is shown that the far-field patterns of the <i>n</i>th diffracted order of the transmitted and reflected waves are simply the algebraic multiplications of the angular spectral amplitude of the beam profile and the transmission and reflection coefficients for the <i>n</i>th-order diffracted plane wave. Numerical results are illustrated for six different beam profiles.

© 1980 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), Chap. 12, p. 579.
  2. R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 485–504 (1970).
  3. W. Klein and B. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
  4. R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).
  5. J. A. Kong, "Second-order coupled-mode equations for spatially periodic media," J. Opt. Soc. Am. 67, 825–829 (1977).
  6. D. L. Lee, An Integral Equation Formulation for Wave Propagation in Spatially-Periodic Media, Ph.D. dissertation, Massachusetts Institute of Technology, 1977 (unpublished).
  7. R. S. Chu and T. Tamir, "Bragg diffraction of Gaussian beams by periodically modulated media," J. Opt. Soc. Am. 66, 220–226 (1976).
  8. R. S. Chu and T. Tamir, "Diffraction of Gaussian beams by periodically modulated media for incidence close to a Bragg angle," J. Opt. Soc. Am. 66, 1438–1440 (1976).
  9. R. S. Chu, J. A. Kong, and T. Tamir, "Diffraction of Gaussian beams by a periodically modulated layer," J. Opt. Soc. Am. 67, 1555–1561 (1977).
  10. M. R. B. Forshaw, "Diffraction of a narrow laser beam by a thick hologram: Experimental results," Opt. Commun. 12, 279–281 (1974).
  11. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Sec. 8, p. 100.

1977

1976

1974

M. R. B. Forshaw, "Diffraction of a narrow laser beam by a thick hologram: Experimental results," Opt. Commun. 12, 279–281 (1974).

1970

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 485–504 (1970).

1967

W. Klein and B. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), Chap. 12, p. 579.

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Sec. 8, p. 100.

Chu, R. S.

Cook, B.

W. Klein and B. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Forshaw, M. R. B.

M. R. B. Forshaw, "Diffraction of a narrow laser beam by a thick hologram: Experimental results," Opt. Commun. 12, 279–281 (1974).

Klein, W.

W. Klein and B. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Kong, J. A.

Lee, D. L.

D. L. Lee, An Integral Equation Formulation for Wave Propagation in Spatially-Periodic Media, Ph.D. dissertation, Massachusetts Institute of Technology, 1977 (unpublished).

Tamir, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), Chap. 12, p. 579.

IEEE Trans. Microwave Theory Tech.

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 485–504 (1970).

IEEE Trans. Sonics Ultrason

W. Klein and B. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

IEEE Trans.Microwave Theory Tech.

R. S. Chu and J. A. Kong, "Modal theory of spatially periodic media," IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

J. Opt. Soc. Am.

Opt. Commun.

M. R. B. Forshaw, "Diffraction of a narrow laser beam by a thick hologram: Experimental results," Opt. Commun. 12, 279–281 (1974).

Other

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Sec. 8, p. 100.

D. L. Lee, An Integral Equation Formulation for Wave Propagation in Spatially-Periodic Media, Ph.D. dissertation, Massachusetts Institute of Technology, 1977 (unpublished).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), Chap. 12, p. 579.

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