Abstract

The theory of Bragg diffraction of finite beams by thick planar gratings is developed, using coupled-wave theory. Simple analytical expressions for the profiles of the transmitted and diffracted beams in the near field are obtained. Detailed diffraction characteristics for the important case of Gaussian-profile beams are presented. It is shown that the diffraction characteristics depend only on two normalized parameters, the grating strength, and a geometry parameter. The diffraction efficiency and the profiles of the transmitted and diffracted beams are calculated as functions of these two controlling parameters.

© 1980 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).
  2. R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).
  3. H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  4. F. G. Kaspar, "Diffraction by thick, periodically stratified gratings with complex dielectric constant," J. Opt. Soc. Am. 63, 37–45 (1973).
  5. L. E. Hargrove, "Effect of ultrasonic waves on Gaussian light beams with diameter comparable to ultrasonic wavelength," J. Acoust. Soc. Am. 43, 847–851 (1968).
  6. D. H. McMahon, "Relative efficiency of optical Bragg diffraction as a function of interaction geometry," IEEE Trans. Sonic Ultrason. SU-16, 41–44 (1969).
  7. R. Guther and S. Kusch, "Kinematic theory of Gaussian beams in volume holography," Sov. J. Quantum Electron. 6, 509–514 (1976).
  8. R. S. Chu and T. Tamir, "Bragg diffraction of Gaussian beams by periodically modulated media," J. Opt. Soc. Am. 66, 220–226 (1976).
  9. R. S. Chu and T. Tamir, "Diffraction of Gaussian beams by periodically modulated media for incidence close to Bragg angle," J. Opt. Soc. Am. 66, 1438–1440 (1976).
  10. 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).
  11. L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820–822 (1977).
  12. W. E. Parry and L. Solymar, "A general solution for the two-dimensional volume holograms," Opt. Quantum Electron. 9, 527–531 (1977).
  13. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1962), Vol. II, pp. 450–459.
  14. A. E. Siegman, "Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating," J. Opt. Soc. Am. 67, 545–550 (1977).
  15. B. W. Batterman and H. Cole, "Dynamic diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681–717 (1964).
  16. P. St. J. Russell, L. Solymar, and M. P. Jordan, "Borrmann-like effects in volume holography," Proc. ICO-11 Conf., 635–638 (1978).
  17. M. R. B. Forshaw, "Diffraction of a narrow laser beam by a thick hologram: experimental results," Opt. Commun. 12, 279–281 (1974).

1977 (4)

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820–822 (1977).

W. E. Parry and L. Solymar, "A general solution for the two-dimensional volume holograms," Opt. Quantum Electron. 9, 527–531 (1977).

A. E. Siegman, "Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating," J. Opt. Soc. Am. 67, 545–550 (1977).

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).

1976 (3)

1974 (1)

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

1973 (1)

1970 (1)

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

1969 (2)

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

D. H. McMahon, "Relative efficiency of optical Bragg diffraction as a function of interaction geometry," IEEE Trans. Sonic Ultrason. SU-16, 41–44 (1969).

1968 (1)

L. E. Hargrove, "Effect of ultrasonic waves on Gaussian light beams with diameter comparable to ultrasonic wavelength," J. Acoust. Soc. Am. 43, 847–851 (1968).

1966 (1)

1964 (1)

B. W. Batterman and H. Cole, "Dynamic diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681–717 (1964).

Batterman, B. W.

B. W. Batterman and H. Cole, "Dynamic diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681–717 (1964).

Burckhardt, C. B.

Chu, R. S.

Cole, H.

B. W. Batterman and H. Cole, "Dynamic diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681–717 (1964).

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1962), Vol. II, pp. 450–459.

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).

Guther, R.

R. Guther and S. Kusch, "Kinematic theory of Gaussian beams in volume holography," Sov. J. Quantum Electron. 6, 509–514 (1976).

Hargrove, L. E.

L. E. Hargrove, "Effect of ultrasonic waves on Gaussian light beams with diameter comparable to ultrasonic wavelength," J. Acoust. Soc. Am. 43, 847–851 (1968).

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1962), Vol. II, pp. 450–459.

Jordan, M. P.

P. St. J. Russell, L. Solymar, and M. P. Jordan, "Borrmann-like effects in volume holography," Proc. ICO-11 Conf., 635–638 (1978).

Kaspar, F. G.

Kogelnik, H.

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kong, J. A.

Kusch, S.

R. Guther and S. Kusch, "Kinematic theory of Gaussian beams in volume holography," Sov. J. Quantum Electron. 6, 509–514 (1976).

McMahon, D. H.

D. H. McMahon, "Relative efficiency of optical Bragg diffraction as a function of interaction geometry," IEEE Trans. Sonic Ultrason. SU-16, 41–44 (1969).

Parry, W. E.

W. E. Parry and L. Solymar, "A general solution for the two-dimensional volume holograms," Opt. Quantum Electron. 9, 527–531 (1977).

Russell, P. St. J.

P. St. J. Russell, L. Solymar, and M. P. Jordan, "Borrmann-like effects in volume holography," Proc. ICO-11 Conf., 635–638 (1978).

Siegman, A. E.

Solymar, L.

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820–822 (1977).

W. E. Parry and L. Solymar, "A general solution for the two-dimensional volume holograms," Opt. Quantum Electron. 9, 527–531 (1977).

P. St. J. Russell, L. Solymar, and M. P. Jordan, "Borrmann-like effects in volume holography," Proc. ICO-11 Conf., 635–638 (1978).

Tamir, T.

Appl. Phys. Lett. (1)

L. Solymar, "A general two-dimensional theory for volume holograms," Appl. Phys. Lett. 31, 820–822 (1977).

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE Trans. Microwave Theory Tech. (1)

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

IEEE Trans. Sonic Ultrason. (1)

D. H. McMahon, "Relative efficiency of optical Bragg diffraction as a function of interaction geometry," IEEE Trans. Sonic Ultrason. SU-16, 41–44 (1969).

J. Acoust. Soc. Am. (1)

L. E. Hargrove, "Effect of ultrasonic waves on Gaussian light beams with diameter comparable to ultrasonic wavelength," J. Acoust. Soc. Am. 43, 847–851 (1968).

J. Opt. Soc. Am. (6)

Opt. Commun. (1)

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

Opt. Quantum Electron. (1)

W. E. Parry and L. Solymar, "A general solution for the two-dimensional volume holograms," Opt. Quantum Electron. 9, 527–531 (1977).

Rev. Mod. Phys. (1)

B. W. Batterman and H. Cole, "Dynamic diffraction of x-rays by perfect crystals," Rev. Mod. Phys. 36, 681–717 (1964).

Sov. J. Quantum Electron. (1)

R. Guther and S. Kusch, "Kinematic theory of Gaussian beams in volume holography," Sov. J. Quantum Electron. 6, 509–514 (1976).

Other (2)

P. St. J. Russell, L. Solymar, and M. P. Jordan, "Borrmann-like effects in volume holography," Proc. ICO-11 Conf., 635–638 (1978).

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1962), Vol. II, pp. 450–459.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.