Abstract

Two-dimensional coupled-wave theory is used to analyze a volume holographic lens for conversion of plane waves into cylindrical waves at fixed frequency. The full two-dimensional solution is found to give good agreement with localized use of one-dimensional theory over a wide range of conditions. It is found that high on-Bragg efficiencies may be achieved if the thickness—focal-length ratio of the lens is small and the recording and reconstructing waves are slowly varying and that reduction in output over the lens surface under off-Bragg conditions is nonuniform.

© 1982 Optical Society of America

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  15. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1965), p. 737.
  16. A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 34.

1981

1979

1978

M. P. Jordan and L. Solymár, "A note on volume holograms," Electron. Lett. 14, 271–272 (1978).

G. Hatakoshi and S. Tanaka, "Grating lenses for integrated optics," Opt. Lett. 2, 142–144 (1978).

M. P. Jordan, L. Solymar, and P. St. J. Russell, "Wavefront conversion by volume holograms between cylindrical and plane waves," Microwaves Opt. Acoust. 2, 156–162 (1978).

1977

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

1976

L. Solymar and M. P. Jordan, "Analysis of cylindrical-to-plane-wave conversion by volume holograms," Electron. Lett. 12, 142 (1976).

1971

J. N. Latta, "Computer-based analysis of holography using ray tracing," Appl. Opt. 10, 2968–2710 (1971).

J. M. Moran, "Compensation of aberrations due to a wavelength shift in holography," Appl. Opt. 10, 1909–1913 (1971).

1969

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 68, 2909–2947 (1969).

1967

Burkhardt, C. B.

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II, p. 449.

Erdélyi, A.

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 34.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1965), p. 737.

Hatakoshi, G.

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II, p. 449.

Jordan, M. P.

M. P. Jordan, L. Solymar, and P. St. J. Russell, "Wavefront conversion by volume holograms between cylindrical and plane waves," Microwaves Opt. Acoust. 2, 156–162 (1978).

M. P. Jordan and L. Solymár, "A note on volume holograms," Electron. Lett. 14, 271–272 (1978).

L. Solymar and M. P. Jordan, "Analysis of cylindrical-to-plane-wave conversion by volume holograms," Electron. Lett. 12, 142 (1976).

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 68, 2909–2947 (1969).

Latta, J. N.

J. N. Latta, "Computer-based analysis of holography using ray tracing," Appl. Opt. 10, 2968–2710 (1971).

Latta, M. R.

Moran, J. M.

Pole, R. V.

Russell, P. St. J.

M. P. Jordan, L. Solymar, and P. St. J. Russell, "Wavefront conversion by volume holograms between cylindrical and plane waves," Microwaves Opt. Acoust. 2, 156–162 (1978).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1965), p. 737.

Solymar, L.

R. R. A. Syms and L. Solymar, "Localized one-dimensional theory for volume holograms," Opt. Quantum Electron. 13, 415–419 (1981).

M. P. Jordan, L. Solymar, and P. St. J. Russell, "Wavefront conversion by volume holograms between cylindrical and plane waves," Microwaves Opt. Acoust. 2, 156–162 (1978).

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

L. Solymar and M. P. Jordan, "Analysis of cylindrical-to-plane-wave conversion by volume holograms," Electron. Lett. 12, 142 (1976).

Solymár, L.

M. P. Jordan and L. Solymár, "A note on volume holograms," Electron. Lett. 14, 271–272 (1978).

Syms, R. R. A.

R. R. A. Syms and L. Solymar, "Localized one-dimensional theory for volume holograms," Opt. Quantum Electron. 13, 415–419 (1981).

Tanaka, S.

Appl. Opt.

Appl. Phys. Lett.

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

Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 68, 2909–2947 (1969).

Electron. Lett.

L. Solymar and M. P. Jordan, "Analysis of cylindrical-to-plane-wave conversion by volume holograms," Electron. Lett. 12, 142 (1976).

M. P. Jordan and L. Solymár, "A note on volume holograms," Electron. Lett. 14, 271–272 (1978).

J. Opt. Soc. Am.

Microwaves Opt. Acoust.

M. P. Jordan, L. Solymar, and P. St. J. Russell, "Wavefront conversion by volume holograms between cylindrical and plane waves," Microwaves Opt. Acoust. 2, 156–162 (1978).

Opt. Lett.

Opt. Quantum Electron.

R. R. A. Syms and L. Solymar, "Localized one-dimensional theory for volume holograms," Opt. Quantum Electron. 13, 415–419 (1981).

Other

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II, p. 449.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1965), p. 737.

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 34.

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