Abstract

The problem of diffraction of an electromagnetic wave by a thick hologram grating can be solved by the famous Kogelnik’s coupled-wave theory (CWT) to a very high degree of accuracy. We confirm this finding by comparing the CWT and the exact result for a typical example and propose an explanation in terms of perturbation theory. To this end we formulate the problem of diffraction as a matrix problem following similar well-known approaches, especially rigorous coupled-wave theory (RCWT). We allow for a complex permittivity modulation and a possible phase shift between refractive index and absorption grating and explicitly incorporate appropriate boundary conditions. The problem is solved numerically exact for the specific case of a planar unslanted grating and a set of realistic values of the material’s parameters and experimental conditions. Analogously, the same problem is solved for a two-dimensional truncation of the underlying matrix that would correspond to a CWT approximation but without the usual further approximations. We verify a close coincidence of both results even in the off-Bragg region and explain this result by means of a perturbation analysis of the underlying matrix problem. Moreover, the CWT is found not only to coincide with the perturbational approximation in the in-Bragg and the extreme off-Bragg cases, but also to interpolate between these extremal regimes.

© 2014 Optical Society of America

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    [CrossRef]

2013

K.-M. Voit and M. Imlau, “Holographic spectroscopy: wavelength-dependent analysis of photosensitive materials by means of holographic techniques,” MDPI Materials 6, 334–358 (2013).

M. Prijatelj, J. Klepp, Y. Tomita, and M. Fally, “Far-off-Bragg reconstruction of volume holographic gratings: a comparison of experiment and theories,” Phys. Rev. A 87, 063810 (2013).
[CrossRef]

2011

2008

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

2006

1999

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

1997

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047 (1997).
[CrossRef]

1994

1990

1984

E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173–178 (1984).
[CrossRef]

1981

1978

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1978).
[CrossRef]

1973

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1948

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Bieringer, S.

M. Imlau, S. Odoulov, T. Woike, and S. Bieringer, “Holographic data storage,” in Nanoelectronics and Information Technology, R. Waser, ed. (Wiley-VCH, 1999), pp. 727–750.

Blanche, P. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Burr, G.

M. Imlau, M. Fally, H. Coufal, G. Burr, and G. Sincerbox, “Holography and optical storage,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 1205–1249.

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Coufal, H.

M. Imlau, M. Fally, H. Coufal, G. Burr, and G. Sincerbox, “Holography and optical storage,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 1205–1249.

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Fally, M.

M. Prijatelj, J. Klepp, Y. Tomita, and M. Fally, “Far-off-Bragg reconstruction of volume holographic gratings: a comparison of experiment and theories,” Phys. Rev. A 87, 063810 (2013).
[CrossRef]

M. Imlau, M. Fally, H. Coufal, G. Burr, and G. Sincerbox, “Holography and optical storage,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 1205–1249.

Flores, D.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Gaylord, T. K.

Gleeson, M. R.

Gu, T.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Guibelalde, E.

E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. 16, 173–178 (1984).
[CrossRef]

Guo, J.

Hilaire, P. St.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Imlau, M.

K.-M. Voit and M. Imlau, “Holographic spectroscopy: wavelength-dependent analysis of photosensitive materials by means of holographic techniques,” MDPI Materials 6, 334–358 (2013).

M. Imlau, S. Odoulov, T. Woike, and S. Bieringer, “Holographic data storage,” in Nanoelectronics and Information Technology, R. Waser, ed. (Wiley-VCH, 1999), pp. 727–750.

M. Imlau, M. Fally, H. Coufal, G. Burr, and G. Sincerbox, “Holography and optical storage,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 1205–1249.

Kamenov, V. P.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Kamshilin, A. A.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Kelly, A. E.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Klepp, J.

M. Prijatelj, J. Klepp, Y. Tomita, and M. Fally, “Far-off-Bragg reconstruction of volume holographic gratings: a comparison of experiment and theories,” Phys. Rev. A 87, 063810 (2013).
[CrossRef]

Klonidis, D.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kowarschik, R.

Kukhtarev, N. V.

J. Strait, J. D. Reed, and N. V. Kukhtarev, “Orientational dependence of photorefractive two-beam coupling in InP:Fe,” Opt. Lett. 15, 209–211 (1990).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1978).
[CrossRef]

Li, G.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Lin, W.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

Moharam, M. G.

Montemezzani, G.

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047 (1997).
[CrossRef]

Nejabati, R.

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Nippolainen, E.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Norwood, R. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

O’Mahony, M. J.

Odoulov, S.

M. Imlau, S. Odoulov, T. Woike, and S. Bieringer, “Holographic data storage,” in Nanoelectronics and Information Technology, R. Waser, ed. (Wiley-VCH, 1999), pp. 727–750.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1978).
[CrossRef]

Peyghambarian, N.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Phillips, D. I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Podivilov, E. V.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Politi, C.

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Prijatelj, M.

M. Prijatelj, J. Klepp, Y. Tomita, and M. Fally, “Far-off-Bragg reconstruction of volume holographic gratings: a comparison of experiment and theories,” Phys. Rev. A 87, 063810 (2013).
[CrossRef]

Prokofiev, V. V.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

Reed, J. D.

Ringhofer, K. H.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, D. J. Webb, R. Kowarschik, E. Shamonina, and K. H. Ringhofer, “Exact solution of the Bragg-diffraction problem in sillenites,” J. Opt. Soc. Am. B 11, 1813–1819 (1994).
[CrossRef]

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, D. I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[CrossRef]

Rokutanda, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Russell, P.St.J.

P.St.J. Russell, “Optical volume holography,” Phys. Rep. 71, 209–312 (1981).
[CrossRef]

Shamonina, E.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, D. J. Webb, R. Kowarschik, E. Shamonina, and K. H. Ringhofer, “Exact solution of the Bragg-diffraction problem in sillenites,” J. Opt. Soc. Am. B 11, 1813–1819 (1994).
[CrossRef]

Sheridan, J. T.

Simeonidou, D.

Sincerbox, G.

M. Imlau, M. Fally, H. Coufal, G. Burr, and G. Sincerbox, “Holography and optical storage,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 1205–1249.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

Strait, J.

Sturman, B. I.

B. I. Sturman, E. V. Podivilov, K. H. Ringhofer, E. Shamonina, V. P. Kamenov, E. Nippolainen, V. V. Prokofiev, and A. A. Kamshilin, “Theory of photorefractive vectorial wave coupling in cubic crystals,” Phys. Rev. E 60, 3332–3352 (1999).
[CrossRef]

B. I. Sturman, D. J. Webb, R. Kowarschik, E. Shamonina, and K. H. Ringhofer, “Exact solution of the Bragg-diffraction problem in sillenites,” J. Opt. Soc. Am. B 11, 1813–1819 (1994).
[CrossRef]

Tay, S.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Thomas, J.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Tomita, Y.

M. Prijatelj, J. Klepp, Y. Tomita, and M. Fally, “Far-off-Bragg reconstruction of volume holographic gratings: a comparison of experiment and theories,” Phys. Rev. A 87, 063810 (2013).
[CrossRef]

Tunc, A. V.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
[CrossRef]

Uchida, N.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1978).
[CrossRef]

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S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunc, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St. Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
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