Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings

A. Heifetz; J. T. Shen; S. C. Tseng; G. S. Pati; J. K. Lee; M. S. Shahriar

doi:10.1016/j.optcom.2007.08.047

Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings

A. Heifetz^*, J. T. Shen, S. C. Tseng, G. S. Pati, J. K. Lee, M. S. Shahriar

^*Corresponding author for this work

Electrical and Computer Engineering

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Abstract

We investigated theoretically and experimentally angular directivity of a diffracted beam in volume holographic gratings. We measured the angular direction of the diffracted beam as a function of Bragg-angle deviation of the read beam and showed that the experimental result agrees well with the Ewald sphere vector model (ESVM). We also showed that the Kogelnik's coupled-wave theory (CWT) is correct in predicting the diffraction efficiency, but is incomplete in its description of the direction of the diffracted wave. We show that the ESVM and the CWT theories taken together produce a self-consistent mathematical model of wave propagation inside the gratings that is confirmed with experimental results. The proper model for the direction of the output beam as presented here is important in developing theoretical models of image propagation through thick gratings for holographic imaging and correlation applications.

Original language	English (US)
Pages (from-to)	311-316
Number of pages	6
Journal	Optics Communications
Volume	280
Issue number	2
DOIs	https://doi.org/10.1016/j.optcom.2007.08.047
State	Published - Dec 15 2007

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Physical and Theoretical Chemistry
Electrical and Electronic Engineering

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10.1016/j.optcom.2007.08.047

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title = "Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings",

abstract = "We investigated theoretically and experimentally angular directivity of a diffracted beam in volume holographic gratings. We measured the angular direction of the diffracted beam as a function of Bragg-angle deviation of the read beam and showed that the experimental result agrees well with the Ewald sphere vector model (ESVM). We also showed that the Kogelnik's coupled-wave theory (CWT) is correct in predicting the diffraction efficiency, but is incomplete in its description of the direction of the diffracted wave. We show that the ESVM and the CWT theories taken together produce a self-consistent mathematical model of wave propagation inside the gratings that is confirmed with experimental results. The proper model for the direction of the output beam as presented here is important in developing theoretical models of image propagation through thick gratings for holographic imaging and correlation applications.",

author = "A. Heifetz and Shen, {J. T.} and Tseng, {S. C.} and Pati, {G. S.} and Lee, {J. K.} and Shahriar, {M. S.}",

note = "Funding Information: In summary, we investigated theoretically and experimentally the directionality of the wave vector of the diffracted beam in off-Bragg readout of volume holographic gratings. We measured the angular deflection of the diffracted beam as a function of the deviation of the probe beam. We explained our experimental results on the basis of a Ewald sphere vector diagram. In addition, we obtained the theoretical expressions for the angular dependence of the diffracted beam wave vector and diffraction efficiency using the formalism of the coupled wave theory. We showed that the two theories taken together produce the correct description of the wave propagation inside the gratings. This analysis is important for construction of a working shift-invariant correlator, because one needs to be able to predict the direction of the correlation beam. Also, the results of this study are needed for developing a generic model for image transmission through a volume grating. This work was supported in part by AFOSR grant # FA49620-03-1-0408.",

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doi = "10.1016/j.optcom.2007.08.047",

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T1 - Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings

AU - Heifetz, A.

AU - Shen, J. T.

AU - Tseng, S. C.

AU - Pati, G. S.

AU - Lee, J. K.

AU - Shahriar, M. S.

N1 - Funding Information: In summary, we investigated theoretically and experimentally the directionality of the wave vector of the diffracted beam in off-Bragg readout of volume holographic gratings. We measured the angular deflection of the diffracted beam as a function of the deviation of the probe beam. We explained our experimental results on the basis of a Ewald sphere vector diagram. In addition, we obtained the theoretical expressions for the angular dependence of the diffracted beam wave vector and diffraction efficiency using the formalism of the coupled wave theory. We showed that the two theories taken together produce the correct description of the wave propagation inside the gratings. This analysis is important for construction of a working shift-invariant correlator, because one needs to be able to predict the direction of the correlation beam. Also, the results of this study are needed for developing a generic model for image transmission through a volume grating. This work was supported in part by AFOSR grant # FA49620-03-1-0408.

PY - 2007/12/15

Y1 - 2007/12/15

N2 - We investigated theoretically and experimentally angular directivity of a diffracted beam in volume holographic gratings. We measured the angular direction of the diffracted beam as a function of Bragg-angle deviation of the read beam and showed that the experimental result agrees well with the Ewald sphere vector model (ESVM). We also showed that the Kogelnik's coupled-wave theory (CWT) is correct in predicting the diffraction efficiency, but is incomplete in its description of the direction of the diffracted wave. We show that the ESVM and the CWT theories taken together produce a self-consistent mathematical model of wave propagation inside the gratings that is confirmed with experimental results. The proper model for the direction of the output beam as presented here is important in developing theoretical models of image propagation through thick gratings for holographic imaging and correlation applications.

AB - We investigated theoretically and experimentally angular directivity of a diffracted beam in volume holographic gratings. We measured the angular direction of the diffracted beam as a function of Bragg-angle deviation of the read beam and showed that the experimental result agrees well with the Ewald sphere vector model (ESVM). We also showed that the Kogelnik's coupled-wave theory (CWT) is correct in predicting the diffraction efficiency, but is incomplete in its description of the direction of the diffracted wave. We show that the ESVM and the CWT theories taken together produce a self-consistent mathematical model of wave propagation inside the gratings that is confirmed with experimental results. The proper model for the direction of the output beam as presented here is important in developing theoretical models of image propagation through thick gratings for holographic imaging and correlation applications.

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Angular directivity of diffracted wave in Bragg-mismatched readout of volume holographic gratings

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