Adjusted intensity nonlocal diffusion model of photopolymer grating formation

Diffusion-based models of grating formation in photopolymers have been proposed in which the rate of monomer polymerization (removal) is directly proportional to the illuminating intensity inside the medium. However, based on photochemical considerations, the rate of polymerization is proportional in the steady state to the square root of the interference intensity. Recently it was shown that, by introducing a nonlocal response function into the one-dimensional diffusion equation that governs holographic grating formation in photopolymers, one can deduce both high-frequency and low-frequency cutoffs in the spatial-frequency response of photopolymer materials. Here the first-order nonlocal coupled diffusion equations are derived for the case of a general relationship between the rate of polymerization and the exposing intensity. Assuming a two-harmonic monomer expansion, the resultant analytic solutions are then used to fit experimental growth curves for gratings fabricated with different spatial frequencies. Various material parameters, including monomer diffusion constant D and nonlocal variance σ, are estimated.

[1]  H. Kogelnik.  Coupled wave theory for thick hologram gratings , 1969 .

[2]  W S Colburn,et al.  Volume hologram formation in photopolymer materials. , 1971, Applied optics.

[3]  R. H. Wopschall,et al.  Dry photopolymer film for recording holograms. , 1972, Applied optics.

[4]  Max Born,et al.  Principles of optics - electromagnetic theory of propagation, interference and diffraction of light (7. ed.) , 1999 .

[5]  Richard T. Ingwall,et al.  Mechanism Of Hologram Formation In DMP-128 Photopolymer , 1989 .

[6]  R. R. A. Syms,et al.  Practical volume holography , 1990 .

[7]  Don A. Gregory,et al.  Photopolymer hologram formation theory , 1991 .

[8]  Pantazis Mouroulis,et al.  Diffusion Model of Hologram Formation in Dry Photopolymer Materials , 1994 .

[9]  Pantazis Mouroulis,et al.  Extension of a Diffusion Model for Holographic Photopolymers , 1995 .

[10]  B K Jenkins,et al.  Holographic grating formation in photopolymers. , 1996, Optics letters.

[11]  Masao Doi,et al.  Introduction to Polymer Physics , 1996 .

[12]  R. Larson,et al.  QUANTITATIVE MODEL OF VOLUME HOLOGRAM FORMATION IN PHOTOPOLYMERS , 1997 .

[13]  Vincent Toal,et al.  Applications of a self-developing photopolymer material: holographic interferometry and high-efficiency diffractive optical elements , 1998, Electronic Imaging.

[14]  Jin Hyuk Kwon,et al.  Analysis of temporal behavior of beams diffracted by volume gratings formed in photopolymers , 1999 .

[15]  Justin R. Lawrence,et al.  Automated recording and testing of holographic optical element arrays , 2000 .

[16]  Vyacheslav V. Obukhovsky,et al.  Spatial transfer of matter as a method of holographic recording in photoformers , 2000 .

[17]  Sheridan,et al.  Nonlocal-response diffusion model of holographic recording in photopolymer , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  Feidhlim T. O'Neill,et al.  Improvement of holographic recording material using aerosol sealant , 2001 .

[19]  Justin R. Lawrence,et al.  Thickness Variation of Self-processing Acrylamide-based Photopolymer and Reflection Holography , 2001 .

[20]  Feidhlim T. O'Neill,et al.  Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses , 2001 .

[21]  J. Sheridan,et al.  Comparison of holographic photopolymer materials by use of analytic nonlocal diffusion models. , 2002, Applied optics.