Diffraction properties of volume holographic diffusers

Claire Gu; Jenn-Ren Lien; Foster Dai; John Hong

doi:10.1364/JOSAA.13.001704

Journal of the Optical Society of America A
Vol. 13,
Issue 8,
pp. 1704-1711
(1996)
•https://doi.org/10.1364/JOSAA.13.001704

Diffraction properties of volume holographic diffusers

Claire Gu, Jenn-Ren Lien, Foster Dai, and John Hong

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Claire Gu, Jenn-Ren Lien, Foster Dai, and John Hong, "Diffraction properties of volume holographic diffusers," J. Opt. Soc. Am. A 13, 1704-1711 (1996)

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Abstract

We present a theoretical model based on the coupled-mode theory and use this model to analyze the diffraction properties of volume holographic diffusers, such as diffraction efficiency and wavelength sensitivity. For small diffraction angles our results predict that the diffraction efficiency exhibits a blue shift for its maximum value and a dip at the recording wavelength. For color displays we propose and analyze the wavelength-multiplexed volume holograms recorded with three primary colors, red, green, and blue. Furthermore, our results demonstrate the enhancement of wavelength tolerance for a thin holographic medium, which can serve as a wideband diffuser over the entire visible range.

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Type of Wave	k_x	k_y	β
Plane wave	0	0	$\frac{2 π}{λ}$
Diffused^a	$\begin{array}{l} - \frac{2 π}{λ_{r}} sin 1 ° to \\ - \frac{2 π}{λ_{r}} sin 10 ° \end{array}$	0	$\begin{array}{l} \frac{2 π}{λ_{r}} cos 1 ° to \\ \frac{2 π}{λ_{r}} cos 10 ° \end{array}$

Gratings	\|n_g\|	K_gx	K_gz
1–10 (645 nm)	7.7 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{R}} sin 1 ° to \\ \frac{2 π}{λ_{R}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{R}} (1 - cos 1 °) to \\ \frac{2 π}{λ_{R}} (1 - cos 10 °) \end{array}$
11–20 (540 nm)	7.15 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{G}} sin 1 ° to \\ \frac{2 π}{λ_{G}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{G}} (1 - cos 1 °) to \\ \frac{2 π}{λ G} (1 - cos 10 °) \end{array}$
21–30 (470 nm)	6.75 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{B}} sin 1 ° to \\ \frac{2 π}{λ_{B}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{B}} (1 - cos 1 °) to \\ \frac{2 π}{λ_{B}} (1 - cos 10 °) \end{array}$

Type of Wave	k_x	k_y	β
Plane wave	0	0	$\frac{2 π}{λ}$
Diffused^a	$\begin{array}{l} - \frac{2 π}{λ_{r}} sin 1 ° to \\ - \frac{2 π}{λ_{r}} sin 10 ° \end{array}$	0	$\begin{array}{l} \frac{2 π}{λ_{r}} cos 1 ° to \\ \frac{2 π}{λ_{r}} cos 10 ° \end{array}$

Gratings	\|n_g\|	K_gx	K_gz
1–10 (645 nm)	7.7 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{R}} sin 1 ° to \\ \frac{2 π}{λ_{R}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{R}} (1 - cos 1 °) to \\ \frac{2 π}{λ_{R}} (1 - cos 10 °) \end{array}$
11–20 (540 nm)	7.15 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{G}} sin 1 ° to \\ \frac{2 π}{λ_{G}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{G}} (1 - cos 1 °) to \\ \frac{2 π}{λ G} (1 - cos 10 °) \end{array}$
21–30 (470 nm)	6.75 × 10⁻⁶	$\begin{array}{l} \frac{2 π}{λ_{B}} sin 1 ° to \\ \frac{2 π}{λ_{B}} sin 10 ° \end{array}$	$\begin{array}{l} \frac{2 π}{λ_{B}} (1 - cos 1 °) to \\ \frac{2 π}{λ_{B}} (1 - cos 10 °) \end{array}$

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Equations (12)

Journal of the Optical Society of America A