Photorefractive ring oscillators

Milan Petrović; Milivoj Belić

doi:10.1364/JOSAB.12.001028

Journal of the Optical Society of America B
Vol. 12,
Issue 6,
pp. 1028-1035
(1995)
•https://doi.org/10.1364/JOSAB.12.001028

Photorefractive ring oscillators

Milan Petrović and Milivoj Belić

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Milan Petrović and Milivoj Belić, "Photorefractive ring oscillators," J. Opt. Soc. Am. B 12, 1028-1035 (1995)

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Abstract

We consider the theory of photorefractive ring oscillators, using our unified solution method. Both unidirectional and bidirectional ring resonators are analyzed, based on the two-wave mixing process with crossed polarization and the four-wave mixing process with parallel polarization in photorefractive crystals. We highlight symmetries between the transmission and the reflection geometries of these processes and use them to write analytical expressions for oscillation conditions in all the cases. Symmetry breaking is noted in the four-wave mixing between the transmission and the reflection grating cases. An optical transistor based on photorefractive rings is proposed.

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Equations (75)

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2WM	TG, RG
1 < \|r\|	\|r\| < τ
\|r\| < 1	τ < \|r\|

2WM, Cross Polarization			4WM, Parallel Polarization

RG	TG	RG	TG
τ = exp(−aΓd)	τ = exp(aΓd)	$τ = \frac{I_{2 d} + I_{10} exp (Γ d)}{I_{10} + I_{2 d} exp (Γ d)}$	$τ \approx \frac{I_{10} + I_{2 d} exp (Γ d)}{I_{2 d} + I_{10} exp (Γ d)}$
$cosh (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$sec (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$cosh (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$sec (u) \approx \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$
$κ = \frac{\| r \| sinh (u)}{\| r \| - cosh (u)}$	$κ = \frac{\| r \| sin (u)}{\| r \| cosh (u) - 1}$	$κ = \frac{\| r \| sinh (u)}{\| r \| - cosh (u)}$	$κ = \frac{\| r \| sin (u)}{\| r \| cos (u) - 1}$
$sinh (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$tan (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$sinh (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$tan (u) \approx \frac{κ (τ - 1)}{τ + κ^{2}}$

2WM	TG, RG
1 < \|r\|	\|r\| < τ
\|r\| < 1	τ < \|r\|

2WM, Cross Polarization			4WM, Parallel Polarization

RG	TG	RG	TG
τ = exp(−aΓd)	τ = exp(aΓd)	$τ = \frac{I_{2 d} + I_{10} exp (Γ d)}{I_{10} + I_{2 d} exp (Γ d)}$	$τ \approx \frac{I_{10} + I_{2 d} exp (Γ d)}{I_{2 d} + I_{10} exp (Γ d)}$
$cosh (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$sec (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$cosh (u) = \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$	$sec (u) \approx \frac{\| r \| (τ + 1)}{τ + {\| r \|}^{2}}$
$κ = \frac{\| r \| sinh (u)}{\| r \| - cosh (u)}$	$κ = \frac{\| r \| sin (u)}{\| r \| cosh (u) - 1}$	$κ = \frac{\| r \| sinh (u)}{\| r \| - cosh (u)}$	$κ = \frac{\| r \| sin (u)}{\| r \| cos (u) - 1}$
$sinh (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$tan (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$sinh (u) = \frac{κ (τ - 1)}{τ + κ^{2}}$	$tan (u) \approx \frac{κ (τ - 1)}{τ + κ^{2}}$

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Equations (75)

Journal of the Optical Society of America B