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Modeling of holographic gratings in graded-index photorefractive planar waveguides

Vittorio M. N. Passaro and Daniele Marseglia

Open Access Open Access

Abstract

A numerical model is presented for the evaluation of the dielectric permittivity tensor changes as induced by guided modes during the formation of holographic gratings in arbitrary photorefractive graded-index planar waveguides. Comparisons among lithium niobate waveguides with different cuts and technology are shown.

©2002 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Δε 11 dielectric perturbation in a Y-cut LiNbO3 graded-index waveguide, x-propagating without overlay at T = 300 K, induced by the collinear TE0-TM0 mode interaction at λ = 632.8 nm.

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Fig. 2.
Fig. 2. Δε 13 dielectric perturbation in the same waveguide.

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Fig. 3.
Fig. 3. Δε 22 dielectric tensor perturbation in the same waveguide.

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Fig. 4.
Fig. 4. Δε 23 dielectric tensor perturbation in the same waveguide.

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Tables (2)

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Table I. Comparison among LiNbO3 cuts in Gaussian profile waveguides.

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Table II. Comparison among different X-cut LiNbO3 technologies.

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Equations (7)

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d 2 φ d cut 2 − K g 2 ε ρ S ε cut S φ = f ( t ) t 0 ε cut S ( − i K g δ ρ ph + ∂ δ cut ph ∂ cut )
φ = φ ( cut , ρ , t ) = φ 0 ( cut , t 0 ) f ( t ) exp ⁡ ( − j K g ρ )
δ ph = β E A E B * exp ⁡ ( − j K g ρ )
d 2 φ 0 d cut 2 − K g 2 ε ρ S ε cut S φ 0 = t 0 ε cut S ( − j K g [ β E A E B ] ρ + ∂ ∂ cut [ β E A E B ] cut )
Δ b p = ∑ k = 1 3 r pk ξ k ∀ p = 1 , … , 6
ξ = ( ξ 1 , ξ 2 , ξ 3 ) = { ( − ∂ φ ∂ x , 0 , j K g φ ) [ X-cut ] ( j K g φ , − ∂ φ ∂ y , 0 ) [ Y-cut ] ( j K g φ , 0 , − ∂ φ ∂ z ) [ Z-cut ]
{ Δ ε 11 = ( b 2 S + Δ b 2 ) ( b 3 S + Δ b 3 ) − Δ b 4 2 det ( b ) − ε 11 S Δ ε 12 = Δ ε 21 = ( b 3 S + Δ b 3 ) Δ b 6 − Δ b 4 Δ b 5 det ( b ) Δ ε 13 = Δ ε 31 = Δ b 4 Δ b 6 − ( b 2 S + Δ b 2 ) Δ b 5 det ( b ) Δ ε 22 = ( b 1 S + Δ b 1 ) ( b 3 S + Δ b 3 ) − Δ b 5 2 det ( b ) − ε 22 S Δ ε 23 = Δ ε 32 = ( b 1 S + Δ b 1 ) Δ b 4 − Δ b 5 Δ b 6 det ( b ) Δ ε 33 = ( b 1 S + Δ b 1 ) ( b 2 S + Δ b 2 ) − Δ b 6 2 det ( b ) − ε 33 S
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