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Weak-wave advancement in nearly collinear four-wave mixing

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Abstract

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.

©2002 Optical Society of America

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Figures (3)

Fig. 1.
Fig. 1. Wave vector configuration for weak-wave advancement.
Fig. 2.
Fig. 2. Signal beam gain as a function of collision half-angle α for λ = 700nm. Note that Δk = 2|k⁽ 1|(1 - cos α).
Fig. 3.
Fig. 3. Logarithm of signal beam amplitude as a function of propagation distance.

Equations (9)

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P 4 = 3 χ xxxx ( 3 ) { E 4 2 E 4 + 2 ( E 1 2 + E 2 2 + E 3 2 ) E 4
+ E 1 E 2 E 4 * exp ( i ( k 1 + k 2 k 3 k 4 ) · z i ( ω 1 + ω 2 ω 3 ω 4 ) t ) }
Δ n = 3 4 n 0 Re [ χ xxxx ( 3 ) ] ( E 1 2 + E 2 2 )
E 4 z = i 4 γ P ( E 4 + 0.5 E 4 * e i ( 6 γ P Δ k ) z e i ( ϕ 1 + ϕ 2 ) )
E 4 = Ae gz e i ( 3 γ P Δ k 2 ) z e i ϕ 4
0 Δ k 6 γP
g = 3 ( γP ) 2 ( γP ) Δ k 0.25 ( Δ k ) 2 .
Δϕ ϕ 1 + ϕ 2 2 ϕ 4 = π 2
γP k Δ k 6 k = 1 3 ( 1 cos α ) 5 × 10 5 .
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