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Properties of quadratic multi-soliton generation near phase-match in periodically poled potassium titanyl phosphate

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Abstract

The properties of the multi-quadratic-soliton generation process have been investigated both theoretically and experimentally near and on phase-match in non-critically-phase-matched, periodically poled, potassium titanyl phosphate (PPKTP). It was found that multi-soliton generation occurs primarily due to asymmetry in the input beam and at phase-matching. The number of solitons generated depended on the input intensity in a non-trivial way.

©2003 Optical Society of America

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Supplementary Material (5)

Media 1: GIF (456 KB)     
Media 2: GIF (173 KB)     
Media 3: GIF (1364 KB)     
Media 4: GIF (404 KB)     
Media 5: GIF (531 KB)     

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Figures (8)

Fig. 1.
Fig. 1. Experimental setup. The prism (inset) can be moved into the path of the beam to alter the direction of the beam asymmetry (but not its shape).
Fig. 2.
Fig. 2. (456 KB) Simulation of the spatial evolution of three soliton generation on phase match with a high input intensity fundamental beam (three times higher than single soliton threshold 3.4GW/cm2, where the input intensity of 1 a.u. in the simulations corresponds to approximately 14GW/cm2). Left-hand-side the fundamental; Right-hand-side the harmonic. The propagation distance between successive frames is about 0.1 in units of diffraction lengths. Simulation parameters: D11=0.0943, D12=0.0847, D21=0.0478, D22=0.0423, α1,2=0, input intensity=0.73 a.u., and the Eqs. (1), (2) are normalized to set Γ=0.01.
Fig. 3.
Fig. 3. The divergence angle (a.u.) and number of solitons predicted by CW simulations after 5 diffraction lengths as a function of input intensity (in arbitrary units). A gaussian beam input with w 1=w 2 was assumed with the anisotropic diffraction appropriate for PPKTP.
Fig. 4.
Fig. 4. (172 KB) FW spatial field for different temporal snapshots at 10 diffraction lengths for an elliptical input beam with w1/w2=1.07. The inset sketches the shape of the temporal profile and the moving dot shows the location of the temporal slice shown.
Fig. 5.
Fig. 5. Fundamental (FW) and second harmonic (SH) output patterns for two cases. (a) Single soliton generation. (b) Multi-soliton generation for a strongly asymmetric input beam. Insets show the input beams.
Fig. 6.
Fig. 6. (1.33 MB) Multiple shots of the fundamental beam output patterns obtained with increasing the intensity from 0.5 GW/cm2 to 26 GW/cm2.
Fig. 7.
Fig. 7. (404 KB) Calculated evolution with propagation distance of the fundamental (left-hand-side) and the harmonic (right-hand-side) at ΔkL≈15π under the same conditions as Fig. 2 (for which ΔkL=0).
Fig. 8.
Fig. 8. (531 KB) Evolution of the output fundamental beam pattern with changing phase-mismatch, ΔkL, and fixed intensity. Note that there is a change in the camera sensitivity scale at around +0.2π to enhance the satellite peaks which saturates the output on the central soliton.

Equations (2)

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i A 1 x + ( D 11 2 A 1 z 2 + D 12 2 A 1 y 2 ) + α 2 ( ω ) 2 A 1 2 A 1 = Γ A 2 A 1 * exp ( i Δ k x )
i A 2 x + ( D 21 2 A 2 z 2 + D 22 2 A 2 y 2 ) + α 2 ( ω ) 2 A 2 2 A 2 = Γ A 1 2 exp ( i Δ k x )
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