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Discrete modulational instability in periodically poled lithium niobate waveguide arrays

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Abstract

Parametric gain associated with discrete modulational instability due to the second order nonlinearity χ(2)(-2ω;ω,ω) was investigated experimentally in periodically poled lithium niobate arrays of weakly coupled channel waveguides for conditions of both positive and negative phase-mismatch for second harmonic generation.

©2005 Optical Society of America

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Figures (7)

Fig. 1.
Fig. 1. Geometry of the wide, high intensity fundamental beam interacting with a PPLN array near its phase-matching condition for second harmonic generation.
Fig. 2.
Fig. 2. The first derivative dky/dkx of the dispersion relation obtained by plotting the centroid at the output facet of a fundamental beam injected into the PPLN arrays as a function of the relative phase between the adjacent channels.
Fig. 3
Fig. 3 Output from PPLN array as a function of increasing input fundamental energy. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.
Fig. 4.
Fig. 4. Spatial Fourier transform of the output intensity patterns shown in Fig. 3.. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch=-40π.
Fig. 5.
Fig. 5. Low and high power output intensity distribution from the array at high (green) and low (blue) powers. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.
Fig. 6.
Fig. 6. Calculated evolution of a seeded fundamental beam in the PPLN array as a function of increasing peak input fundamental power in the middle channel. Experimental parameters were assumed. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.
Fig. 7.
Fig. 7. Distribution across the array of the fundamental beam output power from the PPLN array for incidence of the fundamental beam as a function of the relative input phase between adjacent channels. Positive phase mismatch = 170π on the left; negative phase-mismatch=-40π on the right. The input pulse energy was 0.27μJ corresponding to a peak power of 620W in the middle channel. Regions of high contrast filaments are identified by ellipses.

Equations (2)

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i u n z + i δ u n t + c ( u n + 1 + u n 1 ) + 2 γ u n * v n = 0
i v n z Δ βv n + γ u n 2 = 0 ,
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