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Soliton trains in photonic lattices

Yaroslav V. Kartashov, Victor A. Vysloukh, and Lluis Torner

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Abstract

We address the formation and propagation of multi-spot soliton packets in saturable Kerr nonlinear media with an imprinted harmonic transverse modulation of the refractive index. We show that, in sharp contrast to homogeneous media where stable multi-peaked solitons do not exist, the photonic lattices support stable higher-order structures in the form of soliton packets, or soliton trains. Intuitively, such trains can be viewed as made of several lowest order solitons bound together with appropriate relative phases and their existence as stable objects puts forward the concept of compact manipulation of several solitons as a single entity.

©2004 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. (a) Energy flow versus propagation constant for odd and even solitons at p=3, S=2. (b) Lower cutoff for odd and even solitons versus p at S=0.5. Inset: lower and upper cutoffs for odd and even solitons versus S at p=3. Profiles of odd (c) and even (d) solitons at p=3, S=2, b=0.8.

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Fig. 2.
Fig. 2. Areas of stability and instability (shaded) for odd (a) and even (b) solitons on the (b,S) plane at p=3. Stable propagation of odd (c) and even (d) solitons with b=0.8 at p=3, S=2, perturbed with white noise with variance σ 2 noise=0.02.

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Fig. 3.
Fig. 3. (a) Energy flow versus propagation constant for twisted solitons of first three orders at p=3, S=0.5. (b) Lower and upper cutoffs for first twisted soliton versus S at p=3. Inset: cutoffs versus p at S=0.4. (c) Profile of first twisted soliton at p=3, S=0.4, b=1. (d) Areas of stability and instability (shaded) for first twisted soliton on (b,S) plane at p=3. (e) Profile of third twisted soliton at p=3, S=0.25, b=2, and (f) its stable propagation in the presence of noise with σnoise2=0.02.

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Fig. 4.
Fig. 4. Decay of first (a) and second (b) twisted solitons with U=50 at the boundary (dashed line) of uniform medium and medium with periodic modulation of refractive index at p=3. Escape angle for solitons that appear upon decay of first twisted soliton versus energy flow at p=3 (c), and versus p at U=20 (d). Saturation parameter S=0.05.

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Fig. 5.
Fig. 5. (a) Energy flow versus propagation constant for odd soliton at p=3, S=1.5. (b) Lower and upper cutoffs for odd soliton versus S at p=3. Inset: lower and upper cutoffs versus p at S=0.5. (c) Profile of odd soliton at p=3, S=1.5, b=-0.45, and (d) its stable propagation in the presence of white noise. (e) Profile of even soliton at p=3, S=0.4, b=-1.5, and (f) its stable propagation in the presence of white noise. Noise variance in (d) and (f) σ noise=0.02.

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

i ∂ q ∂ ξ = − 1 2 ∂ 2 q ∂ η 2 + σ q ∣ q ∣ 2 1 + S ∣ q ∣ 2 − p R ( η ) q ,
U = ∫ − ∞ ∞ ∣ q ∣ 2 d η .
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