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Nodal solitons and the nonlinear breaking of discrete symmetry

Albert Ferrando, Mario Zacarés, Pedro Andreés, Pedro Fernández de Córdoba, and Juan A. Monsoriu

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Abstract

We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called nodal solitons are characterized by nodal lines determined by the discrete symmetry of the system. Our physical realization of such a system is a 2D nonlinear photonic crystal fiber owning 𝓒6ν symmetry.

©2005 Optical Society of America

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Supplementary Material (2)

Media 1: GIF (749 KB)     
Media 2: GIF (576 KB)     

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Figures (4)
Fig. 1.
Fig. 1. Two nodal solitons for l=1 (Λ=23µm, a=8µm, γ=0.006 and wavelength λ=1064nm): (a)–(b) amplitude and phase, respectively, of the S nodal soliton; (c)–(d) amplitude and phase, respectively, of the A nodal soliton. Inset: schematic transverse representation of a PCF.

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Fig. 2.
Fig. 2. Effective index of a soliton solution, n sol vs the nonlinear coupling γ for symmetric (dotted line) and antisymmetric (dashed line) solitons and vortex and antivortex solitons with l=1 (solid line).

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Fig. 3.
Fig. 3. Evolution of a diagonal perturbation of a S nodal soliton showing asymptotic stability. (749 KB)

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Fig. 4.
Fig. 4. Non-diagonal perturbation of a S nodal soliton. In this case, an oscillatory instability occurs. (576 KB)

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Equations (3)

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

( L 0 + L N L ( ∣ Φ ∣ ) ) Φ = ∂ 2 Φ ∂ z 2 ,
( L 0 + L N L ( ∣ ϕ ∣ ) ) ϕ = β 2 ϕ .
ϕ δ l ( r , θ ) = 2 r ϕ l s ( r , θ ) cos ⁡ [ l θ + ϕ l p ( r , θ ) + δ ] , l = 1 , 2 .
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