Fig. 3: Numerical simulations of edge quasi-solitons. | Nature Communications

Fig. 3: Numerical simulations of edge quasi-solitons.

From: Observation of edge solitons in photonic graphene

Fig. 3

a First \(\beta^ {\prime}\) and second-order \(\beta^ {\prime\prime}\) derivatives for green branch of edge states from Fig. 1c. Vertical dotted line indicates the Bloch momentum \(k = 0.48\,{\mathit{K}}\). b Nonlinear edge state family at \(k = 0.48\,{\mathit{K}}\). Solid and dashed curves show peak amplitude \(a\) and norm \(P\) versus \(\beta\). c Peak amplitude of the nonlinear edge state with \(\beta = 16.573\) (corresponding to the red dot in (b)) versus distance illustrating the development of modulation instability. d Amplitude \(a_{{\mathrm{nlin}}}\) and center position \(x_c\) of quasi-soliton from panel f versus propagation distance. The amplitude \(a_{{\mathrm{lin}}}\) for the same input in linear medium is shown too. e Nonlinear edge state intensity distributions at different propagating distances corresponding to the dots in (c). f Quasi-soliton intensity distributions at different propagation distances corresponding to the dots in \(a_{{\mathrm{nlin}}}\) curve in (e). g Diffraction in linear medium, distributions shown correspond to the dots in \(a_{{\mathrm{lin}}}\) curve in (d). h Evolution of the peak amplitude \(a_{{\mathrm{nlin}}}\) of the quasi-soliton in the case when input amplitude was increased (top curve) and decreased (bottom curve) by \(10{\mathrm{\% }}\). i Projection \(p\) of the soliton field distribution at different distances on bulk Bloch modes of the system.

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