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Materials 2018, 11(7), 1134; https://doi.org/10.3390/ma11071134

Composition Relation between Nonlinear Bloch Waves and Gap Solitons in Periodic Fractional Systems

1
Department of Physics, Shaanxi University of Science & Technology, Xi’an 710021, China
2
Department of Electronic Information and Physics, Changzhi University, Changzhi 046011, China
*
Author to whom correspondence should be addressed.
Received: 14 May 2018 / Revised: 15 June 2018 / Accepted: 21 June 2018 / Published: 4 July 2018
(This article belongs to the Special Issue Trends in Nonlinear Optical Materials)
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Abstract

Evolution of beams in nonlinear optical media with a fractional-order diffraction is currently attracting a growing interest. We address the existence of linear and nonlinear Bloch waves in fractional systems with a periodic potential. Under a defocusing nonlinearity, nonlinear Bloch waves at the centers or edges of the first Brillouin zone bifurcate from the corresponding linear Bloch modes at different band edges. They can be constructed by directly copying a fundamental gap soliton (in one lattice site) or alternatively copying it and its mirror image to infinite lattice channels. The localized truncated-Bloch-wave solitons bridging nonlinear Bloch waves and gap solitons are also revealed. We thus prove that fundamental gap solitons can be used as unit cells to build nonlinear Bloch waves or truncated-Bloch-wave solitons, even in fractional configurations. Our results provide helpful hints for understanding the dynamics of localized and delocalized nonlinear modes and the relation between them in periodic fractional systems with an optical nonlinearity. View Full-Text
Keywords: nonlinear optics; nonlinear Bloch waves; spatial optical solitons; defocusing Kerr medium; fractional Fourier transforms nonlinear optics; nonlinear Bloch waves; spatial optical solitons; defocusing Kerr medium; fractional Fourier transforms
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Dong, L.; Huang, C. Composition Relation between Nonlinear Bloch Waves and Gap Solitons in Periodic Fractional Systems. Materials 2018, 11, 1134.

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