Deformation of optical solitons in a nonlinear Schrödinger equation with PT-symmetric potentials

What is it about?

Solitons are ubiquitous nonlinear waves with tightly localized single maximum retaining their form during propagation and even surviving collisions with other such waves. Due to their remarkable characteristics, they show multifaceted applications in diverse science, engineering, and technology fields. Solitons undergo modulations in their properties based on the nature of propagating media. Particularly, solitons traveling in inhomogeneous optical media are analyzed through nonlinear Schrödinger equations with distributed dispersion and nonlinearity coefficients. The present work deals with the deformation of such optical solitons for different types of nonlinearities and parity-time (PT⁠)-symmetric potentials. Our analysis has revealed various characteristics showing the amplification with cascaded compression of solitons for step-like nonlinearity, while the localized sech-type nonlinearity gives rise to the phenomena of tunneling through a barrier, cross-over a potential well, and localized excitations. The longitudinally periodic-type nonlinearity reveals the transition of solitons into longitudinal breathers, spatially periodic waves into double-periodic structures, and pulsating breathers. The findings can help us better understand the engineering dynamics of solitons in other physically interesting systems.

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Why is it important?

The modulation of optical solitons due to inhomogeneities in the propagating medium is investigated for three different forms of physically significant PT-symmetric potentials. The theoretical results presented in this work, along with several other studies in the literature, shall provide a valuable framework for experimentalists to explore and verify the deformation of solitons in PT-symmetric systems with spatiotemporal modulation in the context of nonlinear optics, which can be extended to different fields of current potential interest. Furthermore, as a future direction, the present theoretical study can be straightforwardly extended to investigate higher-order solitons, breathers, and rogue waves, along with combined spatial and longitudinally varying dispersion and nonlinear effects in addition to new forms of PT-symmetric potentials to unearth possible applications.

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