Discrete Solitons in Optics

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

https://iopscience.iop.org/article/10.1088/1464-4266/7/5/R02/pdf

Spatiotemporal optical solitons

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (χ(2)) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.

χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.

https://iopscience.iop.org/article/10.1088/1464-4266/6/5/017/pdf

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We review the impressive progress on light self-localisation into spatial optical solitons in nematic liquid crystals. We summarise the basic physics and models, outlining the main properties of nematicons and providing an overview of the most significant experimental achievements in undoped, planar, twisted and chiral nematic liquid crystals.

Nematicons: self-localised beams in nematic liquid crystals

Nonlinear self-focusing of the laser beam in waveguide with nematic homeotropically aligned liquid crystalline layer is analysed theoretically and observed experimentally. The nonlinearity is caused by the reorientational effect and the stable self-trapped beams are created by the spatially periodic reorientation in the liquid crystalline layer.

http://www.if.pw.edu.pl/~karpierz/MCLC98.pdf

Self focusing in liquid crystalline waveguides

Recently, it has been shown experimentally that the nonlinearity in nematic liquid crystals can govern spatial solitons in both waveguide and bulk geometry. Such solitons require a few milliwatts of light power and can be controlled by the state of light polarization or by an external electrical field. In this paper a detailed theoretical analysis of optical solitary waves in nematic liquid crystal waveguides is presented. The self-focusing is induced by reorientation nonlinearity in the homeotropically aligned nematic layer. This configuration corresponds to the experimental setup in which we previously observed such solitary waves. The theoretical results presented in this paper correlate exactly with the experiments.

Solitary waves in liquid crystalline waveguides.

In this article, we show how the substituting different peripheral substituents around the cobalt phthalocyanine core correlate with nonlinear optical properties. We present the results on nonlinear optical properties of solution of cobalt phthalocyanine (CoPc), cobalt phthalocyanine with DNA-CTMA surfactant complex (CoPc-DNA-CTMA), and cobalt phthalocyanine with liquid crystal (CoPc-LC) measured by degenerate four-wave mixing (DFWM) method at the 532 nm wavelength region. We found that the values of third-order nonlinear optical susceptibility (χ⟨3⟩) of CoPc-LC and CoPc-DNA-CTMA increase in comparison with the value of the third-order nonlinear optical susceptibilities of CoPc. We supposed that this is caused by increase of the charge-transfer effects and of the dipole moments of the molecule with the increase of the chain length.

Influence of different peripheral substituents on the nonlinear optical properties of cobalt phthalocyanine core

We report on the experimental studies of the existence of spatial solitons called nematicons in chiral nematic liquid crystal cells. The low absorption allows us to observe soliton propagation at a distance of over a few millimeters in range. The results of our experiment also show that it is possible to create independent nematicons in different layers formed by a helical structure of the liquid crystals.

Miroslaw A. Karpierz

Papers

Nematicons: self-localised beams in nematic liquid crystals

Self focusing in liquid crystalline waveguides

Solitary waves in liquid crystalline waveguides.

Influence of different peripheral substituents on the nonlinear optical properties of cobalt phthalocyanine core

Nematicons in chiral nematic liquid crystals