Dark optical solitons: physics and applications

Singular optics is a branch of modern physical optics that involves a wide class of effects associated with the phase singularities in wave fields and with the topology of wave fronts. Optical singularities (optical vortices) exhibit some fundamental features absent in the "usual" fields with smooth wave fronts. Namely, optical vortices possess orbital angular momentum, topological charge for helical wave front of beams with well-defined direction of propagation. As a result, an interesting spatial evolution can be generated such as optical vortices "nucleation" and "annihilation" by pairs with participation of phase saddles, often called "optical chemistry." To study the structure of the circular edge dislocation, an isolated dark (zero-amplitude) ring is created within a light beam, with an analytical description of the field. A screw wave-front dislocation has a feature that the spatial structure of the wave front has the form of a helicoid around the dislocation axis. The chapter also describes reflection, refraction, interference and diffraction of OVs. Both frequency up- and down-conversion processes possess essential peculiarities for light beams with OVs. The chapter discusses the topology of wave fronts and vortex trajectories. Gouy phase shift in singular optics is also described in the chapter.

Chapter 4 - Singular optics

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrodinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

http://www.physics.sfsu.edu/~laser/pdf/rop347172p20.pdf

Optical spatial solitons: historical overview and recent advances

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

This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.

https://iopscience.iop.org/article/10.1088/1751-8113/43/21/213001/pdf

Dark solitons in atomic Bose–Einstein condensates: from theory to experiments

Spatial dark-soliton (SDS) stripes are experimentally found in the transverse plane of a laser beam that passes through a rectilinear diffraction screen before propagating in a self-defocusing nonlinear material. Materials with different mechanisms of nonlinearity manifest the same qualitative results. The SDS nature of the observed phenomenon is verified by numerical simulations of the (2+1)-D nonlinear Schr\"odinger equation, analytical solutions for the (1+1)-D case, and their comparison with experimental data.

Spatial dark-soliton stripes and grids in self-defocusing materials.

Observations of the self-deflection effect for an asymmetrical continuous-wave laser beam in sodium vapor are described, and comparisons based on theoretical calculations are made. A self-bending angle as large as eight diffraction widths was recorded, and strong attenuation of the on-axis radiation due to self-bending was measured. At ~200°C the self-deflection angle increased linearly with beam power, and we determined that (n2)max ≃ −10−7 cm2/W for intensities below 220 W/cm2. While numerical calculations, based on an inhomogeneously broadened two-level system, predict strong saturation of the self-bending effect, we observed only moderate saturation.

https://www.cis.rit.edu/~grovers/Doc/Publications/CWself.pdf

Continuous-wave self-deflection effect in sodium vapor

Continuous-wave self-deflection of an asymmetrical laser beam, with a deflection angle up to eight diffraction widths, and strong attenuation of the on-axis radiation were achieved in a short sodium-vapor cell. We determined that the nonlinear refractive index Δn varied almost linearly with intensity I, Δn ≈ n2I, with n2 ~ −10−7 cm2/W at ~200°C and intensities less than 220 W/cm2.

https://www.cis.rit.edu/~grovers/Doc/Publications/SelfBend.pdf

H. Yin

Papers

Spatial dark-soliton stripes and grids in self-defocusing materials.

Continuous-wave self-deflection effect in sodium vapor

Self-bending of a cw laser beam in sodium vapor.