Evolution of Cos-Gaussian Beams in a Strongly Nonlocal Nonlinear Medium

Abstract

Abstract-The dynamical properties of cos-Gaussian beams in strongly nonlocal nonlinear (SNN) media are theoretically investigated. Based on the moments method, the analytical expression for the rootmean-square (RMS) of the cos-Gaussian beam propagating in a SNN medium is derived. The critical powers that keep the RMS beam widths invariant during propagation in a SNN medium are discussed. The RMS beam width tends to evolve periodically when the initial power does not equal to the critical power. The analytical solution of the cos-Gaussian beams in SNN media is obtained by the technique of variable transformation. Despite the difference in beam profile symmetries and initial powers, a cos-Gaussian beam always transforms periodically into a cosh-Gaussian beam during propagation and the transformation between the two beams revives after a propagation distance.

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

“…Other types of periodic or large finite arrays of composed of unit cells like spheres and desks also exhibit spatial dispersion effects [146]. Nonlinear materials with observable nonlocality have also been investigated in the optical regime [147]. More recently, much of the reemergence of interest in spatial dispersion stems from the observation that the phenomenon cannot be ignored at the nanoscale [148], especially those of low-dimensional structures like carbon nanotubes [51], [54], [149] and graphene [150], [151].…”

A Fiber Bundle Space Theory of Nonlocal Metamaterials

“…Other types of periodic or large finite arrays of composed of unit cells like spheres and desks also exhibit spatial dispersion effects [50]. Nonlinear materials with observable nonlocality have also been investigated in the optical regime [51]. More recently, much of the reemergence of interest in spatial dispersion stems from the observation that the phenomenon cannot be ignored at the nanoscale, especially those of lowdimensional structures like carbon nanotubes [14] and graphene [52].…”

“…The relation (51) indicates that the source bundle M, R, and the response map L provide a skeleton through which the total response to any EM excitation field defined on an arbitrary EM nonlocality microdomain can be computed. In this way, the vector bundle formalism for electromagnetic nonlocality is essentially complete and the connection between the purely mathematical fiber space and the physical microdomain structures is secured by (51).…”

Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media

“…Note that the nonlocal nonlinearity which can support a variety of nonlocal spatial optical solitons exhibits in many physical systems, and some of them have been observed experimentally [3][4][5][6][7][8][9][10]. Moreover, it has been reported that a great number of optical beams can steadily propagate in SNNM under sufficient conditions, including Gaussian beams and higher-order Gaussian beams, four-petal Gaussian beams, Lorentz-Gaussian beams, the beams carrying wave front dislocations such as Hermite-, Hermite-cosh-or Laguerre-Gaussian beams, and so on [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. As well known, pure wave front dislocations in a monochromatic wave are divided into two types: one is the longitudinal screw dislocation which is also known as the optical vortex with spiral phase, and the other is the transverse edge dislocation with π-phase shift located along a line in the transverse plane.…”