We report a new set of Laguerre-Gaussian wave-packets that propagate with periodical self-focusing and finite beam width in weakly guiding inhomogeneous media. These wave-packets are solutions to the paraxial form of the wave equation for a medium with parabolic refractive index. The beam width is defined as a solution of the Ermakov equation associated to the harmonic oscillator, so its amplitude is modulated by the strength of the medium inhomogeneity. The conventional Laguerre-Gaussian modes, available for homogenous media, are recovered as a particular case.
Using a variational approach, we obtain the self-focusing critical power for a single and for any number of interacting Laguerre-Gauss beams propagating in a Kerr nonlinear optical medium. As is known, the critical power for freely propagating higher-order modes is always greater than that of the fundamental Gaussian mode. Here, we generalize that result for an arbitrary incoherent superposition of Laguerre-Gauss beams, adding interactions between them. This leads to a vast and rich spectrum of self-focusing phenomena, which is absent in the single-beam case. Specifically, we find that interac…
Superpositions of paraxial Laguerre-Gauss laser beam modes to generate optical potentials based on the optical dipole force are investigated theoretically. Parabolic and other monomial potentials with even powers, in cylindrical and spherical symmetry, with large diameters, can be synthesized. This superposition approach promises to help with high quality atom cloud manipulation and imaging.
The present note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker-Planck-like equation can be solved exactly.
Laguerre-Gaussian (LG) beams carrying orbital angular momentum (OAM) have shown promise in deep tissue imaging, medical diagnostics, and optical communication due to their robust propagation properties through scattering media. However, an exact model that provides a mechanism for the enhanced scattering properties of LG beams over Gaussian beams has not been established till date. Here, we examine this issue by studying the propagation of polarized vortex beams transmitted through tissue-like turbid scattering media. We demonstrate that the intensity profile has a much more profound effect on…
We analyze the time reversal of waves in a turbulent medium using the parabolic Markovian model. We prove that the time reversal resolution can be a nonlinear function of the wavelength and independent of the aperture. We establish a duality relation between the turbulence-induced wave spread and the time-reversal resolution which can be viewed as an uncertainty inequality for random media. The inequality becomes an equality when the wave structure function is Gaussian.
We examine the evolution of paraxial beams carrying intrinsic spin and orbital angular momenta (AM) in gradient-index media. A parabolic-type equation is derived which describes the beam diffraction in curvilinear coordinates accompanying the central ray. The center of gravity of the beam experiences transverse AM-dependent deflections -- the spin and orbital Hall effects. The spin Hall effect generates a transverse translation of the beam as a whole, in precise agreement with recent geometrical optics predictions. At the same time, the orbital Hall effect is significantly affected by the diff…
We study the reflection of a Hermite-Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre-Gaussian beams, Hermite-Gaussian beams undergo no significant distortion upon reflection. We report Goos-Hänchen shift for all the spots of a higher order Hermite Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3-d vector beam. We briefly discuss the difficulties as…
Understanding the scattering properties of various media is of critical importance in many applications, from secure, high-bandwidth communications to extracting information about biological and mineral particles dissolved in sea water. In this paper we demonstrate how beams carrying orbital angular momentum (OAM) can be used to detect the presence of symmetric or chiral subsets of particles in disordered media. Using a generalized Mie theory we calculate analytical expressions for quasi-monochromatic structured light scattered by dilute distributions of micro- and nanoparticles. These allow u…
For paraxial propagation of scalar waves the classic electromagnetic theory definition of transverse linear (TLM) and orbital angular (OAM) momenta of the beam wave are represented in terms of the coherence function. We show in examples that neither the presence of optical vortices is necessary for the intrinsic OAM, nor does the presence of optical vortices warrant the non-zero intrinsic OAM. The OAM is analyzed for homogeneously coherent and twisted partially coherent beam waves. A twisted Gaussian beam has an intrinsic OAM with a per-unit power value that can be continuously changed by vary…
We study the nonlinear optical propagation of two different classes of space-varying polarized light beams -- radially symmetric vector beams and Poincaré beams with lemon and star topologies -- in a rubidium vapour cell. Unlike Laguerre-Gauss and other types of beams that experience modulational instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively control…
We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth slightly fluctuates along the propagation direction. We find that, under suitable spectral resonance conditions, small transverse soliton oscillations may get parametrically amplified.
Shortcuts to adiabaticity for rapid soliton compression in nonlocal media
Shanghai University（上海大学）；University of the Basque Country UPV/EHU（巴斯克大学）；Quantum Advanced Research Center (QuARC), CSIC（CSIC量子先进研究中心）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（CSIC马德里材料科学研究所）
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of Riccati type. This substantially simplifies description of Gaussian beams diffraction as compared to full wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lens-like m…
