Search

A spatiotemporal non-paraxial correction to the paraxial solution of ultrashort pulsed beam is obtained by using the Fourier transform and the Taylor expansion. By studying the propagation of an isodiffracting pulsed Gaussian beam with different pulse shapes, we find that there are spectrum-induced changes in the non-paraxial propagation of the pulsed beam. We analyse the influence of pulse spectrum on the non-paraxial property of the ultrashort pulsed beam and explain it base on the paraxial approximation condition.

In this paper, we investigate spatial dark solitons in nonlocal nonlinear media. Based on the nonlocal nonlinear Schrödinger equation and the diffusion equation, the numerical solutions with different propagation constants are obtained by using the Newton iterative method. And it is found that there exist dark soliton solutions .and the relation between the width of dark soliton and the degree of nonlocality for any propagation constant under arbitrary nonlocal degrees different propagation constants. In experiments, we observe the formation of the spatial dark solitons in the solution of dye. The influence of Gaussian background on dark solitons is also discussed, and the numerical results are in agreement with the experimental results.

Based on the nonlocal nonlinear Schrdinger equation and Poisson equation of thermal diffusion, using the slip-step Fourier algorithm and multi-grid method, we numerically investigated the propagation properties of Hermite-Guassian beams in the nonlocal thermal media. The results show that low-order Hermite-Gaussian beams can propagate stably, in contrast with the unstable propagation of high-order Hermite-Gaussian beams. The worse the stability is, the higher the order is. The effect of the boundary of the sample with different cross sections on the propagation properties of Hermite-Guassian beam is also discussed in detail. We found that propagation properties in square geometry are in agreement with those in Snyder-Mitchell model. However, in rectangular sample, the evolution of intensity distribution of Hermite-Gaussian beams differs seriously from that in the square sample.

The propagation of hollow Gaussian beams in strongly nonlocal nonlinear media is studied in detail. Two analytical expressions are derived. For hollow Gaussian beams, the intensity distribution always evolves periodically. However the second-order moment beam width can keep invariant during propagation if the input power is equal to the critical power. The interaction of two hollow Gaussian beams and the vortical hollow Gaussian beams are also discussed. The vortical hollow Gaussian beams with an appropriate topological charge can keep their shapes invariant during propagation.

In this paper, we obtain the analytical solution of the off-waist inputted complex argument Laguerre-Gaussian beams and their mean squared beam width in nonlocal nonlinear media. The propagation of the complex argument Laguerre-Gaussian beams in the nonlocal nonlinear media is investigated in detail. The examples show that the pattern shape of a (n,m) mode complex argument Laguerre-Gaussian beam varies periodically with the period Δz=πzc in strongly nonlocal nonlinear media if n≠0.But if n=0, its pattern shape remains unvaried and the beam width varies periodically during propagation. Under the off-waist incident condition, the propagation of the (0,m)mode complex argument Laguerre-Gaussian beam behaves as a breather during propagation, no matter what the power of the incident beam is. Only when the beam is input at the waist and the input power equals the critical power would the breather be reduced to a soliton.

By using slowly-varying envelope approximation, a family of solutions of the paraxial wave equation are found in theory, which represents a new family of ultrashort pulsed beams called ultrashort pulsed complex argument Sinc-Gaussian beams. These pulsed beams with a certain frequency have a nearly complex argument Gaussian profile, a sinc function temporal shape. The ultrashort pulsed complex argument Sinc-Gaussian beams and their propagation properties in free space are studied detailedly, such as intensity on the axis, transversal intensity distribution of the pulsed beams, polarity reversal, pulse time delay, etc..

Based on the purterbative method which was developed by Lax et al, and by using of the Fourier transform, we obtain a vectorial nonparaxial correction method to the propagation of the few-cycle pulsed beam in free space. the first-order of the transverse component of the correction is the same as that of Fu's in the frequency domain, and is more convenient to obtain the analytical nonparaxial solution in the temporal domain. It is shown in the examples and the analysis that the vector corrections must be included in any study that wants to go beyond the scalar paraxial solution. From the examples, we find that the spatial distribution of the vectorial nonparaxial correction would be influenced by the temporal distribution of the pulse.

We have studied, by numerical simulations, the spatially-induced group velocity dispersion in the propagation of ultrashort-pulsed Bessel beams in free space- The simulation results have confirmed the existence of the spatially-induced dispersions in the propagation of a truncated Bessel beam which can be constructed in practice- It is shown that the spatially-induced dispersion is observed when the diffraction length of truncated Bessel beams is longer than the dispersion length of spatially-induced group velocity dispersion