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An analytical propagation expression of a Pearcey beam in uniaxial crystals orthogonal to the optical axis is derived. The propagations of the Pearcey beam in the tourmaline and the quartz are investigated. The phase distribution and the angular momentum of the Pearcey beam in the tourmaline are also performed. The result shows that the positions of the auto-focusing and the inversion simply relate to the extraordinary refractive index of the crystals. In other words, we can choose the suitable crystals to adjust the positions of auto-focusing and inversion of the Pearcey beam to meet the actual needs. [ABSTRACT FROM AUTHOR]

We investigate the propagation properties and the radiation forces of a radially polarized Pearcey beam (RPPB) in uniaxial crystals analytically and numerically in this paper. Obtaining the propagation expression of an RPPB, we perform the intensity (in the x-direction, in the y-direction and in the synthesizing direction), the polarization direction, the energy flow and the angular momentum of an RPPB with the method of numerical calculation. The propagating properties of an RPPB in the free space are shown for comparison. The auto-focusing and the inversion of an RPPB propagating in uniaxial crystals are demonstrated. The influence of the extraordinary refractive index and the ordinary refractive index on an RPPB in the uniaxial crystals is discussed. [ABSTRACT FROM AUTHOR]

In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex (CAiGV) beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how the linear chirp parameters, the quadratic chirp parameters, and the Gaussian factors influence the nonparaxial propagation dynamics of the CAiGV beams. The intensity, the energy flow, the beam center, and the angular momentum of the CAiGV beams are deeply investigated. It is shown that the Gaussian factors have a great effect on the intensity and the centroid positions of the CAiGV beams. With the Gaussian factors increasing, the intensity of CAiGV beams decreases rapidly. The main lobes of the transverse intensity distribution of the CAiGV beams are similar to triangles. [ABSTRACT FROM AUTHOR]

We introduce a class of rapidly autofocused ring Pearcey Gaussian vortex (RPGV) beams based on the Pearcey function of catastrophe theory. The distribution of beams can be adjusted by changing the spatial distribution factor pS and topological charge m. In particular, by reducing the parameter pS, the beams can autofocus more quickly, and the peak intensity of beams at the focal point can be increased by dozens of times than that at the initial plane. Further, combining temporal Pearcey Gaussian pulses with spatial RPGV beams, spatiotemporal rapidly autofocused RPGV wavepackets are obtained, and the pulse focal point can always reach the spatial focus by setting well the normalized pulse width wT, which makes the light intensity of the spatial focal point further improve. [ABSTRACT FROM AUTHOR]

By using the Huygens–Fresnel diffraction integral, we can obtain the analytical expressions of the chirped-Airy–Gaussian-vortex (CAiGV) beams propagating in the chiral medium. The distributions of the intensity, the phase and the gradient force of the CAiGV beams have been investigated analytically. Firstly, the CAiGV beams split into the left circularly polarized vortex (LCPV) beams and the right circularly polarized vortex (RCPV) beams when propagating in the chiral medium. We find that the values of the topological charges determine the focusing location, and the intensity distribution of the CAiGV beams is affected by the distribution factor χ0 and the chiral parameter γ. With the increase of the chiral parameter γ, the parabolic deflection of the LCPV beams increases and that of the RCPV beams decreases, respectively. Similarly, if the chiral parameter γ increases, the evolution speed of the gradient force's distribution of the LCPV beams will speed up but that of the RCPV beams will slow down. In addition, the propagation trajectory and the diffraction effect of the beams are affected by the first-order and the second-order chirp parameters. Therefore, the propagation trajectory can be modulated effectively by adjusting the chiral parameter γ and the chirp parameters β1 and β2. Moreover, the phase distribution shows that the phase singularity moves outward and the trajectory approximates a straight line when the propagation distance increases. Finally, we find that the results of numerical experiments agree well with the analytical results. [ABSTRACT FROM AUTHOR]

By solving the (3  +  1)-dimensional free-space Schrödinger equation in cylindrical coordinates analytically, we have studied the chirped Airy collinear Laguerre–Gaussian wave packets. The different three-dimensional spatiotemporal profiles can be obtained by selecting a different mode number or relative amplitude, and whether the spatiotemporal profiles rotate or not relies on the mode number during propagation; but the wave packets will accelerate during propagation. Furthermore, we also have done a numerical experiment of the collinear Laguerre–Gaussian beams in free space. In addition, the wave packets will also rotate when varying the relative phase, while they will not only accelerate or decelerate, but reverse when varying the quadratic chirp factor. [ABSTRACT FROM AUTHOR]

The propagation dynamics of a chirped Airy vortex (CAiV) beam with x-polarization in uniaxial crystals orthogonal to the optical axis is studied analytically and numerically. The effect of the ratio of extraordinary and ordinary refractive indices, the chirp parameter, as well as the propagation distance is analyzed, which shows that the focused position of the CAiV beams can be controlled through changing the ratio of the extraordinary and ordinary refractive indices. In addition, with the propagation distance increasing, the asymmetry of the intensity and the angular momentum of the CAiV beam during propagation becomes much more visible. The variation of the chirp parameters can change the attenuation velocity of the vortex as well. [ABSTRACT FROM AUTHOR]

We construct analytically linear self-accelerating Airy elegant Ince–Gaussian wave packet solutions from (3+1)-dimensional potential-free Schrödinger equation. These wave packets have elliptical geometry and show different characteristics when the parameters (p,m) and ellipticity ε are adjusted. We investigate these characteristics both analytically and numerically and give the 3-dimensional intensity and phase distribution of these wave packets. Lastly, we analyze the radiation forces on a Rayleigh dielectric particle. In addition, we also find an interesting phenomenon that if the energy distribution between every part of wave packets is uneven at the input plane, the energy will be transferred between every part in the process of transmission. [ABSTRACT FROM AUTHOR]

By solving the normalized dimensionless linear parabolic (Schrödinger-like) equations in the paraxial approximation, we can obtain the analytic solutions of the chirped Airy–Gaussian (CAiG) beam in a medium with a parabolic potential. We study the propagation properties of the finite energy CAiG beam in a parabolic potential and the influence of the distribution factor and the chirped factor on the CAiG beam. The propagation of the CAiG beam changes drastically with the distribution factor increasing: the CAiG beam tends to the chirped Airy beam when the distribution factor is very small; while as the distribution factor increases further, the CAiG beam tends to the chirped Gaussian beam. At the same time, the CAiG beam with a chirp has big changes when the chirped factor is increasing: the multi-peak structure is not obvious, the accelerated velocity and the peak intensity are larger, but the period does not change; when the CAiG beam has a quadratic chirp, the maximum intensity of the CAiG beam becomes smaller and the envelope is gradually smoother with the increasing of the chirped factor. [ABSTRACT FROM AUTHOR]

The propagation of a Pearcey–Gaussian–vortex beam (PGVB) has been investigated numerically in free space and Kerr media. In addition, we have done a numerical experiment for the beam in free space. A PGVB maintains the characteristics of auto-focusing, self-healing and form-invariance which are possessed by a Pearcey beam and a Pearcey–Gaussian beam. Due to the influence of the optical vortex, a bright speck occurs in front of the main lobe. Compared with a Pearcey beam and a Pearcey–Gaussian beam, a PGVB has the most remarkable intensity singularity and the phase singularity. It is worth noting that the impact of the vortex at the coordinate origins means that a PGVB in the vicinity carries no angular momentum or transverse energy flow. We have investigated and numerically simulated the transverse intensity of a PGVB in Kerr media. We find that the auto-focusing of a PGVB in a Kerr medium becomes stronger with increasing power. [ABSTRACT FROM AUTHOR]

Based on the nonlinear Schrödinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. [ABSTRACT FROM AUTHOR]

We investigate the propagation of an Airy–Gaussian vortex (AiGV) beam in free space and Kerr media. It is interesting to see that the beam will perform self-healing and main lobe focusing both in free space and Kerr media when the vortex locates at the center of the plane. By controlling the number of the topological charge, the beam distribution factor χ0 and the position of the vortex, we can control the intensity distribution of the AiGV beam in the out plane both in free space and Kerr media. It is found that when the vortex is close to the center of the plane, it has a strong effect on the intensity distribution of the beam. When the beam propagates in the number of the topological charge, the partial collapse will take place even with low initial input power. We find that the main lobe focusing contributes to this partial collapse. [ABSTRACT FROM AUTHOR]

Nonlinear optical phenomena are of great practical interest in optics. The evolution of ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium is investigated using the nonlinear Schrödinger equation. Numerical simulations indicate that the distribution factor b can influence the formation of the ring Airy Gaussian beams. Results show that the beams can be oscillating, and the light filament can be achieved under appropriate laser input power. On the other hand, the evolution of the ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium can be implemented, and the numerical simulations of the holographic generation of the ring Airy Gaussian vortex beams propagated in the medium demonstrate that the vortex can be preserved along the propagation. The Poynting vector shows that the energy flow of the ring Airy Gaussian beams flows in the opposite direction on both sides of the focus plane; however, for beams with a spiral phase, the flow direction remains the same; the energy flow can rotate in opposite directions on both sides of the focal plane. [ABSTRACT FROM AUTHOR]

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. [ABSTRACT FROM AUTHOR]

By using the method of moments, the critical power of the Airy–Gaussian (AiG) beam is given for different decay factors and different distribution factors numerically. The critical power Pcr of the AiG beam decreases as the distribution factor increases. Using the split-step Fourier method, the propagations of the AiG beam in the free space and in the Kerr medium are shown. It has been found that the self-acceleration effect becomes weaker when the distribution factor increases. As the initial input power increases, we can observe the quasi-breather finally. From the root mean square (rms) beam width and the peak intensity figures, one can see that the beam with large distribution factor is more sensitive to the change of the initial input power. [ABSTRACT FROM AUTHOR]

We obtain an exact Hermite-Laguerre-Gaussian (HLG) beam solution of the Snyder-Mitchell mode, which is confirmed by the simulation of the nonlocal nonlinear Schrödinger equation. HLG breathers and solitons can be obtained by taking different input power. The HLG beams are a unity of Hermite-Gaussian beams (HGBs) and Laguerre-Gaussian beams (LGBs), which form the exact and continuous transition modes between HGBs and LGBs when an additional parameter changes continuously. [ABSTRACT FROM AUTHOR]

Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\rm \ddot{o} dinger equation. [ABSTRACT FROM AUTHOR]