Chidao Chen

Propagation of sharply autofocused ring Airy Gaussian vortex beams.

Controlling the focal length and the intensity of the optical focus in the media is an important task. Here we investigate the propagation properties of the sharply autofocused ring Airy Gaussian vortex beams numerically and some numerical experiments are performed. We introduce the distribution factor b into the initial beams, and discuss the influences for the beams. With controlling the factor b, the beams that tend to a ring Airy vortex beam with the smaller value, or a hollow Gaussian vortex beam with the larger one. By a choice of initial launch condition, we find that the number of topological charge of the incident beams, as well as its size, greatly affect the focal intensity and the focal length of the autofocused ring Airy Gaussian vortex beams. Furthermore, we show that the off-axis autofocused ring Airy Gaussian beams with vortex pairs can be implemented.

Propagation of Airy-Gaussian beam in Kerr medium

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.

Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials

By using the method of the ABCD matrix, the propagation of Airy Gaussian vortex (AiGV) beams through slabs of right-handed materials (RHMs) and left-handed materials (LHMs) is reported. Based on the Huygens diffraction integral, an approximate analytical propagation equation for AiGV beams is derived. Using numerical simulations, we study the intensity and phase distributions of the AiGV beams in RHMs and LHMs. We find that the optical vortex can destroy the center lobe of the AiGV beams, and the center lobe can reconstruct due to the fact that the acceleration of the vortex and the AiGV beam is not consistent. We also investigate the influence of different χ0 values on the propagation of the AiGV beams through slabs of RHMs and LHMs, which can cause the AiGV beams to tend toward an Airy vortex beam with a smaller value and a Gaussian vortex beam with a larger one. In addition, we elucidate the energy flow and the angular momentum of the AiGV beams.

Virtual source of a Pearcey beam

A virtual source that yields a family of a Pearcey wave is demonstrated. A closed-form expression is derived for the Pearcey wave that simplifies to the paraxial Pearcey beam (PB) in the appropriate limit. From the perturbative series representation of a complex-source-point spherical wave, an infinite series nonparaxial correction expression for a PB is obtained. The infinite series expression of a PB can give accuracy up to any order of the diffraction angle. By applying the integral representation of the Pearcey wave, the first three terms in the nonparaxial correction series to the paraxial PB are provided.

Interaction of Airy?Gaussian beams in saturable media*

Based on the nonlinear Schrodinger 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.

Propagation of a Pearcey–Gaussian–vortex beam in free space and Kerr media

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.

Nonparaxial propagation of a (1+1)-dimensional Pearcey beam

We introduce a virtual source that generates a family of a Pearcey wave. We derive a closed-form expression for the (1+1)-dimensional Pearcey wave that in the appropriate limit yields the paraxial accelerating and non-diffracting Pearcey beam (PB). From the perturbative series representation of a complex-source-point spherical wave, we derive an infinite series nonparaxial correction expression for PB. The infinite series expression of a PB can provide accuracy up to any order of diffraction angle. From the integral representation of the Pearcey wave, the first three orders of nonparaxial corrections to the paraxial Pearcey beam are derived.