We theoretically and experimentally study self-accelerating and self-breathing Bessel-like beams that fol- low arbitrary trajectories, including hyperbolic, hyperbolic secant, and three-dimensional （3D） spiraling trajectories. The beams have an overall Bessel-like profile in transverse dimensions; however, the intensity of their central main lobe breathes while traveling along a curved trajectory. Such beams can be readily generated experimentally through appropriate phase modulation of the optical wavefront. The beams con- tribute to the design of new families of self-accelerating beams.
Based on the nonlinear Schr o¨dinger 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.
We construct analytically linear self-accelerating Airy elegant Ince-Gaussian wave packet solutions from （3＋1）-dimensional potential-free Schr？dinger 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.
Under the paraxial approximation, the analytical propagation expression of an Airy–Gaussian beam（Ai GB） in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the Ai GB is given for different ratios of the extraordinary index to the ordinary refractive index. It has been found that the continuity and the self-bending effect of Ai GB become weaker when the ratio increases. From the figure of the maximum intensity of Ai GB, one can see that the maximum intensity is not monotone decreasing due to the anisotropic effect of the crystals. The intensity distribution of Ai GB in different distribution factors is shown. The Ai GB converges toward a Gaussian beam as the distribution factor increases.
By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams（REGBs） from the right-handed material（RHM） to the left-handed material（LHM）. Based on the propagation equation, we obtain the intensity distributions of the REGBs during the propagation. It is found that the rotating direction of the REGBs is opposite in the RHM and the LHM, and the rotation angles tend to be π /2 as the propagation distance is long enough.Then we analyze the relationship between the refractive index and the rotating velocity. Furthermore, the energy flow and the angular momentum（AM） of the REGBs which can rotate are also obtained.
By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams （REGBs） that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle. The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.
We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex(CAi GV)beams in strongly nonlocal nonlinear medium for the first time through numerical simulations.The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast.Meanwhile,we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam.Furthermore,we can control the peak intensity contrast through choosing properly the truncation factor.As for the radiation force,we study the gradient and the scattering forces of CAi GV beams on Rayleigh dielectric sphere.Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAi GV beams.
