Search

In this paper, we investigate the optical transmission properties of two-dimentional (2D) defective two-segment-connected triangular optical waveguide networks (DTSCTOWNs). By means of the network equation and generalized eigenfunction method (GEM) we calculate the optical transmission spectra of 2D DTSCTOWNs and find many groups of extreme narrow photonic bands (ENPBs), whose number and frequencies are mainly determined by defect types and the number of defect waveguides. The relevant quantitative rules of ENPBs are obtained and this kind of ENPBs will possess applications for the designing of extreme-narrowband filters, high-sensitive optical switches, and other all-optical equipment. In order to analyze the futures of ENPBs, based on the decomposition-decimation method of electronic energy spectra we propose an interesting pseudo dynamic method (PDM). Comparing with GEM, for the same kinds of 2D DTSCTOWNs PDM can not only reduce the computations of ENPBs significantly, but also predict the splitting types of ENPBs directly. Additionally, it is also found that injecting EM waves with the frequencies of ENPBs in 2D DTSCTOWNs strong photonic localizations can be produced at the nodes connecting with defect waveguides. It may be useful for the designing of high-efficient photonic energy storage devices.

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 p S and topological charge m. In particular, by reducing the parameter p S , 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 w T , which makes the light intensity of the spatial focal point further improve.

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 χ 0 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 β 1 and β 2. 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.

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 χ 0 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.

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 Schrodinger 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.

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.