Translated Abstract
In this paper, we mainly research the following aspects both theoretically and numerically:
1) The controllable circular Airy beams via dynamic linear potential; 2) the dual accelerating Airy–Talbot recurrence effect and Fractional nonparaxial accelerating Talbot effect; 3) the nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency; 4) the transport properties in the photonic super-honeycomb lattice — a hybrid fermionic and bosonic system; 5) the fractional SchrÖdinger equation with a periodic PT -symmetric potential.
First of all, we investigate a controllable spatial modulation of circular autofocusing Airy (CAi) beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the CAi is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even eliminated when the linear potential exerts a “pulling” effect on the beam, or if the linear potential exerts a “pushing” effect, the autofocusing effect can be greatly strengthened. Numerical simulations agree with the theoretical results very well. Our results broaden the potential applications of CAi beams in trapping and manipulating microparticles, offering potential use in optics, biology, and other disciplines.
Secondly, we demonstrate the dual accelerating Airy–Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy–Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. Which results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy–Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction. In addition, We demonstrate the fractional Talbot effect of nonparaxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutionsof the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superpositionof the solutions that accelerate along concentric semicirculartrajectories with different radii. Talbot images formalong certain central angles, which are referred to as Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality— it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of the nonparaxial accelerating beams and of the Talbot effect among them.
Thirdly, We theoretically and numerically investigate the nonparaxial self-accelerating beams in a Λ-type three-level energy system of rubidium atomic vapor in the electromagnetically induced transparency (EIT) window. In the EIT window, the absorption
of the atomic vapor is small, and robust nonparaxial selfaccelerating beams can be generated. The reason is that the energy of the tail transfers to themain lobe, which then maintains its shape, owing to the self-healing effect. Media with large absorption would demand large energy to compensate, and the tail would be lifted too high to maintain the profile of an accelerating beam, so that self-accelerating beams cannot be obtained any longer. An atomic vapor with small absorption is the ideal medium to produce such self-accelerating beams and, in return, self-accelerating beams may inspire new ideas in the research associated with atomic vapors and atomic-like ensembles.
Then, we report on the transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. The super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. It also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb lattice will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super-honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super-honeycomb lattice and the modes of Dirac cones with different pseudospins, by the three-beam interference pattern, the pseudospin-mediated vortices will be observed. This work has been published in Annalen der Physik, and is selected as the cover article. It is highly valued by Advanced Science News, which evaluated that ``provides a new platform for investigating light trapping, higher pseudospin states, vortex generation, and other interesting phenomena in this intriguing physical system. In addition, the novel topological properties of the super-honeycomb lattice are now ready for exploration; and deeper investigation of this interesting system may inspire new ideas and bring about new physical phenomena.’’
Finally, we investigate the fractional SchrÖdinger equation with a periodic PT -symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the onedimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the
periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the PT -symmetric potential. This investigation may find applications in novel on-chip optical devices.
Translated Keyword
[Circular Airy beam, loss-proof, nonparaxial self-accelerating beam, super-honeycomb lattice, Talbot effect]
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