Abstract
Generalization of Fractional Schrödinger equation (FSE) into optics is fundamentally important, since optics usually provides a fertile ground where FSE-related phenomena can be effectively observed. Beam propagation management is a topic of considerable interest in the field of optics. Here, we put forward a simple scheme for the realization of propagation management of light beams by introducing a double-barrier potential into the FSE. Transmission, partial transmission/reflection, and total reflection of light fields can be controlled by varying the potential depth. Oblique input beams with arbitrary distributions obey the same propagation dynamics. Some unique properties, including strong self-healing ability, high capacity of resisting disturbance, beam reshaping, and Goos-Hänchen-like shift are revealed. Theoretical analysis results are qualitatively in agreements with the numerical findings. This work opens up new possibilities for beam management and can be generalized into other fields involving fractional effects.
Highlights
Considering the fact that fractional effect can effectively suppress the beam diffraction and the interaction between a beam and a refractive-index potential can be used to control the behaviour of beam evolution, we suggest a simple model for the realization of propagation management
We qualitatively find that the transmission, partial transmission/reflection, and total reflection of a beam occur for small, modulate, and large potential depths, respectively
We investigated the propagation of optical beams in the Fractional Schrödinger equation (FSE) with a double-barrier potential
Summary
Generalization of Fractional Schrödinger equation (FSE) into optics is fundamentally important, since optics usually provides a fertile ground where FSE-related phenomena can be effectively observed. Many interesting phenomena have been reported, such as nondiffractive propagation of light beams in zigzag waveguide arrays[1], structure photonic crystals[2] and Kapitza media[3], Rabi oscillations and periodic shape transformations[4, 5], resonant suppression of light coupling[6,7,8,9], dragging of laser beams[10], diffraction-managed solitons[11, 12], linear and nonlinear unidirectional edge states[13,14,15,16], and all-optical steering and switching[17,18,19], just to name a few. It provides a powerful and effective way for the beam management and can find many applications in optics, such as switching, routing, and reshaping
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