Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array

The dynamics of wave packets in the fractional Schrödinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrödinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.

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Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation

Zhang

et al. 2015

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Light splitting and stopping and their combination via controllable Bloch oscillation in a lattice

Zhang

2020

J. Opt. Soc. Am. B

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We study controllable Bloch oscillation and its potential applications in a one-dimensional lattice with partly phase-modulated hopping rates. Under proper conditions, such a system can be built by using a quasi-one-dimensional sawtooth lattice with Peierls phases induced by a synthetic magnetic field. The amplitude of the Bloch oscillation can be adjusted precisely and continuously by adjusting the phase, and hence we realize tunable light splitting in the presence of a V-type potential. Moreover, we construct two distinct sandwich structures to realize tunable light stopping and delayed splitting, respectively, of which the stopping and delay durations are tunable. Our proposal may imply exciting opportunities for potential applications in optical communications and photonic device fabrication involving unconventional light transports.

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Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array

Cited by 2 publications

References 51 publications

Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation

Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation

Light splitting and stopping and their combination via controllable Bloch oscillation in a lattice

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