Rectification of light refraction in curved waveguide arrays

Rectified Bloch oscillations in dynamically modulated waveguide arrays

We study the dynamics of excitations in dynamically modulated waveguide arrays with an external spatial linear potential. Longitudinally periodic modulation may cause a significant change in the width of the quasi-energy band and leads to the dynamical band suppression with a linear dispersion relation. This substantially affects the Bloch oscillation dynamics. Novel dynamical phenomena with no analogue in ordinary discrete waveguides, named rectified Bloch oscillations, are highlighted. Due to the interplay between directional coupling between adjacent waveguides and diffraction suppression by the introduced onsite energy difference, at odd times of half Bloch oscillations period, the new submodes are continuously excited along two opposite rectification directions and experience same oscillation evolution, and eventually lead to the formation of a diamondlike intensity network. Both the amplitude and direction of the rectified Bloch oscillations strongly depend on the coupling strength. When coupling strength passes the critical value at which dynamical band suppression with a linear dispersion relation occurs, the direction of Bloch oscillations is inverted.

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices

We investigate the discrete Talbot self-imaging effect in Floquet superlattices based on a mesh of directional couplers with periodically varying separation between waveguides, both theoretically and numerically. The modulated discreteness of the lattices sets strong constraints to ensure the Talbot effect generation. We show that discrete Talbot effect occurs only if the incident periods are N = 1, 2, and 4 in dispersive regimes of the Hermitian superlattices. In both dynamic localized and rectification regimes, self-imaging effect can occur for arbitrary input period N. For the rectification case, Talbot distance equals the input period. In the regime of dynamical localization, the Talbot distance remains unchanged irrespective of the pattern period. For non-Hermitian Floquet superlattices, due to the non-zero imaginary part of quasi-energy spectrum arising at the center of the Brillouin zone, where the mode degeneracy occurs, Talbot revival is not preserved when the input period is an even number, and exists only as N = 1 in the dispersive regime. The theoretical calculations and numerical simulations verify each other completely.

Observation of topological transport quantization by dissipation in fast Thouless pumps

Quantized dynamics is essential for natural processes and technological applications alike. The work of Thouless on quantized particle transport in slowly varying potentials (Thouless pumping) has played a key role in understanding that such quantization may be caused not only by discrete eigenvalues of a quantum system, but also by invariants associated with the nontrivial topology of the Hamiltonian parameter space. Since its discovery, quantized Thouless pumping has been believed to be restricted to the limit of slow driving, a fundamental obstacle for experimental applications. Here, we introduce non-Hermitian Floquet engineering as a new concept to overcome this problem. We predict that a topological band structure and associated quantized transport can be restored at driving frequencies as large as the system's band gap. The underlying mechanism is suppression of non-adiabatic transitions by tailored, time-periodic dissipation. We confirm the theoretical predictions by experiments on topological transport quantization in plasmonic waveguide arrays.