Discrete diffraction and Bloch oscillations in non-Hermitian frequency lattices induced by complex photonic gauge fields

Abstract

Non-Hermitian lattice systems with unconventional transport phenomena and topological effects have attracted intensive attention recently. Non-Hermiticity is generally introduced by engineering on-site gain/loss distribution or inducing asymmetric couplings by applying an imaginary gauge field. Here, we extend the concept of non-Hermitian lattices from spatial to frequency dimension and emulate various non-Hermitian transport phenomena arising from asymmetric coupling in synthetic dimension. The non-Hermitian frequency lattice is created by introducing complex gauge potentials through appropriate complex modulations in a slab waveguide. This complex gauge potential can induce asymmetric couplings among spectral modes and give rise to various non-Hermitian transport phenomena such as amplified and decayed frequency diffraction, refraction and non-Hermitian Bloch oscillations. The latter manifest themselves as both power oscillation and asymmetric oscillation patterns, and can be exploited to probe in the bulk the non-Hermitian skin effect. Frequency-domain Bloch oscillations with both exponentially growing oscillation amplitude and energy are also predicted. Our results pave the way towards emulating non-Hermitian transport phenomena and topological effects in synthetic dimension on a photonic platform, with potential applications to spectral manipulation of optical signals and energy harvesting.

Unraveling the non-Hermitian skin effect in dissipative systems

“…In such classical systems, decoherence arises by averaging over an ensemble of stochastic but unitary dynamics. A possible implementation in optics is provided by spectral photonic lattices [78][79][80][81][82][83]. A long light pulse circulating in a fiber loop with negligible dispersion and periodically kicked by a phase modulator realizes a spectral lattice where the spectral curves H (k) and P(k) in Eq.…”

Two-dimensional anisotropic non-Hermitian Lieb lattice

“…Furthermore, non-Hermitian skin effect itself is also a topological effect manifested by the spectral winding on the complex energy plane with a reference energy. Importantly, the non-Hermitian topological phenomena have been observed experimentally in various experimental platforms including the optical waveguide lattices, photonic crystals, and electronic circuits [70][71][72][73][74][75][76][77][78][79][80][81][82][83].…”

Topological Phase Transition and Eigenstates Localization in a Generalized Non‐Hermitian Su–Schrieffer–Heeger Model

“…[ 8–12 ] A mass of novel phenomena cluster in non‐Hermitian system induced by asymmetric coupling in comparison to Hermitian system. [ 13–22 ] An important difference between Hermitian system and non‐Hermitian system caused by asymmetric coupling is that all the eigenstates are localized in non‐Hermitian system but far from it in Hermitian system, that is, non‐Hermitian skin effect. [ 23–26 ] Another particular attractive difference consists in that the bulk‐boundary correspondence seems to be flawless in Hermitian systems but not accurate in non‐Hermitian systems any more with traditional means.…”