Absence of Exceptional Points in Square Waveguide Arrays with Apparently Balanced Gain and Loss

Basic modelling of transport in 2D wave-mechanical nanodots and billiards with balanced gain and loss mediated by complex potentials

Non-Hermitian quantum mechanics with parity-time (PT) symmetry is presently gaining great interest, especially within the fields of photonics and optics. Here, we give a brief overview of low-dimensional semiconductor nanodevices using the example of a quantum dot with input and output leads, which are mimicked by imaginary potentials for gain and loss, and how wave functions, particle flow, coalescence of levels and associated breaking of PT symmetry may be analysed within such a framework. Special attention is given to the presence of exceptional points and symmetry breaking. Related features for musical string instruments and 'wolf-notes' are outlined briefly with suggestions for further experiments.

Light propagation in ordered and disordered optical waveguide arrays with a transverse loss gradient

We first investigate the propagation of an initially localized optical beam through an ordered waveguide array in which the real part of the refractive index of all waveguides is the same, while there is a linear gradient loss along the transverse direction x. When the optical loss is an increasing function of x, the beam injected into every point of the array propagates to the left edge of the array. But for the case at which optical loss is a decreasing function of x, the optical beam propagates to the right edge of the array. In both cases, as the beam reaches the array edge, it is first reflected by the edge due to the presence of a repulsive potential near the array boundary, and then its width remains constant. We next study the wave propagation through a disordered array of waveguides in which the real parts of the refractive indices of waveguides are random numbers, and there exists a transverse loss gradient. For different random realizations with the same disorder level, when the beam is injected into the central waveguide, the beam becomes localized near the array edge with the lower loss.

Complex band structure of one-dimensional polariton crystal

The exceptional point (EP), at which the relevant eigenvalues and eigenstates are simultaneously identical, typically exists in non-Hermitian systems with parity-time (PT) symmetric complex potentials, and gives rise to many intriguing behaviors in various physical realms. In this work, we explore the complex band structure of one-dimensional "polariton crystals" that can be constructed in waveguide-resonator coupled systems, with PT-symmetric potential. Analysis based on the transfer matrix and the coupled mode theory shows that the complex band structure is intimately determined by the interaction between the Bragg resonance and the polariton one, the gain/loss coefficients, in addition to the coupling strength. A miniband is induced due to the interaction of these two resonances, which is a defect-like band and appears quite different for the band structure evolution. Furthermore, PT-symmetric phase transition occurs in the momentum space for certain amounts of non-Hermiticity. As the non-Hermiticity increases, the EP formed in the original polariton gap approaches another EP formed at the touch point of the folded Bragg bands (where the thresholdless transition occurs). Then they coalesce at a specific non-Hermiticity, and finally disappear. Subsequently, the transmission spectra of such polariton crystals show intriguing phenomena induced by the EPs. Our results provide a different perspective to understand PT-symmetric polariton crystals and may find applications in gain/loss induced lasing by 'polaritons'.

Strong hybridization of edge and bulk states in dimerized PT-symmetric coupled waveguide chain

We study mode coupling of an edge state with bulk states in a coupled waveguide chain in the presence of gain and losses. In a low non-Hermiticity regime, it is found that the edge state associated with the interface between two topologically different waveguide chains is well isolated from the bulk states, sharing the exact same features as the well-known Su-Schrieffer-Heeger Model. As the non-Hermiticity increases, the two bands of the overall waveguide chain merge together, which leads to the overlap in the band diagram between the edge state and states of lower bands. We find that before the PT-symmetry breaking, the edge state is strongly coupled to bulk states of lower bands, evident by the anti-crossing feature in the band diagram. The strong mode hybridization is verified by a non-Hermitian coupled mode theory developed from reaction conservation, and is further examined using phenomenological models. We envisage that the strong coupling between the edge state and the bulk state may be useful in expanding our understanding in topological photonics in non-Hermitian condition, as well as in applications such as mode conversion between edge and bulk states.