One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables 1 . In the case of the Hamiltonian operator, this requirement not only implies real eigenenergies but also guarantees probability conservation. Interestingly, a wide class of non-Hermitian Hamiltonians can still show entirely real spectra. Among these are Hamiltonians respecting parity‐time (PT) symmetry 2‐7 . Even though the Hermiticity of quantum observables was never in doubt, such concepts have motivated discussions on several fronts in physics, including quantum field theories 8 , nonHermitian Anderson models 9 and open quantum systems 10,11 , to mention a few. Although the impact of PT symmetry in these fields is still debated, it has been recently realized that optics can provide a fertile ground where PT-related notions can be implemented and experimentally investigated 12‐15 . In this letter we report the first observation of the behaviour of a PT optical coupled system that judiciously involves a complex index potential. We observe both spontaneous PT symmetry breaking and power oscillations violating left‐right symmetry. Our results may pave the way towards a new class of PT-synthetic materials with intriguing and unexpected properties that rely on non-reciprocal light propagation and tailored transverse energy flow. Before we introduce the concept of spacetime reflection in optics, we first briefly outline some of the basic aspects of this symmetry within the context of quantum mechanics. In general, a Hamiltonian HD p 2 =2mCV(x

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Observation of parity–time symmetry in optics

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.

Parity–time-symmetric whispering-gallery microcavities

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.

Parity–time synthetic photonic lattices

Effective manipulation of cavity resonant modes is crucial for emission control in laser physics and applications. Using the concept of parity-time symmetry to exploit the interplay between gain and loss (i.e., light amplification and absorption), we demonstrate a parity-time symmetry-breaking laser with resonant modes that can be controlled at will. In contrast to conventional ring cavity lasers with multiple competing modes, our parity-time microring laser exhibits intrinsic single-mode lasing regardless of the gain spectral bandwidth. Thresholdless parity-time symmetry breaking due to the rotationally symmetric structure leads to stable single-mode operation with the selective whispering-gallery mode order. Exploration of parity-time symmetry in laser physics may open a door to next-generation optoelectronic devices for optical communications and computing.

http://science.sciencemag.org/content/sci/346/6212/972.full.pdf

Single-mode laser by parity-time symmetry breaking.

In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-Hermitian, can still exhibit entirely real spectra provided that they obey parity-time requirements or PT symmetry. Here we demonstrate experimentally passive PT-symmetry breaking within the realm of optics. This phase transition leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.

Observation of PT-Symmetry Breaking in Complex Optical Potentials

https://crn2.3it.usherbrooke.ca/guide_sb/publications/ref_1776_2009_linzon_wave_interactions.pdf

Wave interactions and wave-structure scattering in nonlinear patterned waveguides

We study experimentally and numerically the nonlinear scattering of wave packets by local multisite guiding centers embedded in a continuous dielectric medium as a function of the input power and angle of incidence. The extent of trapping into the linear modes of different sites is manipulated as a function of both the input power and the angle of incidence, demonstrating power-controlled switching of nonlinear trapping by local photonic potentials.

Power-dependent switching of nonlinear trapping by local photonic potentials

We demonstrate a technique for a single shot mapping of nonlinear phase shift profiles in spatial solitons that are formed during short pulse propagation through one-dimensional slab AlGaAs waveguides, in the presence of a focusing Kerr nonlinearity. The technique uses a single beam and relies on the introduction of a lithographically etched reflective planar mirror surface positioned in proximity to the beam's input position. Using this setup we demonstrate nonlinearity-induced sharp lateral phase variations for certain initial conditions, and creation of higher spatial harmonics when the beam is in close proximity to the mirror.

M. Volatier-Ravat

Papers

Observation of PT-Symmetry Breaking in Complex Optical Potentials

Wave interactions and wave-structure scattering in nonlinear patterned waveguides

Power-dependent switching of nonlinear trapping by local photonic potentials

Single beam mapping of nonlinear phase shift profiles in planar waveguides with an embedded mirror