Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard.

Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard--a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.

Electric-current-induced unidirectional propagation of surface plasmon-polaritons.

Nonreciprocity and one-way propagation of optical signals are crucial for modern nanophotonic technology, and typically achieved using magneto-optical effects requiring large magnetic biases. Here we suggest a fundamentally novel approach to achieve unidirectional propagation of surface plasmon-polaritons (SPPs) at metal-dielectric interfaces. We employ a direct electric current in metals, which produces a Doppler frequency shift of SPPs due to the uniform drift of electrons. This tilts the SPP dispersion, enabling one-way propagation, as well as zero and negative group velocities. The results are demonstrated for planar interfaces and cylindrical nanowire waveguides.

Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials.

One of the basic functionalities of photonic devices is the ability to manipulate the polarization state of light. Polarization components are usually implemented using the retardation effect in natural birefringent crystals and, thus, have a bulky design. Here, we have demonstrated the polarization manipulation of light by employing a thin subwavelength slab of metamaterial with an extremely anisotropic effective permittivity tensor. Polarization properties of light incident on the metamaterial in the regime of hyperbolic, epsilon-near-zero, and conventional elliptic dispersions were compared. We have shown that both reflection from and transmission through λ/20 thick slab of the metamaterial may provide nearly complete linear-to-circular polarization conversion or 90° linear polarization rotation, not achievable with natural materials. Using ellipsometric measurements, we experimentally studied the polarization conversion properties of the metamaterial slab made of the plasmonic nanorod arrays in different dispersion regimes. We have also suggested all-optical ultrafast control of reflected or transmitted light polarization by employing metal nonlinearities.

Anomalous time delays and quantum weak measurements in optical micro-resonators.

Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos-Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale.

Fractal structures and multiparticle effects in soliton scattering.

We study in detail the interaction of composite solitary waves and consider, as an example, the breather collisions in a weakly discrete sine-Gordon equation. We reveal a physical mechanism of fractal soliton scattering associated with multiparticle effects, and demonstrate chaotic interaction of two breathers with incommensurable frequencies.

Parametric localized modes in quadratic nonlinear photonic structures.

We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi(2)) nonlinear interfaces embedded in a linear layered structure--a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi(2) equations) and find, numerically and analytically, the spatially localized solutions--discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media.

Nonlinearity and disorder: classification and stability of nonlinear impurity modes.

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.

Switching dynamics of solitons in fiber directional couplers.

A simple analytical approach based on a variational formalism is applied to an analysis of the switching dynamics of solitons in fiber nonlinear directional couplers. It is demonstrated that soliton switching may be described by a simplified Hamiltonian model that displays three different regimes of soliton dynamics, depending on the universal parameter, which is the ratio of the squared intensity nu(2) to the coupling parameter kappa. It follows from the analysis presented that perfect soliton switching may be achieved only for the case nu(2)/kappa < pi/2.

Dark optical solitons near the zero-dispersion wavelength.

Propagation of a dark optical soliton is investigated in the neighborhood of the zero-group-dispersion wavelength. Analytical results are obtained in the small-amplitude limit when the soliton is described by the Korteweg-de Vries equation. It is predicted that dark solitons may exist near the zero-group-dispersion point, and the region is found where they are unstable and may be transformed into bright solitons on a pedestal.

Perturbation-induced dynamics of small-amplitude dark optical solitons.

It is demonstrated that the dynamics of small-amplitude dark solitons in optical fibers may be described by the wellknown Korteweg-de Vries equation. This approach allows us to explain analytically the temporal self-shift of dark solitons due to the Raman contribution to the nonlinear refractive index, which has been observed experimentally by Weiner et al. [Opt. Lett. 14, 868 (1989)].

Dark solitons in dispersive quadratic media.

We analyze dark solitons supported by second-order parametric interactions between the fundamental and second harmonics in the presence of dispersion and group-velocity mismatch. We reveal various types of solitary waves, including a family of two-wave dark solitons propagating on a modulationally stable background, dark solitons with nonmonotonic tails, and bound states of dark solitons.

Instabilities of dark solitons.

Optical dark solitons described by the generalized nonlinear Schrödinger equation are discussed, and the criterion of soliton instability is presented. This analytical criterion is confirmed numerically for an exactly solvable model of nonlinear saturation.

Vector dark solitons.

It is shown that a novel class of optical soliton is possible in the form of vector dark solitons. These nonlinear waves describe bound states of two gray solitons with different background intensities in each mode that are strongly coupled through cross-phase modulation.

Raman-induced optical shocks in nonlinear fibers.

It is demonstrated that the stimulated Raman scattering in optical fibers supports kink solitons (shocks) not only in the recently considered case of anomalous dispersion but also in the normal-dispersion regime. In both cases there is a family of the kinks depending on an arbitrary (positive) wave number of the carrying wave. Although all the kinks are unstable because of the inherent instability of the cw background behind them, in the normal-dispersion regime the instability, induced solely by the stimulated Raman scattering, is essentially weaker than that in the case of anomalous dispersion.

Decay of dark solitons due to the stimulated Raman effect.

It is demonstrated analytically and numerically that dark solitons always disappear owing to the stimulated Raman effect. Instead of dark solitons, the stable propagation of optical kinks on the cw background in the region of the normal group-velocity dispersion is possible.

Spatial optical solitons governed by quadratic nonlinearity.

We demonstrate that a dielectric medium with purely quadratic nonlinearity [the so-called chi((2)) material] can display self-focusing phenomena through a new type of modulational instability of the interacting fundamental and second-harmonic field components and therefore can support propagation of (two-wave) optical solitons. We prove the existence of a family of such solitons, which are found numerically and, in some particular cases, also analytically. The two-wave solitons are stable in the whole parameter region in which they exist.

Drift instability of dark solitons in saturable media.

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

Optical gap solitons in nonresonant quadratic media.

We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or chi(2)] periodic optical media. We derive a novel physical model for gap solitons in chi(2) nonlinear Bragg gratings.

Nonlinear theory of soliton-induced waveguides.

We develop a nonlinear theory of soliton-induced waveguides that describe a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium. We suggest an effective way to control the interaction of these soliton-induced waveguides and also show that, in sharp contrast with scalar dark solitons, the dark-soliton waveguides can attract each other and even form stationary bound states.

Nonlinear localized waves in a periodic medium.

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.