Skin solitons.

Recently, the concept of skin effect has gained considerable attention in the context of non-Hermitian photonics. The experimental realization of Hatano-Nelson systems in optical coupled cavities has provided the opportunity to consider the effect of optical nonlinearity. In this work, we probe the interplay between Kerr nonlinearity and non-Hermiticity in a Hatano-Nelson lattice. In particular, we examine the relation between self-focusing and the skin effect under single-channel excitation. Moreover, we numerically identify skin soliton solutions, which exhibit power threshold and spatial asymmetry.

Higher order exceptional points in infinite lattices.

One of the hallmarks of non-Hermitian photonics is the existence of unique degeneracies, the so-called higher order exceptional points (HEPs). So far, HEPs have been examined mostly in finite coupled systems. In this paper, we present a systematic way to construct infinite optical waveguide lattices that exhibit exceptional points of higher order. The spectral properties and the sensitivity of these lattices around such points are investigated by employing the method of pseudospectra.

Transient growth and dissipative exceptional points.

In the context of non-Hermitian photonics, we study the physics of transient growth in coupled waveguide systems that exhibit higher-order exceptional points. We demonstrate the counterintuitive effect of transient growth despite the decaying spectrum, which is a direct consequence of the underlying modal nonorthogonality. Eigenvalue analysis fails to capture the power dynamics and thus we have to rely on methods of nonmodal stability theory, namely singular value decomposition and pseudospectra. The relation between the order of the exceptional point and transient growth is also examined. Our work provides a general methodology that can be applied to any non-Hermitian system that contains complex elements with more loss than gain, and exploits the boundaries of transient amplification in dissipative environments.

Nonlinear scattering by non-Hermitian multilayers with saturation effects.

We theoretically investigate the optical properties of a one-dimensional non-Hermitian dispersive layered system with saturable gain and loss. We solve the nonhomogeneous Helmholtz equation perturbatively by applying the modified transfer matrix method and we obtain closed-form expressions for the reflection or transmission coefficients for TM incident waves. The nonreciprocity of the scattering process can be directly inferred from the analysis of the obtained expressions. It is shown that by tuning the parameters of the layers we can effectively control the impact of nonlinearity on the scattering characteristics of the non-Hermitian layered structure. In particular, we investigate the asymmetric and nonreciprocal characteristics of the reflectance and transmittance of multilayered parity-time (PT)-symmetric slab. We demonstrate that incident electromagnetic wave may effectively tunnel through the PT-symmetric multilayered structures with zero reflection. The effect of nonlinearity to the scattering matrix eigenvalues is systematically examined.

Equal-intensity waves in non-Hermitian media.

A novel type of waves is examined in the context of non-Hermitian photonics. We can identify a class of complex guided structures that support localized paraxial solutions whose intensity distribution is exactly the same as the intensity of a corresponding solution in homogeneous media (free or bulk space). In other words, intensity-wise the two solutions are identical and their phase is different by a factor exp[iθ(x,y)]. The non-Hermitian potential is determined by the phase θ, as well as the amplitude and phase of the bulk space solution that contributes to the imaginary and real part of the potential, respectively. That way we can connect the plane waves and Gaussian beams of free space to constant-intensity waves and what we call the equal-intensity waves (EI waves) in non-Hermitian media. Such a relation allows us to study three different physical problems: Propagating EI waves inside random media, interface lattice solitons, and moving solitons in photonic waveguide structures with free-space characteristics. The relation of EI waves to unidirectional invisibility and Bohmian photonics is also examined.

Topologically protected bound states in photonic parity-time-symmetric crystals.

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Constant-intensity waves and their modulation instability in non-Hermitian potentials.

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

Accelerating diffraction-free beams in photonic lattices.

We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

Optical transitions and Rabi oscillations in waveguide arrays.

It is theoretically demonstrated that Rabi interband oscillations are possible in waveguide arrays. Such transitions can take place in optical lattices when the unit-cell is periodically modulated along the propagation direction. Under phase-matching conditions, direct power transfer between two Floquet-Bloch modes can occur. In the nonlinear domain, periodic oscillations between two different lattice solitons are also possible.

Optical spatial solitons at the interface between two dissimilar periodic media: theory and experiment.

Discrete spatial solitons traveling along the interface between two dissimilar one-dimensional arrays of waveguides were observed for the first time. Two interface solitons were found theoretically, each one with a peak in a different boundary channel. One evolves into a soliton from a linear mode at an array separation larger than a critical separation where-as the second soliton always exhibits a power threshold. These solitons exhibited different power thresholds which depended on the characteristics of the two lattices. For excitation of single channels near and at the boundary, the evolution behavior with propagation distance indicates that the solitons peaked near and at the interface experience an attractive potential on one side of the boundary, and a repulsive one on the opposite side. The power dependence of the solitons at variable distance from the boundary was found to be quite different on opposite sides of the interface and showed evidence for soliton switching between channels with increasing input power.

Beam dynamics in PT symmetric optical lattices.

The possibility of parity-time (PT) symmetric periodic potentials is investigated within the context of optics. Beam dynamics in this new type of optical structures is examined in detail for both one- and two-dimensional lattice geometries. It is shown that PT periodic structures can exhibit unique characteristics stemming from the nonorthogonality of the associated Floquet-Bloch modes. Some of these features include double refraction, power oscillations, and eigenfunction unfolding as well as nonreciprocal diffraction patterns.

Optical solitons in PT periodic potentials.

We investigate the effect of nonlinearity on beam dynamics in parity-time (PT) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in optical PT synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.

Power thresholds of families of discrete surface solitons.

We have investigated both theoretically and experimentally the power threshold of discrete Kerr surface solitons at the interface between a discrete one-dimensional (1D) (waveguide array) and a continuous 1D (slab waveguide) AlGaAs medium. Decreasing power thresholds were predicted and measured for soliton trapping at sites with increasing distance from the boundary. The thresholds approached asymptotically the power required for a discrete soliton of equivalent width in an infinite lattice. The minimum threshold coincided with a minimum in the interchannel coupling strength.

Theory of coupled optical PT-symmetric structures.

Starting from Lagrangian principles we develop a formalism suitable for describing coupled optical parity-time symmetric systems.

Observation of two-dimensional surface solitons.

We report the first experimental observation of two-dimensional surface solitons at the boundaries (edges or corners) of a finite optically induced photonic lattice. Both in-phase and gap nonlinear surface self-trapped states were observed under single-site excitation conditions. Our experimental results are in good agreement with theoretical predictions.

Optical modes at the interface between two dissimilar discrete meta-materials.

We have studied theoretically and experimentally the properties of optical surface modes at the hetero-interface between two meta-materials. These meta-materials consisted of two 1D AlGaAs waveguide arrays with different band structures.

Observation of discrete surface solitons.

We report the first observation of discrete optical surface solitons at the interface between a nonlinear self-focusing waveguide lattice and a continuous medium. The effect of power on the localization process of these optical self-trapped states at the edge of an AlGaAs waveguide array is investigated in detail. Our experimental results are in good agreement with theoretical predictions.

All-optical switching and multifrequency generation in a dual-core photonic crystal fiber.

We demonstrate all-optical switching at 1550 nm between two weakly coupled cores in a photonic crystal fiber for intensities up to 0.5 TW/cm2. Spectrum analysis at higher intensities reveals that the output was dominated by continuum generation primarily towards shorter wavelengths.

Solitons in dispersion-inverted AlGaAs nanowires.

We demonstrate that optical solitons can exist in dispersion-inverted highly-nonlinear AlGaAs nanowires. This is accomplished by strongly reversing the dispersion of these nano-structures to anomalous over a broad frequency range. These self-localized waves are possible at very low power levels and can form in millimeter long nanowire structures. The intensity and spectral evolution of solitons propagating in such AlGaAs nanowaveguides is investigated in the presence of loss, multiphoton absorption and higher-order dispersion.