Constant-intensity Waves Research Articles

Observation of photonic constant-intensity waves and induced transparency in tailored non-Hermitian lattices.

Light propagation is strongly affected by scattering due to imperfections in the complex medium. It has been recently theoretically predicted that a scattering-free transport through an inhomogeneous medium is achievable by non-Hermitian tailoring of the complex refractive index. Here, we implement photonic constant-intensity waves in an inhomogeneous, linear, discrete mesh lattice. By extending the existing theoretical framework, we experimentally show that a driven non-Hermitian tailoring allows us to control the propagation and diffraction of light even in highly disordered systems. In this vein, we demonstrate the transmission of shape-preserving beams and the seemingly undistorted propagation of light excitations across a strongly inhomogeneous non-Hermitian photonic lattice that can be realized by coupled optical fiber loops. Our results lead to a deeper understanding of non-Hermitian wave control and further contribute to the development of non-Hermitian photonics.

Topological constant-intensity waves.

Topological constant-intensity (TCI) waves are introduced in the context of non-Hermitian photonics. Unlike other known examples of topological defects, the proposed TCI waves exhibit a counterintuitive behavior because a phase difference occurs across space without any accompanying intensity variations. Such solutions exist only on non-Hermitian systems, because the associated nonzero phase difference is directly related to the real and imaginary parts of the potential. The free space diffraction and the existence of such waves in two spatial dimensions are also discussed in detail.

Higher order effects on constant intensity waves of nonlinear Schrödinger equation with [formula omitted] symmetric potential

Constant intensity solutions of nonlinear Schrödinger equation that includes terms accounting for third order dispersion, self steepening, self frequency shift and PT symmetric potential are obtained. The complex potential is constructed as a solution to an inverse problem which predicts the potential supporting the desired solution. These constant intensity waves are then used to perform a modulational instability analysis both in anomalous and normal dispersion regime. The linear stability results are supplemented with direct numerical simulations. The role of third order dispersion, self steepening and self frequency shift on modulational instability of the constant intensity states has been investigated. Effect of variation of amplitude of constant intensity solutions on modulational instability is studied too.

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.

Scattering-free pulse propagation through invisible non-Hermitian media

We demonstrate a new design principle for unidirectionally invisible non-Hermitian structures that are not only invisible for one specific wavelength but rather for a broad frequency range. Our idea is based on the concept of constant-intensity waves, which can propagate even through highly disordered media without back-scattering or intensity variations. Contrary to already existing invisibility studies, our new design principle requires neither a specific symmetry (like $\mathcal{PT}$-symmetry) nor periodicity, and can thus be applied in a much wider context. This generality combined with broadband frequency stability allows a pulse to propagate through a disordered medium as if the medium was entirely uniform.

Self-acceleration in non-Hermitian systems

We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian system. We explore self-accelerating waves with constant intensity and integrable self-accelerating waves. We find that self-accelerating constant intensity waves are possible even when gain and loss are not balanced in the system.

Families of stable solitons and excitations in the PT-symmetric nonlinear Schr\xf6dinger equations with position-dependent effective masses

Since the parity-time-(pmb{mathscr{P}}pmb{mathscr{T}}-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with pmb{mathscr{P}}pmb{mathscr{T}}-symmetric potentials have been investigated. However, previous studies of pmb{mathscr{P}}pmb{mathscr{T}}-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized pmb{mathscr{P}}pmb{mathscr{T}}-symmetric Scarf-II potentials. The broken linear pmb{mathscr{P}}pmb{mathscr{T}} symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than pmb{mathscr{P}}pmb{mathscr{T}}-symmetric ones, but feature similar properties. Our results may suggest new experiments for pmb{mathscr{P}}pmb{mathscr{T}}-symmetric nonlinear waves in nonlinear nonuniform optical media.

Wave propagation through disordered media without backscattering and intensity variations

A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multi-path interference. Here we show that these intensity variations can be entirely suppressed by adding disorder-specific gain and loss components to the medium. The resulting constant-intensity waves in such non-Hermitian scattering landscapes are free of any backscattering and feature perfect transmission through the disorder. An experimental demonstration of these unique wave states is envisioned based on spatially modulated pump beams that can flexibly control the gain and loss components in an active medium.

Guest Editorial Introduction to the Issue on Parity Time Photonics

The 17 papers in this special issue focus on parity time photonics, a new field of modern applied physics and design engineering. The enabling concept of parity time symmetry has garnered attention, in particular in the fields of optics, photonics and the design of new materials as well forward looking photonic integrated circuits. This is a result of applying such concepts for the design of photonic devices that has opened up many new technology paths and device functionalities. Examples include Bragg gratings with unidirectional invisibility, single mode nano-lasers based on parity time symmetry breaking and super-sensitive sensors, even new acoustic phononic devices. Equally important, non-Hermitian photonic structures that deviate from the exact Parity Time symmetry can also exhibit novel behavior such as pump-controlled random lasing, a loss-induced lasing onset and constant intensity waves in a non-uniform scattering landscape. The objective of this issue is to highlight recent progress and trends in this field.

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.