arXiv subjects

K. G. Makris

Publications and source records attributed to K. G. Makris.

13 recordsLinked to original sources

arXiv2025

Non-Hermitian off-diagonal disordered optical lattices

Within the framework of non-Hermitian photonics, we investigate the spectral and dynamical properties of one- and two-dimensional non-Hermitian off-diagonal disordered optical lattices, where randomness is applied to the couplings rather than to the on-site potential terms. We analyze eigenvalue distributions and the localization properties of the eigenmodes, comparing them with those of the corresponding Hermitian lattices. Furthermore, we study their transport behavior under single-channel excitation and identify unconventional phenomena such as jumps between distant lattice regions in systems with a purely real spectrum, as well as complex spectrum-induced Anderson jumps, reported here for the first time in two dimensions. Our results establish a reference framework for non-Hermitian off-diagonal disorder and open new directions for future studies of localization phenomena.

cond-mat.dis-nn↗

arXiv2025

Evolving disorder in non-Hermitian lattices

The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features, including jumpy wave evolution. By contrast, much less is known about how transport is modified when the on-site disorder evolves during propagation. Here we address this problem by investigating two pertinent non-Hermitian lattice models with disorder altered at regular intervals, characterized by a finite disorder period. In lattices with symmetric couplings and complex on-site disorder, short disorder periods suppress localization and give rise to diffusion-like spreading, while longer periods allow the emergence of jumps. In Hatano-Nelson lattices with real on-site disorder, the non-Hermitian skin effect asymptotically dominates regardless of the disorder strength, while the disorder period reshapes the drift velocity and modulates its competition with Anderson localization. These results establish evolving disorder as a novel way of tuning non-Hermitian transport.

cond-mat.dis-nn↗

arXiv2025

Non-Hermitian impurity problem

The problem of a single Hermitian impurity has long served as a cornerstone in condensed matter physics, offering fundamental insights into the mechanisms of Anderson localization. Yet, despite the increased interest in the spectral and localization properties of non-Hermitian lattices with defects, the non-Hermitian extension of the single impurity problem remains largely unexplored. In this work, we investigate the role of a single complex impurity in one-, two-, and three-dimensional infinite tight-binding lattices. Our study reveals a series of counterintuitive phenomena, including regions where localization vanishes and re-emerges as the impurity strength varies. Next, we study the corresponding finite-sized lattices, which are highly relevant to experimental realizations in readily accessible photonic platforms, revealing a variety of exotic features, such as scale-free localized states, exceptional points, and peculiar cross-shaped localized eigenstates, whose profiles deviate from the conventional exponential localization. This work paves the way for future studies on transport phenomena in non-Hermitian disordered lattices.

cond-mat.dis-nn↗

arXiv2025

Effect of imaginary gauge on wave transport in driven-dissipative systems

Wave transport in disordered media is a fundamental problem with direct implications in condensed matter, materials science, optics, atomic physics, and even biology. The majority of studies are focused on Hermitian systems to understand disorder-induced localization. However, recent studies of non-Hermitian disordered media have revealed unique behaviors, with a universal principle emerging that links the eigenvalue spectrum of the disordered Hamiltonian and its statistics with its transport properties. In this work we show that the situation can be very different in driven-dissipative lattices of cavities, where a uniform gain applied equally to all the components of the system can act as a knob for controlling the wave transport properties without altering the eigenvalue statistics of the underlying Hamiltonian. Our results open a new avenue for developing a deeper insight into the transport properties in disordered media and will aid in building new devices as well. Our work which is presented in the context of optics generalizes to any physical platforms where gain can be implemented. These include acoustics, electronics, and coupled quantum oscillators such as atoms, diamond centers and superconducting qubits.

cond-mat.dis-nn↗

arXiv2024

Anderson localization versus hopping asymmetry in a disordered lattice

In the framework of non-Hermitian photonics, we investigate the interplay between disorder and non-Hermiticity in a one-dimensional Hatano-Nelson lattice. While Anderson localization dictates the wave's evolution in conservative random systems, the introduction of non-Hermiticity tends to force the beam to unidirectionally propagate towards one edge of the potential due to the existence of skin modes. As we show, the antagonism between these effects results in qualitatively distinct phases of wave diffraction, including counter-intuitive characteristics regarding the relationship between the strength of disorder and the wavepacket's velocity.

cond-mat.dis-nn↗

arXiv2023

Twisted polarization domains and their dynamics

We provide a theoretical investigation of optical Poincaré beams that exhibit interwinding chiral polarized domains upon propagation. We employ both analytical and numerical methods in order to investigate this phenomenon. Specifically, we introduce the theoretical framework that elucidates the formation and spiraling behavior of chiral polarized domains of light. Additionally, we define dynamic quantities that help us understand and quantify the angular motion of these domains. We apply this method to cylindrically symmetric optical beams, thereby unveiling their distinct radial and longitudinal propagation dynamics.

physics.optics↗

arXiv2022

Robustness versus sensitivity in non-Hermitian topological lattices probed by pseudospectra

Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectra theory on the prototypical non-Hermitian SSH (NHSSH) lattice. Topological modes are robust with respect to chiral perturbations and sensitive to parity-time (PT) symmetry preserving perturbations. In fact, the chiral symmetry exactly at the exceptional point leads to the suppression of its sensitivity, corresponding to a lower order exceptional point. However, counterintuitively, they are most sensitive with respect to unstructured perturbations, leaving the fingerprint of the pertinent higher order exceptional (HEP) point.

physics.optics↗

arXiv2021

Light confinement by local index tailoring in inhomogeneous dielectrics

The engineering of light confinement is a topic with a long history in optics and with significant implications for the control of light-matter interaction. In inhomogeneous and disordered media, however, multiple scattering prevents the application of conventional approaches for the design of light fields with desired properties. This is because any local change to such a medium typically affects these fields in a non-local and complicated fashion. Here, we present a theoretical methodology for tailoring an inhomogeneous one-dimensional (1D) Hermitian dielectric index distribution, such that the intensity profile of an incoming light field can be controlled purely locally, i.e., with little or no influence on the field profile outside of a designated region of interest. Strongly increasing or decreasing the light's intensity at arbitrary positions inside the medium thereby becomes possible without, in fact, changing the external reflectance or transmittance of the medium. These local modifications of the medium can thus be made undetectable to unidirectional far field measurements. We apply our approach to locally control the confinement of light inside 1D materials with inhomogeneous continuous refractive index profiles and extend it to multilayer films as well as to chains of coupled micro-resonators.

physics.optics↗

arXiv2021

Transport and spectral features in non-Hermitian open systems

We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their distribution is either the usual rectangular one or a binary pair-correlated one possessing, in its Hermitian version, delocalized states, and unusual transport properties. Contrary to the Hermitian case, all states in our non-Hermitian system are localized. In addition, the eigenvalue spectrum, for the binary pair-correlated case, exhibits an unexpected intricate fractallike structure on the complex plane and with increasing non-Hermitian disorder, the eigenvalues tend to coalesce in particular small areas of the complex plane, a feature termed "eigenvalue condensation". Despite the strong Anderson localization of all eigenstates, the system appears to exhibit transport not by diffusion but by a new mechanism through sudden jumps between states located even at distant sites. This seems to be a general feature of open non-Hermitian random systems. The relation of our findings to recent experimental results is also discussed.

cond-mat.dis-nn↗

arXiv2020

Shape-preserving beam transmission through non-Hermitian disordered lattices

We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenomena in the context of discrete photonics.

cond-mat.dis-nn↗

arXiv2019

Non-Hermitian disorder in two-dimensional optical lattices

In this paper, we study the properties of two-dimensional lattices in the presence of non-Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss distributions on every waveguide channel (on site disorder). Our work provides a systematic study of the interplay between disorder and non-Hermiticity. In particular, we study the eigenspectrum in the complex frequency plane and we examine the localization properties of the eigenstates, either by the participation ratio or the level spacing, defined in the complex plane. A modified level distribution function vs disorder seems to fit our computational results.

cond-mat.dis-nn↗

arXiv2015

Spectral method for efficient computation of time-dependent phenomena in complex lasers

Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time and space in conventional FDTD approaches. We describe here an efficient spectral method to overcome these shortcomings in complex lasers of arbitrary shape, gain medium distribution, and pumping profile. We apply this approach to a quasi-degenerate two-mode laser in different dynamical regimes and compare the results in the long-time limit to the Steady State Ab Initio Laser Theory (SALT), which is also built on a spectral method but makes a more specific ansatz about the long-time dynamical evolution of the semiclassical laser equations. Analyzing a parameter regime outside the known domain of validity of the stationary inversion approximation, we find that for only a narrow regime of pump powers the inversion is not stationary, and that this, as pump power is further increased, triggers a synchronization transition upon which the inversion becomes stationary again. We provide a detailed analysis of mode synchronization (aka cooperative frequency locking), revealing interesting dynamical features of such a laser system in the vicinity of the synchronization threshold.

physics.optics↗

arXiv2014

Scalable numerical approach for the steady-state ab initio laser theory

We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need of setting up a parametrized basis of constant flux states. We validate this approach in one-dimensional as well as in cylindrical systems, and demonstrate its scalability to full-vector three-dimensional calculations in photonic-crystal slabs. Our method paves the way for efficient and accurate simulations of lasing structures which were previously inaccessible.

physics.optics↗