Related papers: Long-range interaction and nonlinear localized mod…
We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals…
We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even…
In this article, localized linear defect modes due to bandgap guidance in two-dimensional photonic lattices with localized or non-localized defects are investigated theoretically. First, when the defect is localized and weak, eigenvalues of…
Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is…
In this article, we present a numerical study of the optical properties of a metal nanowire interacting with a localized cavity in a two dimensional photonic crystal. The nature of the modes, their wavelength and width are investigated as a…
Guided wave optics, including most prominently fiber optics and integrated photonics, very often considers only one or very few spatial modes of the waveguides. Despite being known and utilized for decades, multi-mode guided wave optics is…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be…
Near the band edge of photonic crystal waveguides, localized modes appear due to disorder. We demonstrate a new method to elucidate spatial profile of the localized modes in such systems using precise local tuning. Using deconvolution with…
We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as the cases of effectively defocusing and…
Artificial intelligence in the form of deep learning is now very popular and directly implemented in many areas of science and technology. In the present work we study time evolution of Discrete Breathers in one-dimensional nonlinear chains…
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…
Here, extending our previous work on this topic, we derive a dynamic closed-form dispersion relation for a rigorous analysis of guided wave propagation along coupled parallel linear arrays of plasmonic nanoparticles, operating as optical…
It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such…
We derive general coupled-mode equations describing the nonlinear interaction of electromagnetic modes in media with loss and gain. Our approach is rigorously based on the Lorentz reciprocity theorem, and it can be applied to a broad range…
We demonstrate the spontaneous formation of spatial patterns in a damped, ac-driven cubic Klein-Gordon lattice. These patterns are composed of arrays of intrinsic localized modes characteristic for nonlinear lattices. We analyze the…
Synthetic photonic lattice with temporally controlled potentials is a versatile platform for realizing wave dynamics associated with physical areas of optics and quantum physics. Here, discrete optics in one-dimensionally synthetic photonic…
A theoretical study of photonic bands for one-dimensional (1D) lattices embedded in planar waveguides with strong refractive index contrast is presented. The approach relies on expanding the electromagnetic field on the basis of guided…
Atom arrays are a new type of quantum light-matter interface. Here, we propose to employ one-dimensional ordered arrays as atomic waveguides. These arrays support optical guided modes that do not decay into free space. We show that these…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…