arXiv subjects

Andrey V. Gorbach

Publications and source records attributed to Andrey V. Gorbach.

14 recordsLinked to original sources

arXiv2025

Topological gap solitons in equidistant lithium niobate waveguide arrays

Equidistant 1D arrays of thin film lithium niobate waveguides can exhibit non-trivial topology due to a specific interplay between inter- and intra-modal couplings of two families of guided modes. In this work we analyze two-colour spatial solitons, emerging due to $χ_2$ nonlinear interactions between the modes of non-trivial topology in the fundamental harmonic field, and modes of trivial topology in the second harmonic field. We discuss solitons localized in the bulk of the array (bulk solitons), and at an edge of a finite-size array (edge solitons). The latter emerge due to the nonlinear interactions between a topological edge mode in the fundamental harmonic and bulk modes in the second harmonic. We reveal that for each type of soliton, bulk or edge, there generally exist two families of solutions with different internal structures and ranges of propagation constants. All bulk solitons can only be excited above a certain power threshold dictated by the coupling strength in the second harmonic field and the phase matching between the fundamental and second harmonics. The power threshold for edge solitons generally appears to be much lower, and, by tuning the phase matching, it can be reduced to zero.

nlin.PS↗

arXiv2023

Topological edge states in equidistant arrays of Lithium Niobate nano-waveguides

We report that equidistant 1D arrays of thin-film Lithium Niobate nano-waveguides generically support topological edge states. Unlike conventional coupled-waveguide topological systems, the topological properties of these arrays are dictated by the interplay between intra- and inter-modal couplings of two families of guided modes with different parities. Exploiting two modes within the same waveguide to design a topological invariant allows us to decrease the system size by a factor of two and substantially simplify the structure. We present two example geometries where topological edge states of different types (based on either quasi-TE or quasi-TM modes) can be observed within a wide range of wavelengths and array spacings.

physics.optics↗

arXiv2021

Solitons near avoided mode crossing in $χ^{(2)}$ nanowaveguides

We present a model for $χ^{(2)}$ waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.

physics.optics↗

arXiv2020

Raman solitons in waveguides with simultaneous quadratic and Kerr nonlinearities

We analyse Raman-induced self-frequency shift in two-component solitons supported by both quadratic and cubic nonlinearities. Treating Raman terms as a perturbation, we derive expressions for soliton velocity and frequency shifts of the fundamental frequency and second harmonic soliton components. We find these predictions compare well with simulations of soliton propagation. We also show that Raman shift can cause two-component solitons to approach the boundary of their own existence and subsequently trigger soliton instabilities. In some cases these instabilities are accompanied by an almost complete transfer of power to the second harmonic, and emergence of a single-component Kerr solitonic pulse.

physics.optics↗

arXiv2019

Discrete Diffraction for Spectral Purification in Spontaneous Four Wave Mixing: a Recipe

Linear discrete diffraction of light within a waveguide array allows control over the longitudinal spatial profile of light. We propose a method of using this control to effectively modulate the nonlinearity in a spontaneous four wave mixing system. This allows the removal spurious frequency correlations between the generated signal and idler photon pairs. Weaving our method into a recipe for waveguide design, we demonstrate a spectral purity improvement from P = 0.78 to near saturation at P = 0.97, for a simple silicon-on-insulator geometry.

quant-ph↗

arXiv2019

Temporal quadratic solitons and their interaction with dispersive waves in Lithium Niobate nano-waveguides

We present a model of soliton propagation in waveguides with quadratic nonlinearity. Criteria for solitons to exist in such waveguides are developed and two example nano-waveguide structures are simulated as proof of concept. Interactions between quadratic solitons and dispersive waves are analysed giving predictions closely matching soliton propagation simulations. The example structures are found to support five different regimes of soliton and quasi-soliton existence. Pulse propagation in these example waveguides has been simulated confirming the possibility of soliton generation at experimentally accessible powers. Simulations of multi-soliton generation, Cherenkov radiation and quasi-solitons with opposite signs of dispersion in the fundamental and second harmonic are also presented here.

physics.optics↗

arXiv2019

Spontaneous Parametric Down-Conversion in asymmetric couplers: photon purity enhancement and intrinsic spectral filtering

We analyze the process of photon-pair generation via spontaneous parametric down-conversion in a quadratic nonlinear asymmetric waveguide coupler. The two waveguides have different geometry, such that light coupling only occurs within a narrow bandwidth of one of the generated (signal) photon modes, while the other (idler) photon together with the pump stay localized in one (driven) arm of the coupler. We demonstrate that such a setup represents a powerful and flexible tool for engineering spectral properties of generated photon pairs. Mode hybridization and dispersion of coupling can be utilized for shifting the balance between group velocities of interacting pump, signal and idler fields, subsequently leading to a significant increase of spectral factorisability (purity) of photons. We also show that for interaction lengths shorter than one beat length, generated pairs with signal photon being localized in the auxiliary (not pumped) arm of the coupler appear to be spectrally localized in both signal and idler components. The bandwidth of such intrinsic filtering of generated photons can be controlled by several geometrical parameters.

physics.optics↗

arXiv2019

Parametric Resonances and Resonant Delocalization in Quasi-Phase Matched Photon-pair Generation and Quantum Frequency Conversion

The existing widely-accepted theory of photon-pair generation via spontaneous down-conversion (SPDC) in nonlinear optical crystals and waveguides is incomplete, as it fails to account for the important physical phenomenon of parametric resonances. We demonstrate that exponential gain of classical fields in the regime of parametric resonance corresponds to resonant delocalization in the Glauber-Fock model of quantum SPDC. We propose a quantitative measure of localisation of Floquet eigen-modes as an analogue of classical gain to identify regimes of resonant delocalization. Using this method, we are able to reconstruct the classical "Arnold tongues" map of domains of instabilities for SPDC. We also predict novel regimes of resonant delocalization in the two-level model describing quantum frequency conversion processes.

physics.optics↗

arXiv2016

Perturbation theory for graphene integrated waveguides: cubic nonlinearity and third harmonic generation

We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\hbarω=(2/3)E_F$.

physics.optics↗

arXiv2015

Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects

The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self-frequency shift- ing solitons and dispersive waves is observed. A mechanism of broadening of the Cherenkov radiation through Hopf instability of the frequency locked solitons is also reported.

physics.optics↗

arXiv2006

Optical ratchets with discrete cavity solitons

We propose a setup to observe soliton ratchet effects using discrete cavity solitons in a one-dimensional array of coupled waveguide optical resonators. The net motion of solitons can be generated by an adiabatic shaking of the holding beam with zero average inclination angle. The resulting soliton velocity can be controlled by different parameters of the holding beam.

nlin.PS↗

arXiv2005

Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect

We study the two-dimensional extension of the Fano-Anderson model on the basis of a two-dimensional optical waveguide array with a bi-modal defect. We demonstrate numerically the persistence of the Fano resonance in wavepacket scattering process by the defect. An analytical approximation is derived for the total scattered light power.

nlin.PS↗

arXiv2004

Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schrödinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.

nlin.PS↗

arXiv2003

Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model

We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of 'exchange of stability' between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.

nlin.PS↗