Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.Comment: 6 pages, 5 figure

Propagation of light in complex photonic lattices with saturable nonlinearity

U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efekti koji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonske rešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, na primer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali, moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dve uniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako u nelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. U doktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričke metode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni i eksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćeni matematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina, tačnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostima Kerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenom metoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih u tezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) i Runge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultati pokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom, tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanje nelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, u nelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeni odgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju na postojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskoj strukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizom međusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih na površini rešetke.In this dissertation the linear and nonlinear effects accompanying the propagation of visible laser light through a different one-dimensional (1D) photonic lattices made of material with a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are both investigated, theoretically and experimentally. Due to the nonlinear response of these materials to the intensity of incident radiation, the light passing through the photonic lattice causes local change in the refractive index, providing necessary conditions for the formation of stable localized spatial structures at the interfaces between two uniform lattices of the same or different periods, and also within the binary superlattices, in the nonlinear regime, as well as in the linear regime when the localization occurs in the vicinity of the defect. In this dissertation, appropriate mathematical models are developed and various numerical methods for obtaining the relevant results are applied. Some of the results have been confirmed experimentally in 1D nonlinear photonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupled difference- differential equations, namely the 1D discrete nonlinear Schrödinger equation with the nonlinear term of Kerr and saturable type, while the stability of the obtained solutions was investigated using the method of linear stability analysis. To solve stationary and dynamic equations presented in this dissertation, numerical methods such as the Gauss-Newton and Runge-Kutta methods are performed, respectively. The obtained numerical and experimental results show that the presence of the defect affects the formation of localized modes in the nonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation of the nonlinear response of the medium. Furthermore, the results indicate to the possible appearance of the symmetry breaking of the mode profiles of certain nonlinear localized solutions when appropriate conditions are met. In the case of light propagation through binary superlattices, results show the emergence of new types of localized solutions and the opening of an additional gap in the observed energy spectrum of the lattice. Additionally, numerical results obtained by analyzing the mutual interaction of soliton solutions, as well as examining the properties of localized modes at the surface of the lattice, are presented as well

Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates

We introduce a discrete model for binary spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC) trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the SOC, while the usual hopping is negligible, \textit{emulates} condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components.\ Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.Comment: Journal of Physics B , in pres

Coupled vortex generator in active multi-core fibers

Optical vortex is a coherent localized structure carrying energy around the pivot point. It is characterized by an optical angular momentum (OAM) mathematically described by azimuthal phase term exp(ilφ). Here, the integer number l stands for the winding number or topological charge of the vortex [1]. Particularly interesting are vortices generated in discrete systems [2]. They are specified by quantized topological charge and exhibit inherent robustness on perturbations within the system [3]. One of the structures that support discrete vortices is multi-core fiber (MCF) [4]. Here, we study MCF structure composed of two concentric hexagonal rings, A and B (Fig. 1). Beside equal coupling constants among nearest sites of A and B ring, we also consider a presence of artificial flux (Φ) which affects coupling between sites in the A ring [5]. The presence of artificial flux does not change the topological charge of vortices, only shifts their corresponding eigenvalues. Moreover, vortex excitation in one of the rings produces a regular periodical energy exchange between A and B rings in a form of stable breathing coupled-vortex structure. In passive MCF the vortex excitation is necessary to propagate vortex through the system. However, including the saturable gain and linear loss in the MCF, the vortices of different topological charge can be excited even from the uniform background by tuning the flux value. Numerical simulations show high robustness of newly formed vortices, which offers possibility to utilize the proposed setup as highly controllable vortex generator. Moreover, this can be of particular importance in the ring array based lasers [6,7].IX International School and Conference on Photonics : PHOTONICA2023 : book of abstracts; August 28 - September 1, 2023; Belgrad

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

We consider a system of generalized coupled Discrete Nonlinear Schr\"{o}dinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are $\pm \pi/4$ with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin-orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts $\pi/2$ out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes.Comment: 18 pages, 11 figures. Revised version with minor additions to text and reference list. To be published in Journal of Physics Communication

Electromagnetic wave propagation through chiral metamaterials composed of twisted closed ring resonators

Chiral metamaterial consists of periodically placed resonant elements exhibiting chiral effects such as circular dichroism and optical activity. They appear due to the coupling of electric and magnetic fields which is result of an interaction of electromagnetic wave and chiral metamaterial. Numerous designs of chiral resonant elements are proposed providing applications for polarization conversion, filtering and absorption in THz frequency range [1, 2]. Here, we analyze propagation of electromagnetic waves through chiral metamaterial composed of twisted closed ring resonators (TCRR). The proposed chiral metamaterial is ultrathin structure which makes this design easy to fabricate and, at the same time, maintains effects which can be observed in conventional chiral 3D metamaterial structures. Dimensions of chiral elements are chosen to provide resonances within THz frequency range. Different geometrical parameters are varied in order to determine their influence on resonant frequency and losses [3]. For our TCRR chiral metamaterial structure, the analysis is made from microscopic as well as from macroscopic point of view. Through numerical simulations, we calculate electromagnetic field distribution, scattering coefficients, absorption and consequently, circular dichroism. Additionally, we examine losses in our chiral structure in terms of radiative and non-radiative ones [4] and explore its influence on the circular dichroism.VI International School and Conference on Photonics and COST actions: MP1406 and MP1402 : PHOTONICA2017 : August 23 - September 1, 2017; Belgrade

Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor

In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = = ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrad

Time Delay in Thin Dielectric Slabs with Saturable Nonlinearity

Time delays for an intense transverse electric wave propagating through a slab with saturable nonlinearity are investigated. The nonlinearity is assumed in a form of the Vinetskii-Kukhtarev model, which is relevant for the slabs made of nonlinear photorefractive crystals, such as GaAs and LiNbO(3), which feature a saturable nonlinearity. The expressions for the group delay and the dwell time are derived and the relation between them is studied. It is shown that the difference between them has three different contributions. The first one corresponds to the self-interference associated with the dispersion of the medium surrounding the slab. The other two appear due to the nonlinearity of the slab and oblique incidence of the transverse electric wave. All the results are compared with the case of dielectric slabs with cubic (Kerr) nonlinearity.10th Annual Conference of the Materials-Research-Society-of-Serbia, Sep 08-12, 2008, Herceg Novi, Montenegr

Propagation of light in photonic lattices with saturable nonlinearity comprising a defect

Linear and nonlinear effects accompanying the propagation of visible laser light through geometrically different one-dimensional photonic lattices made of material with a saturable nonlinearity are investigated, both theoretically and experimentally. Existence, stability and dynamics of various types of nonlinear localized modes (solitons) found to occur in lattices with a defect are explored. Additionally, the phenomenon of spontaneous symmetry breaking of a certain type of solitons is observed in symmetric lattices comprising a defect.4th International School and Conference on Photonics, Aug 26-30, 2013, Belgrade, Serbi

Modeling of tunneling times in anisotropic non-magnetic metamaterials

Tunneling times in an anisotropic structure composed of alternately placed layers of two linear, dispersive and absorptive materials are analyzed in this paper. For such a structure, a general expression for the relation between the two most common tunneling time definitions, namely the dwell time and the group delay, is obtained. Numerical calculations are performed for a new type of semiconductor metamaterial. The results show a peak position frequency mismatch between the dwell time and the group delay, and between the dwell time and the absorption.3rd International School and Conference on Photonics, Aug 29-Sep 02, 2011, Belgrade, Serbi