Nonlinear Layered Structures Research Articles

Loss-compensated active nonlinear layered structures with gain saturation

In this paper, we investigate the possibility of using gain material to overcome losses in periodic semiconductor layered metamaterial. A generic approach, based on the modified transfer matrix method and perturbation theory, was devised here to take into account a gain saturation effect. It is demonstrated that the introduction of nonlinear saturation of the linear gain leads to nonreciprocal response of the system. Taking advantage of the conservation relation, we determine the relation between the gain coefficient and geometrical parameters of the layers to get full compensation of the losses in the nonlinear stack. It is obtained that depending on the parameters of the layers and angle of electromagnetic wave incidence, the full gain–loss balance in the nonlinear system can be maintained taking the gain coefficient above or below the threshold determined for the lossless linear stack. It is shown that the input intensity strongly affects the reflection and transmission coefficients for the nonlinear periodic stack and can be used as the additional mechanism to mitigate the losses.

Role of volume and surface spontaneous parametric down-conversion in the generation of photon pairs in layered media

A rigorous description of volume and surface spontaneous parametric down-conversion in 1D nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations which solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.

Об одном подходе к анализу резонансного рассеяния и генерации волн нелинейными слоистыми и периодическими структурами

Об одном подходе к анализу резонансного рассеяния и генерации волн нелинейными слоистыми и периодическими структурами

The multifunctional process of resonance scattering and generation of oscillations by nonlinear layered structures

AbstractThe paper focuses on the development of a mathematical model, an effective algorithm and a self-consistent numerical analysis of the multifunctional properties of resonant scattering and generation of oscillations by nonlinear, cubically polarizable layered structures. The multifunctionality of such layered media is caused by the nonlinear mechanism between interacting oscillations—the incident oscillations (exciting the nonlinear layer from the upper and lower half-spaces) as well as the scattered and generated oscillations at the frequencies of excitation/scattering and generation. The study of the resonance properties of scattering and generation of oscillations by a nonlinear structure with a controllable permittivity in dependence on the variation of the intensities of the components of the exciting wave package is of particular interest. In the present paper, we extend our former results, and furthermore we analyze the realizability of multifunctional properties of nonlinear electromagnetic ...

“Wandering” soliton in a nonlinear photonic crystal

On the basis of computer simulation, we demonstrate the possibility of a new type of “wandering” solitons implementation in nonlinear periodic layered structures. “Wandering” soliton moves across the layers, repeatedly changing its direction of motion due to the reflection from the photonic crystal (PC) boundaries with the ambient medium. The initial soliton is located inside a PC and occupies several of its layers. Its profile can be found as the solution of the corresponding nonlinear eigenvalue problem. “Wandering” solitons are formed as a result of a large perturbation of the wave vector, which leads to the soliton motion across photonic crystal layers. In the process of reflection from the boundary with the ambient medium, the soliton partly penetrates into the ambient medium at a depth equal to the width of several PC layers. A slow return of light energy, which previously left the PC, can take place at this moment.

Formation of an oscillating soliton near a photonic crystal surface

By means of computer simulation, we demonstrate the possibility of formation of a new type of surface solitons in nonlinear layered structures. The initial soliton is located inside a photonic crystal and occupies several of its layers. Its profile can be found from the solution to the eigenvalue problem for a nonlinear Schrodinger equation with periodic linear and nonlinear coefficients. Surface solitons are formed as a result of perturbation of the wave vector, which leads to soliton motion across photonic crystal layers. After several reflections from the side boundaries of the crystal, under certain conditions, the soliton becomes attached to the side boundary. A characteristic feature of the discussed soliton is the fact that its penetration depth into the photonic crystal medium is equal to the thickness of several crystal layers.

Photon-pair generation in nonlinear metal-dielectric one-dimensional photonic structures

Nonlinear metal-dielectric layered structures are shown to be able to efficiently generate entangled photon pairs using spontaneous parametric down-conversion. Increase of electric-field amplitudes in these structures enhanced by the presence of metal layers is sufficient to compensate for losses inside thin metal layers. As an example, photon pairs emitted from a structure composed of alternating nonlinear dielectric GaN layers and metal Ag layers are analyzed in spectral, temporal, as well as spatial domains. Also, correlations and entanglement between two photons in a pair are determined. Very narrow photon-pair spectra together with strong directionality of photon-pair emission are observed making the photons suitable for photon-atom interactions. Highly enhanced electric-field amplitudes provide high photon-pair generation efficiencies.

Влияние слабых полей кратных частот на процесс резонансного рассеяния и генерации колебаний нелинейными слоистыми структурами

Влияние слабых полей кратных частот на процесс резонансного рассеяния и генерации колебаний нелинейными слоистыми структурами

MATHEMATICAL MODELS OF ELECTRODYNAMICAL PROCESSES OF WAVE SCATTERING AND GENERATION ON CUBICALLY POLARISABLE LAYERS

Results of a self-consistent computational analysis based on a mathematical model of resonance scattering and generation of waves on an isotropic nonmagnetic nonlinear layered dielectric structure excited by a packet of plane waves are presented, where the analysis is performed in the domain of resonance frequencies. Physically interesting properties of the nonlinear permittivities of the layers as well as their scattering and generation characteristics are obtained, for instance the characteristic dynamical behaviour of the relative Q-factor of the eigenmodes and the energy of higher harmonics generated by canalising as well as decanalising nonlinear layers. The results demonstrate the possibility to control the scattering and generating properties of a nonlinear structure by means of the excitation intensities.

Multiple quasi-phase-matching in a one-dimensional aperiodically poled optical superlattice

A new method to enhance the output efficiency of the multi-frequency second harmonic generation process has been presented in the one-dimensional aperiodic optical superlattice by sandwiching linear layers between nonlinear media. The linear and nonlinear domain arrangements of aperiodic crystal are designed using the simulated annealing optimization method. The dependence of the output efficiency of second harmonic generation on the linear length has been investigated in detail; the most optimized structure being suggested. A comparison between pure nonlinear and linear–nonlinear layered structures is presented which shows an increasing amount of the output efficiency in the presence of linear layers for the nonlinear aperiodic crystals.

Spatial properties of entangled photon pairs generated in nonlinear layered structures

A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also, structures efficiently generated photon pairs showing antibunching and anticoalescence can be obtained. Three reasons for splitting the correlated area in photonic-band-gap structures are revealed: zig-zag movement of photons inside the structure, spatial symmetry, and polarization-dependent properties. Also, spectral splitting can be observed in these structures.

PARAMETER CONTROL OF OPTICAL SOLITON IN ONE‐DIMENSIONAL PHOTONIC CRYSTAL

The paper deals with finding of soliton solution for Schrödinger equation with periodic linear and nonlinear properties of medium in 1D case. Such structure is named as photonic crystal. To find soliton solution the corresponding problem for finding of eigenfunctions and eigenvalues is formulated. Iterative process is proposed for solution of this problem. Using the technique of continuation on parameter we investigate a dependence of soliton location on its maximum intensity, on ratio between light frequency and frequency of structure, on ratio between dielectric permittivity of alternating linear and nonlinear layers and on position between centre of initial distribution of eigenfunction and center of considered photonic structure area. The results of this paper confirm the features of soliton self‐formation investigated early in our papers [37, 38, 39, 40, 41, 42], in which one considered a propagation of femtosecond laser pulse through nonlinear layered structure.

Emission of photon pairs at discontinuities of nonlinearity in spontaneous parametric down-conversion

In order to fulfill the continuity requirements for electric- and magnetic-field amplitudes at discontinuities of ${\ensuremath{\chi}}^{(2)}$ nonlinearity, additional photon pairs have to be emitted in the area of discontinuity. Generalized two-photon spectral amplitudes can be used to describe properties of photon pairs generated in this process that we call surface spontaneous parametric down-conversion. The spectral structure of such photon pairs is similar to that derived for photon pairs generated in the volume. Surface and volume contributions to spontaneous down-conversion can be comparable as an example of nonlinear layered structures shows.

Photon-pair generation in random nonlinear layered structures

Nonlinearity and sharp transmission spectra of random 1D nonlinear layered structures are combined together to produce photon pairs with extremely narrow spectral bandwidths. Indistinguishable photons in a pair are nearly unentangled. Also two-photon states with coincident frequencies can be conveniently generated in these structures if photon pairs generated into a certain range of emission angles are superposed. If two photons are emitted into two different resonant peaks, the ratio of their spectral bandwidths may differ considerably from one and two photons remain nearly unentangled.

Random nonlinear layered structures as sources of photon pairs for quantum-information processing

Random nonlinear layered structures have been found to be a useful source of photon pairs with perfectly indistinguishable un-entangled photons emitted into a very narrow spectral range. Localization of the interacting optical fields typical for random structures gives relatively high photon-pair fluxes. By superposing photon-pair emission quantum paths at different emission angles, several kinds of twophoton states (including states with coincident frequencies) useful in quantum-information processing can easily be generated.

Surface Spontaneous Parametric Down-Conversion

Surface spontaneous parametric down-conversion is predicted as a consequence of continuity requirements for electric- and magnetic-field amplitudes at a discontinuity of chi;{(2)} nonlinearity. A generalization of the usual two-photon spectral amplitude is suggested to describe this effect. Examples of nonlinear layered structures and periodically poled nonlinear crystals show that surface contributions to spontaneous down-conversion can be important.

Quantum interference: experiments and applications

We describe the simplest single–photon encoding schemes and introduce the concept of a quantum optical gate. These gates can be used to build up arbitrary entangled states of many initially separate single photons. Experimental realization of such a gate involves the development of nonlinear phase shift elements sensitice at the single quantum level. We report our experimental efforts using linear optical elements and non–classical sources where we are able to demonstrate interference and entanglement of initially separate single–photon pulses.