Impact of interparticle dipole-dipole interactions on optical nonlinearity of nanocomposites

In this paper, effect of dipole-dipole interactions on nonlinear optical properties of the system of randomly located semiconductor nanoparticles embedded in bulk dielectric matrix is investigated. This effect results from the nonzero variance of the net dipole field in an ensemble. The analytical expressions describing the contribution of the dipole-dipole coupling to nonlinear dielectric susceptibility are obtained. The derived relationships are applicable over the full range of nanoparticle volume fractions. The factors entering into the contribution and depending on configuration of the dipoles are calculated for several cases. It is shown that for the different arrangements of dipole alignments the relative change of this contribution does not exceed 1/3.Comment: 5 pages, 1 figur

Possibility of negative refraction for visible light in disordered all-dielectric resonant high index metasurfaces

Effective refractive index of disordered all-dielectric metasurfaces consisting of gallium phosphide (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532~nm. It is shown that a mixture of the high index nanoparticles with sizes close to the first magnetic and electric resonances randomly dispersed on metasurface may possess negative refraction. The dependence of the metasurface effective refractive index on the nanoparticle concentration and size is constructed. The feasibility of negative refraction at large concentrations of the high index resonant spheres is demonstrated. The negative effective refractive index is exhibited only for a monolayer of GaP spheres.Comment: 7 pages, 6 figures, 1 tabl

Giant enhancement and sign inversion of optical Kerr nonlinearity in random high index nanocomposites near Mie resonances

High index dielectric nanoantennas excited at Mie-type resonances have exhibited enormous enhancement of optical nonlinearity. Such nanostructures have been actively studied by researchers in the last years. The present work provides the first numerical analysis study of the optical Kerr effect of nanocomposites consisting of high refractive index (GaP) spheres at the wavelength of 532~nm. This is done by means of three-dimensional finite-difference time-domain (FDTD) simulations. The effective nonlinear refractive index of $0.8$~$\mu$m thick nanocomposites and metasurfaces is evaluated. It is shown that the optical Kerr nonlinearity of the nanocomposites rises by orders in proximity to Mie resonances and may exceed the second-order refractive index of the bulk material. It is revealed that the sign of the effective optical Kerr coefficient is inverted near the Mie resonances. This effect may be of interest in developing nonlinear optical metadevices.Comment: 8 pages, 7 figures, 2 table

Retrieving nonlinear refractive index of nanocomposites using finite-difference time-domain simulations

In this Letter, it is proposed a method which utilizes three-dimensional finite-difference time-domain (FDTD) simulations of light propagation for restoring the effective Kerr nonlinearity of nanocomposite media. In this approach, a dependence of the phase shift of the transmitted light on the input irradiance is exploited. The reconstructed values of the real parts of the nonlinear refractive index of a structure of randomly arranged spheres are in good agreement with the predictions of the effective medium approximations.Comment: 4 pages, 2 figures, 2 table

Optical Kerr nonlinearity of disordered all-dielectric resonant high index metasurfaces with negative refraction

The optical Kerr effect of material with negative refraction is estimated for the first time. This is done via three-dimensional finite-difference time-domain (FDTD) simulations of disordered bidisperse metasurfaces consisting of high index (GaP) spheres at the wavelength of 532~nm. The metasurfaces comprise spherical particles randomly arranged on plane having two sizes close to the magnetic and electric dipole Mie resonances. The real part of the effective nonlinear refractive index of the metasurfaces is computed in the vicinity of the Mie resonances where the metasurface possesses the negative index of refraction. The optical Kerr nonlinearity has a peak under the condition for the negative refraction. Intensity-dependent refractive index of the bidisperse metasurfaces is studied through concentration transition to the negative refraction state. It is shown that the nonlinear Kerr coefficient of the monolayer metasurface has maximum when the effective linear refractive index is close to zero.Comment: 5 pages, 4 figure

Reconstructing signal from fiber-optic measuring system with non-linear perceptron

A computer model of the feed-forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber-optic measuring system. The Gaussian distributions of some physical quantity are selected as learning patterns. Neural network is learned by error back-propagation using the conjugate gradient and coordinate descent minimization of deviation. Learned neural network reconstructs the two-dimensional scalar physical field with distribution having one or two Gaussian peaks.Comment: 3 pages, Latex, 1 postscript figur

Multivariate subordination of stable processes

This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out that they are more appropriate for describing stock prices if the amount of transactions is used for a stochastic time change. In this paper, we provide a detailed discussion of the model, which is based on two popular concepts - multivariate subordination and L{\'e}vy copulas.Comment: 2

Coadjoint orbits of the group UT(7,K)UT(7,K)

We present the classification of coadjoint orbits of the unitriangular group $UT(7, K)$. We also describe subregular orbits of $UT(n, K)$ for an arbitrary $n$.Comment: 27 page

Subregular characters of the group UT(n,R)

The formulas for subregular characters of the unitriangular Lie group are obtained. The supports of regular and subregular characters are described in terms of the orbit method.Comment: 14 page

Dipolar induced anisotropy in the random-field Ising model

The crystalline ferromagnet with dipole-dipole interactions is studied within the framework of the three-dimensional random-field Ising model. The field distribution function and the analytic expression for temperature dependent free energy are found. The dipolar induced magnetic anisotropy energy of bulk cubic ferromagnetic materials is calculated.Comment: LaTeX, 3 page