Nonlinear Dielectric Permittivity Research Articles

Modes of a Nonlinear Fiber Containing a Parabolic Graded-Index Core with Light Induced Variable Radius

"New features of the light localization in a nonlinear and graded-index medium in the case of radial symmetry are described analytically. The model of nonlinear graded-index fiber assumes that the dielectric permittivity changes abruptly when the electric field amplitude reaches a certain level. The dielectric permittivity depends on the polar radius according to a parabolic law, in the regions where the electric field amplitude exceeds a certain level. Explicit exact solution to the wave equation is found, in terms of the Whittaker function and the modified Bessel function of the second kind, describing a new type of optical localized structure. The influence of the propagation constant and parameters of the nonlinear graded-index dielectric permittivity on the field profile over the fiber radius is analyzed. It is derived that the core radius and the dielectric permittivity of the core depend on the propagation constant. The dependence of the core radius on the propagation constant causes the appearance of local dispersion."

A phenomenological model for the magnetodielectric effect in magnetoelectric composites

This paper proposes a phenomenological description for the nonlinear dielectric permittivity dependence on magnetic field, also called Magnetodielectric (MD) Effect, in strain mediated magnetoelectric composites. The description is derived by incorporating the dielectric dependence on electric polarization, thermodynamic constitutive equations, and magneto-mechanical effects. Moreover, the proposed expression successfully reproduces the experimental behavior reported in existing literature and can provide an explanation for the observed anisotropic effect. Simulations performed using the derived expression demonstrate an inherent correlation between the coupling of piezoelectric and magnetostrictive coefficients and the observed MD coefficient curves as measured in experiments. The validity of the model was verified by application to KNN/CFO and KNN/NFO multiferroic particulate composite samples.

Non-linear dielectric spectroscopy for detecting and evaluating structure-property relations in a P(VDF-TrFE-CFE) relaxor-ferroelectric terpolymer

Non-linear dielectric spectroscopy (NLDS) is employed as an effective tool to study relaxation processes and phase transitions of a poly(vinylidenefluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE)) relaxor-ferroelectric (R-F) terpolymer in detail. Measurements of the non-linear dielectric permittivity {varepsilon _{2}^{'}} reveal peaks at 30 and 80,^circC that cannot be identified in conventional dielectric spectroscopy. By combining the results from NLDS experiments with those from other techniques such as thermally stimulated depolarization and dielectric-hysteresis studies, it is possible to explain the processes behind the additional peaks. The former peak, which is associated with the mid-temperature transition, is found in all other vinylidene fluoride-based polymers and may help to understand the non-zero varepsilon _mathrm {2}^{'} values that are detected on the paraelectric phase of the terpolymer. The latter peak can also be observed during cooling of P(VDF-TrFE) copolymer samples at 100,^circC and is due to conduction and space-charge polarization as a result of the accumulation of real charges at the electrode–sample interface.

On the ferroelectric dc nonlinear dielectric permittivity and its relation with the macroscopic polarization

On the ferroelectric dc nonlinear dielectric permittivity and its relation with the macroscopic polarization

Macroscopic polarization in the nominally ergodic relaxor state of lead magnesium niobate

Macroscopic polarity and its dynamic response to external electric fields and temperature in the nominally ergodic relaxor phase of pristine lead magnesium niobate crystals and ceramics, Pb(Mg1/3Nb2/3)O3 (PMN), were investigated. Dynamic pyroelectric measurements provide evidence for persistent macroscopic polarity of the samples. Annealing experiments below and above Burns temperature of polarized samples relate this polarity to the presence of polar nano-entities and their dynamics. The dc electric field strength required for macroscopic polarization reversal is similar to the amplitude of the ac field where dynamic nonlinear dielectric permittivity reaches its maximum. Consequently, the aforementioned maximum is related to the reorientation of polar nano-entities. The results question the existence of an ergodic state in PMN below Burns temperature.

Effects of relativistic and ponderomotive nonlinearities on the interaction of high‐power laser beam with an inhomogeneous warm plasma

AbstractThe influence of relativistic‐ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high‐power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.

Characteristics of Self-Focusing of a Gaussian Laser Pulse Under Lateral and Axial Plasma Density Variations

In this paper, we present a paraxial description of relativistic self-focusing of a Gaussian laser beam in a plasma channel with the density distribution as a function of radial and axial variations. We have derived the nonlinear dielectric permittivity of plasma due to ponderomotive force and relativistic effects. The effect of different conditions of the inhomogeneous plasma and the laser pulse on self-focusing and defocusing of Gaussian laser beam propagation in the plasma is studied. We find that with an increase in the value of intensity of the beam, self-focusing enhances and shifts toward lower values of normalized propagation distance. The self-focusing length also increases with an increase in channel width. When the density rapidly increases along the propagation distance, the nonlinearity increases and gives self-focusing at shorter values of $z$ .

Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal.

The properties of hybrid nonlinear surface-phonon-plasmon-polaritons (SP3) at the interface of nonlinear medium and graphene-covered hexagonal boron nitride (hBN) are investigated theoretically. It is demonstrated that the hybrid nonlinear SP3 can be tuned by controlling the chemical potential, layer number and relaxation time of graphene. The real and imaginary parts of the propagation constant increase by decreasing the Fermi energy or the layer number of the graphene in the frequency outside of the upper Reststrahlen band of hBN. Moreover, we show that the nonlinear dielectric permittivity has great effect on the propagation constant. The real part of the propagation constant increases with positive nonlinear dielectric permittivity at different frequency for low frequency mode; while the imaginary part of the propagation constant decreases in the upper Reststrahlen band of hBN, keeps nearly constant in the lower band, and increases outside the Reststrahlen band with positive nonlinear dielectric permittivity for low frequency mode.

Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show that the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.

Absorption of short laser pulses in underdense plasma by considering ohmic heating and ponderomotive force effects

The effect of the non-relativistic ponderomotive force in the interaction of an intense laser pulse with isothermal and non-isothermal underdense collisional plasmas is studied. In this work by considering the ohmic heating of plasma electrons and the ponderomotive force, the nonlinear dielectric permittivity of the plasma medium is obtained and the equation of electromagnetic wave propagation is solved. It is shown that due to the effect of the ponderomotive force in both isothermal and non-isothermal plasmas, the increasing of laser pulse intensity leads to the steepening of the electron density profile and the narrowing of electron bunching. Since the ponderomotive force modifies the electron density and temperature distribution, the spatial damping rate of laser energy and the absorption coefficient are obtained in the collisional regime of isothermal and non-isothermal plasmas. It is shown that in these plasmas, the amplitude of the electric field is increased by increasing laser pulse energy while their wavelength is decreased. Furthermore, by increasing laser pulse intensity, the absorption coefficient is decreased strongly.

Nonlinear Steepening of Density Profile by Intense Laser Radiation in Collisional Inhomogeneous Plasmas

The interaction between a high-power electromagnetic wave with an inhomogeneous underdense plasma is studied by considering the ohmic heating caused by laser radiation. Considering the plasma inhomogeneity and ohmic heating, the nonlinear dielectric permittivity is obtained in the collisional regimes. The wave equation is numerically solved and the electromagnetic fields, electron density, electron temperature, and dielectric permittivity profiles are achieved. These profiles show that in the presence of three density profiles, by increasing the laser energy flux, the modified electron density deviates from background electron density and its structure near the critical density becomes highly peaked. Finally, it is found that the amplitude of electron density distribution decreases by increasing the laser wavelength.

Dielectric properties of [formula omitted] solid solutions

In this paper we present our measurements of the linear and nonlinear dielectric permittivity of 0.4Na0.5Bi0.5TiO3–(0.6-x)SrTiO3–xPbTiO3 solid solutions (x=0, 0.05, 0.1, 0.15). The dielectric anomaly increases in the system with respect to the concentration of lead, showing that interactions between dipolar entities are modified. The system exhibits dipolar-glass-like behaviour at low values of x (0⩽x<0.1). Relaxor behaviour emerges in the sample where x=0.1. Furthermore, a spontaneous first-order phase transition from relaxor to normal ferroelectric is observed at x⩾0.15. A few peculiar dispersion regions are observed in the ferroelectric phase, which we attribute to the coexistence of ferroelectric and dipolar glass phases. On the other hand, the nonlinear dielectric response indicates the existence of compressible polar nanoregions as common elementary dipolar entities in both relaxor and glass-like states. Dielectric spectra were approximated with empirical Cole–Cole or Havriliak–Negami equations. It is shown that the temperature dependencies of mean relaxation times, which were obtained from dielectric spectra, follow the Vogel–Fulcher equation in all samples. Moreover, distributions of relaxation times are obtained and a phase diagram is presented.

On the electrodynamic model of ultra-relativistic laser-plasma interactions caused by radiation reaction effects

A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notions, such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions, we show that about 50% of laser energy can be converted into gamma-rays in the optimal conditions of laser-foil interaction.

Nonlinear dielectric response and transient current: An effective potential for ferroelectric domain wall displacement

Ferroelectric domain walls are modeled as rigid bodies moving under the action of a potential field in a dissipative medium. Assuming that the dielectric permittivity follows the dependence ε′∝1/(α+βE2), it obtained the exact expression for the effective potential. Simulations of polarization current correctly predict a power law. Such results could be valuable in the study of domain wall kinetic and ultrafast polarization processes. The model is extended to poled samples allowing the study of nonlinear dielectric permittivity under subswitching electric fields. Experimental nonlinear data from PZT 20/80 thin films and Fe+3 doped PZT 40/60 ceramic are reproduced.

Linear and nonlinear dielectric properties of chloroform–bromoform and chloroform–dichloromethane liquid mixtures

Experimental linear and nonlinear dielectric permittivity and density data have been obtained for chloroform–bromoform and chloroform–dichloromethane liquid mixtures with different mole fractions at T=298.15K temperature. The experimental linear and nonlinear dielectric permittivity data are compared with the corresponding mean spherical approximation (MSA) based theoretical results. The comparison shows that the molecular dipole moments obtained from the MSA overestimate the gas-phase experimental dipole moments. Using the corresponding pure-component fitting data, the linear and nonlinear dielectric properties of the mixtures can be described within the experimental error.

Study of nonlinear ohmic heating and ponderomotive force effects on the self-focusing and defocusing of Gaussian laser beams in collisional underdense plasmas

In the present paper, the propagation characteristics of a linearly polarized gaussian laser beam in a non-isothermal underdense collisional plasma is studied. By considering the effects of the ponderomotive force and ohmic heating of plasma electrons as the nonlinear mechanisms, the second order differential equation of the dimensionless beam width parameter has been obtained and solved at several initial ion temperatures. Furthermore, by using the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the gaussian laser pulse, the perturbed electron density ne/n0e is obtained and its variation in terms of the dimensionless plasma length is analyzed at different initial ion temperatures. Our results show that the dimensionless beam width parameter is strongly influenced by the initial plasma ion temperature. It is found that, for the self-focusing regime, the plasma electron density perturbation continuously oscillates between the initial density distribution and a minimum, and for the defocusing regime, the plasma electron density perturbation continuously oscillates between the initial density distribution and a maximum.

Collisions effect in the heating of underdense plasma by a high-intensity short laser pulse

Nonlinear heating of collisional plasma when the temporal extent of the laser pulse is smaller than the ambipolar diffusion time has been investigated. The nonlinearity in a collisionless plasma arises through the ponderomotive force, whereas in collisional plasmas ohmic nonlinearity prevails. In this case, by considering the nonrelativistic ponderomotive force effect and the variation of the collision frequency between electrons and ions due to the temperature change, the nonlinear dielectric permittivity of the plasma medium is obtained and the equation of the electromagnetic wave propagation in underdense plasma is solved. It is shown that in this case, due to the ohmic heating of electrons, the effect of the ponderomotive force in the nonrelativistic regime leads to steepening of the electron density profile and decreases the temperature of the plasma electrons noticeably. Bunches of electrons in plasma become narrower and by increasing the laser pulse strength the wavelength of density oscillations decreases. In this regime of laser–plasma interaction, the electron temperature decreases sharply with increasing the intensity of laser pulses.

Modified tunable dielectric properties by addition of MgO on BaZr 0.25Ti 0.75O 3 ceramics

Phase composition, microstructure and tunable dielectric properties of (1 − x)BaZr 0.25Ti 0.75O 3– xMgO (BZTM) composite ceramics fabricated by solid-state reaction were investigated. It was found Mg not only existed in the matrix as MgO, there was also trace amount of Mg 2+ ions dissolved in the BZT grains, which led to Curie temperature of the BZTM composites ceramics shifting to below −100 °C. Dielectric permittivity of the BZTM composite ceramics was reduced from thousands to hundreds by manipulating the content of MgO. Johnson's phenomenological equation based on Devonshire's theory was used to describe the nonlinear dielectric permittivity of the ceramics with increasing applied DC field. With increasing content of MgO, anharmonic constant α ( T) increased monotonously. Dielectric permittivity was 672, while dielectric tunability was as high as 30.0% at 30 kV/cm and dielectric loss was around 0.0016 for the 0.6BaZr 0.25Ti 0.75O 3–0.4MgO sample at 10 kHz and room temperature.

Relativistic effects in the interaction of high intensity ultra-short laser pulse with collisional underdense plasma

In this paper, the effect of weakly relativistic ponderomotive force in the interaction of intense laser pulse with nonisothermal, underdense, collisional plasma is studied. Ponderomotive force modifies the electron density and temperature distribution. By considering the weakly relativistic effect and ohmic heating of plasma electrons, the nonlinear dielectric permittivity of plasma medium is obtained and the equation of electromagnetic wave propagation in plasma is solved. It is shown that with considering the ohmic heating of electrons and collisions, the effect of ponderomotive force in weakly relativistic regime leads to steepening the electron density profile and increases the temperature of plasma electrons noticeably. Bunches of electrons in plasma become narrower. By increasing the laser pulse strength, the wavelength of density oscillations decreases. In this regime of laser-plasma interaction, electron temperature increases sharply by increasing the intensity of laser pulse. The amplitude of electric and magnetic fields increases by increasing the laser pulse energy while their wavelength decreases and they lost their sinusoidal form.

Theory of wideband instability at combination frequencies of a plane electromagnetic wave propagating in a nonlinear medium

We study the propagation of electromagnetic waves in nonlinear media with the polynomial dependence of the dielectric permittivity on the intensity of the electric field. The instability of a plane wave with respect to noncollinear perturbations is studied in a wide band of combination frequencies. The perturbation growth rate and their dependencies on angles and frequencies are found. It is shown that waves with frequencies close to the second harmonic of the frequency of the propagating wave can increase faster than the perturbations in the case of the well-known modulation instability. We discuss application of the developed theory for the description of the light wave propagation in air, for which a representation of the nonlinear dielectric permittivity in the form of the electric field polynomial is known. The results of the work can be useful in explaining the properties of optical rogue waves.