Self focusing of laser beams in a degenerate nonparabolic semiconductor: Kinetic approach

Using rigorous kinetic treatment the steady state self-focusing of laser beams in a degenerate nonparabolic semiconductor (e.g. n-InSb) has been investigated beyond the perturbation limit. The nonlinearity arises due to the energy dependence of the electron mass in the conduction band. The energy loss of electron energy is assumed to be due to polar optical phonons and momentum transfer due to ionised impurity scattering/polar optical phonon scattering. It is found that nonlinearity in the dielectric constant or the self-focusing is more pronounced in the case of ionised impurity case as compared to polar optical phonon case. The effect of absorption is to suppress the self-focusing but the latter is also enhanced by degeneracy.     

Hybrid nonlinearity supported by nonconventionally biased photorefractive crystals

We theoretically and experimentally demonstrate that a nonconventionally biased photorefractive crystal can support hybrid nonlinearity, i.e., coexistence of self-focusing and self-defocusing nonlinearities under an identical bias condition. It is revealed that the nonlinearity experienced by a one-dimensional (stripe) beam can be switched between self-focusing and self-defocusing solely by changing the beam orientation. For a two-dimensional beam, the hybrid nonlinearity leads to unusual nonlinear beam dynamics with enhanced anisotropy and nonlocality.     

Effect of Higher Order Axial Electron Temperature on Self-Focusing of Electromagnetic Pulsed Beam in Collisional Plasma

Effect of higher order axial electron temperature on self-focusing of electromagnetic pulsed beam in collisional plasma is investigated. It is shown that higher order axial electron temperature T_p4 is not trivial than T_p0 and T_p2, which can modify slightly radial redistribution of electron density and increases effective dielectric constant. As a result, on one hand, slightly reduce electromagnetic beam self-focusing in the course of oscillatory convergence, on the other hand, quicken beam divergence in the course of steady divergence, i.e., higher order axial electron temperature T_p4 can decrease the influence of collisional nonlinearity in collisional plasma.     

Wideband modulation instability at combination frequencies in wave beams

We study theoretically wideband modulation instability at combination frequencies in media having cubic nonlinearity of self-focusing type along with the higher-order defocusing nonlinearity. It is assumed that in a medium with a purely cubic nonlinearity, the medium dispersion does not permit modulation instability. In this case, a collapse of the wave field exists if the beam power is higher than the critical power of self-focusing. The higher-order nonlinearity limits the field at the nonlinear focus, and the instability at combination frequencies becomes possible. It turns out that the field at the nonlinear focus increases with increasing excess of the beam power over the critical power of self-focusing. The obtained values of the nonlinear dielectric permittivity are used for determination of the growth rates of instability at combination frequencies. These growth rates ensure an increase in the combination fields from noise levels up to values comparable with the field of the high-power beam. Such an increase takes place if the beam power is severalfold higher than the critical one. The developed theory can be used for explanation of spectrum superbroadening during self-focusing of sufficiently short laser pulses and high-harmonic generation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 522–532, June 2007.     

Enhancement of self focusing of laser beams in a degenerate magnetoactive solid state plasma

This paper presents an investigation of the enhancement of self focusing of high frequency EM waves in a compensated degenerate magnetoactive solid state plasma. The nonlinearity in the dielectric constant responsible for self focusing arises due to nonuniform heating and consequent redistribution Of carriers. A rigorous kinetic treatment valid beyond the perturbation limit has been presented assuming the carrier relaxation time to be energy dependent. The results show that the self-focusing of extraordinary waves is enhanced while that of ordinary waves is reduced with $\text{ω}{}_{\mathrm{c}}\text{ω}$ increasing. However the focusing of extraordinary waves is not possible when ω_c > ω. The effect of degeneracy is also found to enhance the self-focusing of the waves while that of the enhanced absorption is to suppress the self-focusing process.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity:Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated.An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field,with linear absorption and due to saturation effects for arbitrary large intensity.The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters.Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode.Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence.The beam is more focussed at lower intensity in both cases viz.extraordinary and ordinary mode.     

Coupling surface plasmon waves across gaps in a dielectric/metal interface by transformation optics

Propagation of a Gaussian laser beam in a plasma is analyzed by including the nonlinearity associated with the relativistic mass and the ponderomotive force. We set up the nonlinear differential equation for beam width parameter using parabolic equation approach and solve it numerically. Our results show that the ponderomotive self-focusing contributes in the relativistic self-focusing of the laser beam. An impact of plasma electron temperature, relative density parameter, and intensity parameter on the propagation of the laser beam has been explored.     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Adiabatic self-focusing in media with spatially variable nonlinearity

An optical medium whose nonlinearity can be spatially adjusted is considered to study beam reshaping. The concept is applied to perform adiabatic self-focusing of broad beams. Experimental results are obtained in a photorefractive lithium niobate crystal where the self-focusing nonlinearity is controlled over propagation by a temperature gradient. As a demonstration, gradual self-focusing is shown to transform an incoming beam into an output circular spot 10 times smaller over a 2 cm long crystal submitted to a 30 °C temperature gradient. Once formed, the adiabatic self-focused beam has inscribed a funnel waveguide in the crystal.     

New solutions in the theory of self-focusing with saturating nonlinearity

On the basis of an approximate analytic solution of a Cauchy problem for a nonlinear Schrödinger (NLS) equation describing steady-state light beams in a medium with saturating nonlinearity by the method of renormgroup (RG) symmetries, a classification of self-focusing solutions is given depending on two control parameters: the relative contributions of diffraction and nonlinearity and the saturation strength of the nonlinearity. The existence of tube-type self-focusing solutions is proved for an entering beam with Gaussian radial distribution of intensity. Numerical simulation is carried out that allows one to verify the theory developed and to determine its applicability limits.     

Self-focusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient

In this paper, the propagation of Cosh Gaussian laser beam and its interaction with isothermal plasma without temperature gradient as well as the effect of the exponential electron temperature gradient are investigated. Here the ponderomotive nonlinearity force is effective mechanism. This force can modify the electron density distribution. All the investigations are carried out for different initial plasma temperatures. Using Maxwell’s equations we obtained the nonlinear second-order differential equation of the dimensionless beam-width parameter (f) on the distance of propagation for several initial electron temperatures and exponential temperature variations. These equations are solved numerically by taking WKB and paraxial approximation. Under the effect of initial electron temperature, self-focusing and defocusing of hyperbolic cosine (cosh) Gaussian laser beam is distinguished. Furthermore, the exponential temperature gradient cause to stationary propagation mode breaks, and self-focusing or defocusing properties is observable.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Steady-state vortex-screening solitons formed in biased photorefractive media

We report the observation of steady-state photorefractive vortex-screening solitons. As a singly charged circular vortex nested on a broad beam propagates through a biased strontium barium niobate crystal, it self-traps in both transverse dimensions despite the inherent anisotropy of the photorefractive nonlinearity. When the vortex beam is a doughnut-shaped narrow beam, it breaks up into two elongated slices (with a self-defocusing nonlinearity) or into two focused filaments (with a self-focusing nonlinearity). We demonstrate the optical guidance of a probe beam in a circular waveguide induced by the self-trapped vortex.     

具有电与磁非线性效应超常介质中光束的聚焦特性

基于Drude模型,采用解析法与数值模拟法研究了具有电与磁非线性效应超常介质中光束的聚焦特性。结果表明超常材料中光束聚焦现象不但可以发生在自聚焦非线性介质中(正折射区)而且可以发生在自散焦非线性介质中(负折射区),且光束中心频率离介质的等离子频率越近,其聚焦效应越明显。特别是当电与磁非线性极化率为异号时,超常介质的非线性符号可以通过调控电与磁等离子频率的相对大小控制,这为主动操控光束的传输提供一种新的自由度。     

Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes,gap solitons and truncated nonlinear Bloch waves,in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,supported by a combination of linear and nonlinear periodic lattice potentials.The former is found to be stable once placed inside a single well of the nonlinear lattice,it is unstable otherwise.Contrary to the case with constant self-focusing nonlinearity,where the latter solution is always unstable,here,we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices.The practical possibilities for experimental realization of the predicted solutions are also discussed.     

Formation of elliptically polarized ring-shaped electric field structures on the self-focusing of light in an isotropic medium featuring a spatially disperse nonlinearity

The possibility is demonstrated that the self-focusing of an elliptically polarized beam in a medium featuring a spatially disperse cubic nonlinearity can give rise to several radially symmetric ring-shaped regions of the same sense of rotation (right or left) of the electric-field vector in the cross-section of the beam. The formation dynamics and propagation features of such electric field structures are studied for various parameters of the incident radiation and nonlinear medium.     

Self-focusing of elliptically shaped high-power laser beams in a fully ionized plasma

The effect of self-focusing of a high-power light beam with an elliptical cross-section in a strongly ionised plasma has been evaluated. The mechanism of self-focusing considered is non-uniform heating of plasma by an electromagnetic wave having transverse variation of amplitude along its wave front. The heating causes redistribution of carriers which lead to a nonlinear relationship between the electron density and the electric vector and hence to a field-dependent effective dielectric constant. It is found that the beam gets focused at different focal points in different directions exhibiting the effect of astigmatism. There are several critical powers, below thex=0,y=0 planes; at higher powers one dimension focuses while the other defocusses, an oscillatory waveguide is formed in both dimensions. Above the highest critical power both dimensions self-focus, the dimensionless beam width parametersf ₁ andf ₂ forx andy focusing reach different minima corresponding to different self-focusing distances beyond which both dimensions continue diverging. The effect of energy loss through absorption from the beam has also been considered. It has been observed that absorption brings about a reduction in the extent of self-focusing and favours defocusing of the beam.