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.     

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.     

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.     

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.     

Self-focusing of electromagnetic waves in a degenerate electron-hole plasma

The free carrier nonlinear dielectric constant of a degenerate electron-hole plasma (e.g., Ge) in the presence of a Gaussian electromagnetic beam has been studied by a kinetic treatment. The redistribution of carriers (electrons and holes) is the source of nonlinearity and is effective in causing the self-focusing of the beam. The rise in carrier temperature due to the wave field is almost unaffected by the degeneracy, whereas the nonlinearity is considerably affected by it. The increase of degeneracy (by increasing the equilibrium carrier concentration at the fixed lattice temperature) increases the nonlinear dielectric constant. Hence self-focusing is enhanced by degeneracy. This work was supported by NSF (USA) and CSIR (India).     

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.     

Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma

In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.     

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.     

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.     

Relativistic Self-Focusing of Hermite-cosine-Gaussian Laser Beam in Collisionless Plasma with Exponential Density Transition

This work reveals an exploration of self-focusing of Hermite-cosine-Gaussian laser beam in a collisionless plasma under relativistic nonlinearity. Self-focusing along with self-trapping of Hermite-cosine-Gaussian laser beam are analyzed for different values of laser intensity, plasma density, and decentered parameters. Mathematical analysis displays that these parameters play a major role in achieving the stronger and earlier self-focusing. Further, a comparative study between self-focusing of Hermite-cosine-Gaussian laser beam with and without exponential density ramp profile is introduced. Plasma density transition with exponential profile is found to be more effective in order to have stronger self-focusing. The present analysis may lead to very useful applications in the field of efficient harmonic generation, laser driven fusion etc.     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

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.     

Shifting bright spatial solitons in LiNbO₃

We observe spatial bright solitons in a transversely shifting LiNbO₃ crystal. In this scheme, the photovoltaic nonlinearity in LiNbO₃ can be switched from self-defocusing to self-focusing by continuous shifting of the beam. Moreover, the shifting velocity has a strong influence on the wave shape of the bright spatial solitons.     

Lie-optic matrix algorithm for computer simulation of paraxial self-focusing in a plasma

Propagation algorithm for computer simulation of stationary paraxial self-focusing laser beam in a medium with saturating nonlinearity is given in Lie-optic form. Accordingly, a very natural piece-wise continuous Lie transformation that reduces to a restricted Lorentz group of the beam results. It gives rise to a matrix method for self-focusing beam propagation that is constructed and implemented. Although the results use plasma nonlinearities of saturable type, and a gaussian initial beam, these results are applicable for other media like linear optical fibers and to more general situations.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

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-focusing effects in a nematic liquid crystal at 10.6 $\mathsf{\mu}$m

E7 is a room temperature nematic liquid crystal that presents both a high temperature nematic-to-isotropic transition and a high positive dielectric anisotropy. The optical characteristics of this liquid crystal have been widely investigated in the visible region of the spectrum, while less experiments have been performed in the middle infrared spectral region, where, nevertheless, potential applications are important. We investigate the self-focusing of a middle infrared laser beam when it passes through a film of E7. We also take into account the heating of the liquid crystal film caused by the partial absorption of the laser light by means of a thermographic technique. A theoretical interpretation of the self-focusing phenomenon is given in terms of the reorientation of the molecules with respect to their unperturbed direction and an estimation of the average value of the elastic constants of the liquid crystal is given by fitting the experimental data with the theoretical model.Received: 16 April 2003PACS: 42.70.Df Liquid crystals - 42.65.-k Nonlinear optics - 42.55.Lt Gas lasers including excimer and metal-vapor lasers