Isotropic Nonlinear Medium Research Articles

Approximate solutions to a nonintegrable problem of propagation of elliptically polarised waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes

Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and ‘chaotic’ change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed.

The angle between the stress deviator and the strain-rate deviator in a tensor nonlinear isotropic medium

An expression for the angle between the symmetric stress deviator and the strain-rate deviator in a tensor nonlinear isotropic continuous medium is derived. A dependence of this angle on a certain orientation parameter in the three-dimensional space of principal strain rates is analyzed.

Chirped elliptically polarized waves in an isotropic gyrotropic nonlinear medium: approximate solution to the propagation problem

An approximate solution to the nonintegrable propagation problem for chirped elliptically polarized waves in an isotropic gyrotropic medium with local and non-local parts of the cubic nonlinear optical response and second order frequency dispersion has been obtained. Conditions for excitation of waves with periodic changes in the polarization state (chirped elliptically polarized cnoidal waves) and implementation of aperiodic propagation regimes similar to polarization ‘chaos’ have been determined.

Magnetoelectric birefringence as a unique effect in isotropic media

Aspects of magnetoelectric birefringence phenomena are investigated in the context of electromagnetic wave propagation in isotropic nonlinear media in the eikonal approximation. It is shown that these phenomena can be produced as a unique effect in isotropic systems in the presence of external electric and magnetic fields, provided specific dielectric properties are present.

A Discrete Geometric Approach to Solving 2-D Non-Linear Magnetostatic Problems

The aim of this paper is to introduce a Discrete Geometric Approach to solving 2-D non-linear magnetostatic problems. In particular, an efficient algorithm will be presented to solve magnetostatics in isotropic non-linear media by means of a Newton-Raphson scheme, in which the Jacobian is calculated analytically. Results on a reference configuration (TEAM Workshop Problem 25) are reported and discussed.

Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices

We report our recent work on self-trapping of doubly-charged vortices (DCVs) in two-dimensional optically induced photonic lattices. We show that in an ideal isotropic nonlinear periodic medium self-trapping of a DCV can lead to formation of a rotating ‘quasi-vortex’ soliton with periodic charge-flipping, but the vortex breaks up into multiple singly-charged vortices in an anisotropic nonlinear medium. Such topological transformation of high-order vortices under conventional four-site excitation in a square photonic lattice has been observed in our experiment and corroborated with numerical simulations. With geometrically extended eight-site excitation, however, discrete self-trapping of a DCV into a stable high-order vortex soliton can be realized with both self-focusing and self-defocusing nonlinearities.

Intensity-dependent change in polarization state of light in normal incidence on an isotropic nonlinear Kerr medium

It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.

Theoretical investigation and computational modeling of the difference frequency generation by interaction of few cycle laser pulses in a GaAs crystal

We present the results of theoretical studies of the generation process of difference frequency radiation arising via interaction of mutually orthogonal linearly polarized few-cycle laser pulses propagating in an isotropic nonlinear medium. Numerical time-integration by the finite-difference method of nonlinear Maxwell-equation systems has been performed. We consider the interaction of pulses having the central wavelengths of 1.98 and 1.55 µm, duration of 30 fs with the corresponding electric field amplitudes of 295 × 106 and 463 × 106 V m−1, propagating along the normal to the ⟨110⟩ plane in 854 µm thickness of GaAs crystal. The process of difference frequency pulse formation arising via spectral filtration of a supercontinuum formed in the spectra of pump pulses at the output of a nonlinear crystal is studied.

Modeling the terahertz radiation generation process, obtained by filtration of spectral supercontinuum, formed during propagation of femtosecond laser pulse in GaAs crystal

We present the results of theoretical studies of the process of generation of terahertz radiation arising via interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium. Numerical time-integration, by the finite-difference method, of the system of nonlinear Maxwell equations has been performed. We consider the interaction of mutually-orthogonal linearly polarized pulses, both having the central wavelength of 1.98 μm, durations of 30 fs, and the energies of 30 nJ, propagating along the normal to the 〈110〉 plane in a 1 mm-thickness GaAs crystal. In the nonlinear part of the medium polarization the without-inertia nonlinear second-order susceptibility is taken into account. The process of formation of a terahertz pulse arising via spectral filtration of supercontinuum formed in the spectra of pump pulses at the output of nonlinear crystal is studied. The dependences of both the current frequency of the pump pulses on time for different lengths of nonlinear crystal and of pump pulse durations on the crystal length are obtained. Also the dependences of the current frequency of the terahertz pulse on time at different crystal lengths, as well as of the efficiency of generation of terahertz radiation on the length of nonlinear crystal and on the energy of pump pulses are obtained.

Generation of terahertz radiation upon filtration of a supercontinuum produced during the propagation of a femtosecond laser pulse in a GaAs crystal

The results of a theoretical study of the formation of a supercontinuum produced due to the interaction of femtosecond laser pulses with an isotropic nonlinear medium are presented. The system of nonlinear Maxwell's equations was numerically integrated in time by the finite-difference method. The interaction of mutually orthogonal linearly-polarised 1.98-μm, 30-fs, 30-nJ pulses propagating along the normal to the 110 plane in a 1-mm-long GaAs crystal was considered. In the nonlinear part of the polarisation medium, the inertialless second-order nonlinear susceptibility was taken into account. The formation process of a terahertz pulse obtained due to the supercontinuum filtration was studied.

Evolutions of polarization and nonlinearities in an isotropic nonlinear medium

The evolutions of polarization and nonlinearities in an isotropic medium induced by anisotropy of third-order nonlinear susceptibility were studied experimentally and theoretically. The anisotropy of imaginary part of third-order susceptibility was verified to exist by the change of ellipticity of polarization ellipse in the isotropic nonlinear medium CS(2). The changes of nonlinear refraction and nonlinear absorption depending upon the ellipticity of polarization ellipse are also presented. The numerical simulations based on two coupled nonlinear Schrödinger equations (NLSE) provide an excellent quantitative agreement with experimental results.

Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium

The change in nature of light in propagation through a lossless isotropic nonlinear Kerr medium is studied. Considering a monochromatic unidirectional light beam, we see that coherent light remains coherent but the polarization state changes in general, and completely unpolarized light retains its nature in all respects. For a light beam having a coherent signal and unpolarized noise, a change in polarization state of the signal and depolarization occurs in general. For circular and plane polarized signals, the polarization states of the signal do not change and depolarization is absent for the former and maximum for the latter. Numerical calculations for a practical case indicate that these effects are observable.

Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons

We introduce a new class of elliptically modulated self-trapped singular beams in isotropic nonlinear media where nonlocality plays a crucial role in their existence. The analytical expressions in the highly nonlocal nonlinear limit of these elliptically shaped self-trapped beams, or ellipticons, is obtained and their existence in more general nonlocal nonlinear media is demonstrated. We show that the ellipticons represent a generalization of several known self-trapped beams, for example vortex solitons, azimuthons, and the Hermite and Laguerre solitons clusters. For the limit of the highly nonlocal nonlinear medium, the ellipticons are described in close form in terms of the InceGauss functions.

Interaction of few-cycle laser pulses in an isotropic nonlinear medium

The interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium is studied theoretically. A system of nonlinear Maxwell's equations is integrated numerically with respect to time by the finite difference method. The interaction of mutually orthogonal linearly polarised 0.81-μm, 10-fs pulses is considered. Both the instant Kerr polarisation response and Raman inertial response of the medium in the nonlinear part of the medium are taken into account. The spectral shift of the probe pulse caused by the cross-action of the reference pulse is studied. The spectra of the interacting pulses are studied for different time delays between them and the shifts of these spectra are obtained as a function of the time delay.

Third-harmonic generation in isotropic media by focused pulses

For focused pulses of light in isotropic nonlinear media, third-harmonic generation can be strongly affected by group-velocity mismatch between the fundamental and third-harmonic. There is a characteristic time determined by the group-velocity mismatch and the Rayleigh range of the focused pulse. The dynamics depend on two dimensionless quantities, namely the ratio of the characteristic time to the pulse duration and the phase-velocity mismatch times the Rayleigh range. Pulses shorter than the characteristic time have physics described by simple analytic formulas. Pulses near the characteristic time have an intermediate behavior given by an explicit but more complicated formula. Pulses longer than the characteristic time tend to the continuous-wave case.

Vector Soliton Fission

We investigate the vectorial nature of soliton fission in an isotropic nonlinear medium both theoretically and experimentally. As a specific example, we show that supercontinuum generation in a tapered fiber is extremely sensitive to the input state of polarization. Multiple vector solitons generated through soliton fission exhibit different states of elliptical polarization while emitting nonsolitonic radiation with complicated polarization features. Experiments performed with a tapered fiber agree with our theoretical description.

Polar light and symmetry of electro-optical effects

General regularities of the interaction of a polar light wave synthesized from the Fourier harmonics of a fundamental frequency with a transparent centrosymmetric optically nonlinear medium are considered. The notion of light polarity is introduced and transverse electro-optical effects specific for the problem of interaction between polar light and isotropic nonlinear media (optical rectification and the linear electro-optical effect) are analyzed. Estimates of values of the effects in combination with published experimental data on optically encoded second harmonic generation in glasses indicate promising opportunities for practical application of the effects of the interaction of polar light and matter in optical systems of information recording and processing.

CHANGE IN THE POLARIZATION STATE AND THE INTENSITY OF A WEAK LIGHT BEAM IN A LOSSY ISOTROPIC NONLINEAR MEDIUM IN THE PRESENCE OF AN INTENSE CO-PROPAGATING LIGHT BEAM

The effect of an intense plane wave on a co-propagating weak plane wave in a lossy isotropic nonlinear medium is studied using the exact solution of H. Prakash et al.1 The presence of a plane-polarized intense beam changes the initial circular polarization of the weak beam to elliptical in general. The plane containing the direction of the major axis and the propagation oscillates about the plane of polarization of the intense beam. At the extreme positions, the elliptical polarization reduces to plane polarization and switches its handedness. For the lossless case, the plane of the major axis remains fixed at 45° to the plane of polarization of the intense beam and the polarization oscillates between circular and plane, switching the handedness when the plane polarization occurs, and there effects are periodic in distance within the medium. The presence of a circularly polarized intense beam changes the initial plane polarization of the weak beam to elliptical, whose major axis rotates in propagation. For the lossless case, the weak beam remains plane-polarized and rotates at a uniform rate in propagation. Suggestions for experimental observations of these effects are given and the values of observable quantities estimated for carbon disulfide.

Fresnel analysis of wave propagation in nonlinear electrodynamics

We study the wave propagation in nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of general nonlinear Lagrangian models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains non-trivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

Polarization effects in nanoaggregates of silver caused by local and nonlocal nonlinear-optical responses

A theoretical and experimental study is made into the combined manifestation of local and nonlocal optical responses in a cubic nonlinear isotropic medium such as an aggregated colloidal silver solution. The phenomenological treatment of polarization effects is performed for the general case with due regard for the frequency dispersion of both local and nonlocal nonlinearities and for the noncollinear propagation of pump and probe light waves. The inverse Faraday effect, the optical Kerr effect, and the self-rotation of the polarization ellipse in a fractal-disordered nonlinear medium are observed for the first time. The tensor components of the local and nonlocal cubic nonlinearities of colloidal silver solutions are measured for different degrees of aggregation. It is demonstrated that, as the size of silver aggregate increases, the nonlocal nonlinear response increases much more strongly than the local one. An inference is made that the mechanical motion of metal nanoparticles because of their dynamic interaction with the light wave field can contribute to the nonlinear polarization effects.