Isotropic Kerr Media Research Articles

Generation of polarization singularities in the self-focusing of an elliptically polarized laser beam in an isotropic Kerr medium

We have numerically and analytically shown that polarization singularities can emerge when a homogeneously elliptically polarized light beam undergoes self-focusing in an isotropic third-order Kerr medium without frequency and spatial dispersion (fused silica, liquids, gases etc.) In the case of axially symmetric beam the emerging C-lines have the shape of circumference with the center at the beam’s axis and they are located in the separate transversal planes in the medium. If the axial symmetry of the incident beam is broken then the even number of C-points with opposite topological charges are nucleated in the medium. They exist in a certain propagation coordinate range and then they collide and annihilate each other.

Few-cycle vector solitons of light

We present a class of few-cycle elliptically polarized solitary waves in an isotropic Kerr medium. It is proved numerically that they are stable and can be easily excited during pulse propagation. We also propose a method of producing multisolitons with different polarization states and study their binary collisions. It is shown that collisional properties strongly depend on their relative polarization rotation.

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.

Phase matched vectorial three-wave mixing in isotropic Kerr media

A theoretical analysis of vectorial three-wave mixing in isotropic Kerr media is presented. The analysis based on the coupled-wave equations describes the amplification of a weak wave by coupling with a strong pump wave phase matched by optically induced change of average refractive index. The phase matching condition for interacting waves with different polarizations is calculated, allowing a large amplification of a weak wave by three-wave mixing in thick Kerr media. The main conclusions of our theoretical analysis are supported by the results of experiments in CS 2 liquid medium.

Proposal for electro-optic multiplier based on dual transverse electro-optic Kerr effect

A novel electro-optic multiplier is proposed, which can perform voltage multiplication operation by use of the Kerr medium exhibiting dual transverse electro-optic Kerr effect. In this kind of Kerr medium, electro-optic phase retardation is proportional to the square of its applied electric field, and orientations of the field-induced birefringent axes are only related to the direction of the field. Based on this effect, we can design an electro-optic multiplier by selecting the crystals of 6/mmm, 432, and m3m classes and isotropic Kerr media such as glass. Simple calculation demonstrates that a kind of glass-ceramic material with a large Kerr constant can be used for the design of the proposed electro-optic multiplier.

Fourier analysis of non-paraxial self-focusing

In this paper we deduce a vectorial non-paraxial equation describing the self-focusing of light in a homogeneous isotropic Kerr medium. The equation is derived via transformation to the spatial frequency domain, which clarifies the physical nature of the approximations made. We also present numerical solutions for a linearly polarized Gaussian input beam and discuss the dependence of the self-focusing length on beam width and input power.

Copropagation of two waves of different frequencies and arbitrary initial polarization states in an isotropic Kerr medium

Using a circularly polarized basis, we derive the differential equations governing the copropagation of two waves of different frequencies and arbitrary initial amplitudes and polarizations in an isotropic Kerr medium, and we give exact analytical solutions for waves that are initially linearly polarized. In this latter case, the ellipticities and orientations of both polarization ellipses generally vary periodically as the waves propagate through the medium; when each wave is linearly polarized, the deviation of the orientation of its polarization ellipse from its initial value is either zero or close to its maximum value. Situations are identified in which this deviation is close to \ensuremath{\pi}/2, thus allowing one wave to switch the other on and off with the aid of a linear polarizer placed at the exist from the medium. All the results obtained are generalizable to copropagation in nonbirefringent optical fibers.

Domain walls of linear polarization in isotropic Kerr media

We present a new type of domain-wall vector solitary waves in isotropic self-defocusing Kerr media. These domain walls consist of localized structures separating uniform field domains of orthogonal linear polarizations. They result from the interplay between diffraction, self-phase modulation and cross-phase modulation in cases where the nonlinear birefringence coefficient B = χxyyx(3)χxxxx(3) is negative. Numerical simulations show that these new vector solitary waves are stable.

Influence of transverse effects on self-induced polarization changes in an isotropic Kerr medium

Allowing for an isotropic optical nonlinearity of third order, we derive approximate Gaussian solutions of the paraxial wave equation. They describe a monochromatic elliptically polarized light signal of finite extension both in space and in time. In contrast to plane-wave results, the state of polarization is found to be strongly nonuniform in the transverse direction. Both the orientation and the shape of the polarization ellipse are not conserved. For low intensities, parameters measuring the induced optical activity depend on the intensity quadratically instead of linearly. For high intensities, saturation sets in. It is argued that by means of nonlinear ellipsometry one can evaluate two tensor components, namely, Re χxyyx(3) and Re χxxxx(3). Upon taking into account transverse as well as temporal effects, the magnitude of these components may decrease by a factor of 10.

Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media.

An analytical and numerical study of the coupled nonlinear Schr\"odinger equations that govern light propagation in isotropic Kerr materials reveals the existence of a novel class of bound vector solitary waves. These solutions are shown to bifurcate from circularly polarized solitons. For certain values of the wave parameters they represent stationary bound states of several linearly polarized solitons. These solitary waves may find application to optical communications where they have the potential to increase the bandwidth of transmission lines.

Spatial polarization instabilities due to transverse effects in nonlinear guided-wave systems

The elliptically polarized nonlinear beam propagation in a two-dimensional optical guided-wave system that contains isotropic Kerr media is solved numerically by using the finite-element method. Computed results for the nonlinear substrate exhibit novel transverse effects, such as spatial modulational instabilities for solitons emitted from the film. Since soliton emission can be interpreted in terms of self-induced Cerenkov radiation, these instabilities can be classified as Cerenkov instabilities. The sensitivity of the beam propagation to the initial state of polarization suggests the possibility of constructing new photonic devices.

Instabilities and chaos in the polarizations of counterpropagating light fields.

We show that the polarizations of counterpropagating light waves in an isotropic Kerr medium are temporally unstable when their total intensity exceeds a certain threshold value. Periodic and chaotic temporal behavior can occur in the output polarizations and under certain conditions also in the output intensities.

Optical multistability in collinear degenerate four-wave mixing

The theory of collinear degenerate four-wave mixing in a lossless, isotropic Kerr medium is described and solved numerically. Multiple solutions to the equations governing the spatial evolution of the probe and signal fluxes are found when the input fluxes exceed a critical intensity determined by the electric susceptibility and the interaction length of the medium. This treatment includes all phase-matched contributions to the equations of motion of all fields, including the cross-coupled waves appearing in the collinear geometry.