Kerr-like Media Research Articles

Extreme self-compression of laser pulses in the self-focusing mode resistant to transverse instability

We show that a self-focusing mode for intense laser pulses comprising less than about ten optical cycles is resistant to the transverse modulational instability. For such pulses, a method of pulse self-compression based on adiabatic decrease of the duration of a solitonlike wave packet and transverse cumulating of energy during the self-focusing in Kerr-like media with anomalous dispersion is proposed. This method can be used for generation of high-quality, high-energy, few-cycle pulses down to a single-cycle duration.

Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schrödinger Equation

In this paper, we consider two singular nonlinear planar dynamical systems created from the studies of one-dimensional bright and dark spatial solitons for one-dimensional beams in a nonlocal Kerr-like media. On the basis of the investigation of the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, peakon and periodic peakons, compacton solutions, etc.) under different parameter conditions.

Fractional revivals of superposed coherent states

We study the dynamics of superposed wave packets in a specific nonlinear Hamiltonian which models the wave packet propagation in Kerr-like media and the dynamics of Bose–Einstein condensates. We show the dependence of fractional revival times on the initial superposed wave packets using analysis based on the expectation values, Rényi entropy and Wigner function. We also show how the selective identification of fractional revivals using moments of appropriate observables depends on the number of wave packets present in the initial state.

Random walk of solitary and shock waves in nonlocal disordered media

We study the random walk of solitons and characteristic lines of shock fronts in the presence of disorder for the one-dimensional nonlinear Schrödinger equation in Kerr-like media. We analyze the interplay of nonlocality and randomness, and the way their competition affects strongly coherent nonlinear waves is theoretically and numerically investigated.

Counterpropagating pattern dynamics: From narrow to broad beams

The development of patterns in counterpropagating (CP) beams in saturable Kerr-like media is investigated in a numerical study, by varying the width of beams. A model of interacting mutually incoherent beams is adopted, with slow local changes in the index of refraction, and a numerical simulation of propagating beams is performed for different values of the driving parameters. Linear stability analysis (LSA) of CP beams is carried out, and a modulational instability threshold for the appearance of side beams is determined. The results of LSA, concerning the instability of plane waves, are compared with the numerical results concerning broad hyper-Gaussian beams whose width is varied. Qualitative agreement is found, due to the similarity between plane waves and flat-top hyper-Gaussian beam profiles. Owing to very slow quasi-steady-state changes in the system during time evolution, the transverse characteristics of beam distributions, determined by LSA, are found to persist for long in the transient evolution of CP beams.

Inorganic glasses as Kerr-like media

High-refractive index chalcogenide and heavy-metal oxide glasses have been developed recently for their application as all-optical switching devices in telecommunication networks. Depending upon the nature of electromagnetic phenomena, the switching speed may vary between milliseconds in a rare-earth doped glass and femtoseconds for surface plasmon relaxation in a nano-scale dispersion of metal particles in glasses.

ENERGY TRANSFER BETWEEN LIGHT WAVES IN NONLINEAR MEDIA WITH TWO DIFFERENT RESPONSE TIMES

In this work we extend the conventional theory of the two-wave mixing in Kerr-like media, in order to take into account two different contributions to nonlinear gain. To this end, we use a modified Debye relaxation relation to obtain the dynamical behavior of the nonlinearity and consequently, derive the expressions for pump and probe wave intensities. The two-wave mixing gain coefficient Γ1 is calculated as a function of several parameters.

Partially Coherent Solitons of Variable Shape

We present analytical and numerical results related to partially coherent solitons (PCS) of a novel class. In effect, there is freedom to choose the shape of a PCS as it is governed by $2N\ensuremath{-}1$ parameters, where $N$ is the number of linear modes contributing to the soliton. In particular, we show that a PCS may have an asymmetric shape. The PCS shape becomes arbitrary in the limit of complete incoherence. Another remarkable new feature of a PCS is that collisions in Kerr-like media cause the PCS to change its shape, although each beam remains a stationary soliton after the collision.

Vectorial electromagnetic theory of degenerate four-wave mixing in isotropic Kerr-like media

The polarization properties of the phase-conjugate wave generated by means of degenerate four-wave mixing in isotropic Kerr-like media are analysed for monochromatic plane waves of arbitrary polarizations using the Laplace transformation to solve the coupled wave equations. The model presented enables us to find the reflection and transmission matrices defined for the electric and magnetic strength vectors and to discuss the efficiency and fidelity of the phase conjugation.

Spatial solitons in Kerr and Kerr-like media

This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues.

Interactions between one-dimensionalquadratic soliton-like beams

The interaction between two quadratic soliton-like beams was investigated for beams launched parallel to one another, and at small crossing angles. The experiments were performed in titanium in-diffused lithium niobate slab waveguides near a Type I phase-matching condition for second harmonic generation (SHG). Only beams at the fundamental frequency were launched and the second harmonic required for quadratic soliton formation was generated upon propagation into the waveguide. The results of the interaction were found to depend on the relative phase between the input fundamental beams, the net phase mismatch for SHG and on the beam crossing angle. Good agreement with numerical simulations of the different interactions was found. In general, the results of the interactions were similar to those found in saturable Kerr-like media.

Two-photon Jaynes–Cummings model in Kerr-like media

In the present paper are found the solution of a model-Hamiltonian that describes the three-level two cavity mode Jaynes–Cummings model in Kerr-like media (nondegenerate case). Finally we calculate atom level populations as well as squeezing for the quadrature components of the cavity modes and of the total field.

Quality investigation of the phase-conjugate mirror based on four-wave mixing

The quality of the optical phase conjugation, realized by means of the four-wave mixing in Kerr-like media, is examined. The fidelity of the generated replica of a signal field is investigated in suitable approximations and related problems are solved applying the Fourier transformation. The presented methods are based on the derivation of integro-differential mode equations valid for general conditions, including interaction of polych romatic nonparaxial waves.

Stability analysis of stationary nonlinear guided waves in self-focusing and self-defocusing Kerr-like layered media.

In this paper, we develop a linear stability analysis of stationary nonlinear guided waves in self-focusing and self-defocusing Kerr-like layered media. The analysis is applicable to the general problem of the stability of stationary nonlinear guided waves in layered structures including one or more self-defocusing media, a previously unsolved problem. Further, as a demonstration of its use, the technique is applied to the case of the fundamental dark surface wave (FDSW), a wave guided near the interface between two dissimilar defocusing media. We obtain results consistent with a numerical stability analysis of the FDSW performed previously [J. Opt. Soc. Am. B 8, 2265 (1991)]. Finally, the generalization of this technique to arbitrary layered structures of Kerr-like media is discussed.

Waveguides and Y junctions formed in bulk media by using dark spatial solitons

Dark spatial solitons are created when intense quasi-plane waves containing amplitude or phase discontinuities propagate through self-defocusing, Kerr-like media. We show that dark solitons form not only stable waveguides but also structures equivalent to Y-junction splitters and other devices.

Coherent-beam amplification and polarization switching in a birefringent medium-photorefractive crystal

A recent theory of polarization switching and beam amplification effect in Kerr-like media is extended to birefringent photorefractive crystals. In this class of material, the birefringence allows a new mechanism for coherent nonlinear mixing effects among the extraordinary and ordinary waves, leading to amplification and polarization switching effects. Analytic solutions of the parametric equations governing these interacting waves are solved for both the phase-matched and phase-mismatched geometries. The authors also present an experimental confirmation of the predicted polarization switching effect.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Self-squeezing of light in saturable nonlinear media

A simple model for saturation effects in self-squeezing of light in Kerr-like media is analytically solved in the limit of large number of photons. It is shown that the inclusion of the saturation into the model can modify or even eliminate the squeezing effects.

Stationary nonlinear surface waves and their stability in diffusive Kerr-like nonlinear media

Stationary TE nonlinear surface waves at the interface separating two nonlinear diffusive Kerr-like media are computed for differing diffusion mechanisms and diffusion lengths. The stability of the surface waves on each branch of stationary solutions is determined by launching the appropriate wave and following its evolution, using the beam-propagation method. The stability criteria follow those determined earlier [ J. Opt. Soc. Am. B5, 559 ( 1988)] for non-diffusive Kerr media. The critical power necessary for observing surface waves is determined and shown to depend on the nature of the diffusion process. Analysis supports the observed numerical behavior of the diffusion coefficient at the interface as a function of increasing diffusion length.

Phase conjugation by four-wave mixing with a nonstationary pumping wave

Collinear schemes of transient phase conjugation during degenerate four-wave mixing are investigated in inertion-less Kerr-like media. The analytical solution of this problem is presented for the case when one of the pumping waves is monochromatic but the other one is an ultrashort laser pulse.

Optical bistability based on self-induced polarization-state change in anisotropic Kerr-like media

A new scheme is proposed for the realization of all-optical ultrafast functional devices, such as self-modulators and multistable elements, utilizing a nonresonant chi((3)) process. The basic physical mechanism involved is the intensity-dependent self-induced change in the polarization state of light during propagation in an optically anisotropic Kerr-like medium with a large linear birefringence.