Kerr-type Media Research Articles

Helmholtz-Manakov solitons

A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices

We consider parametric amplification of two-dimensional spatial soliton oscillations in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which gives rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton oscillations along one transverse axis, and enhancement of soliton spiraling.

Stabilization of vector solitons in optical lattices

We address the properties and dynamical stability of one-dimensional vector lattice solitons in a Kerr-type cubic medium with harmonic transverse modulation of the refractive index. We discovered that unstable families of scalar lattice solitons can be stabilized via cross-phase modulation (XPM) in the vector case. It was found that multihumped vector solitons that are unstable in uniform media where the XPM strength is higher than that of self-phase modulation can also be stabilized by the lattice.

On the dynamic properties of “elastic” interactions between wave solitons consisting of a few field oscillation cycles

By the numerical simulation of the dynamics of the optical circularly polarized field in the Kerr-type medium, it has been shown that the binary collisions between wave solitons consisting of a few field oscillation cycles with respect to their energy characteristics exhibit the properties of the collisions of Schrodinger solitons. The corresponding spectral characteristics change according to the conservation of the soliton-like structure of the envelop. In dependence on the absolute difference of the field phases, there are three different interaction regimes: the passage of one structure through another, their repulsion, and the exact replication of one initial wave structure by another.

Volume holographic recording and readout for 90-deg geometry

When a prerecorded cross-beam hologram is reconstructed (so-called edge-lit readout) with a uniform plane wave and a point source, the resulting exact solutions reveal Bessel-function-type dif- fracted beam profiles, which are fundamentally modified under weak propagational diffraction. The case of a profiled beam readout with propagational diffraction may be analyzed using a transfer function ap- proach based on 2-D Laplace transforms. In a second series of investi- gations, dynamic readout from a cross-beam volume hologram recorded with two orthogonal uniform plane waves is considered for various de- pendences of the refractive index modulation with intensity. Typically, refractive index profiles that are proportional to the intensity (as in the case of Kerr-type media or photorefractives with predominantly photovol- taic effect) and to the derivative of the intensity (as in diffusion-dominated photorefractives) are considered. Two-dimensional nonlinear coupled equations are developed for the two (Bragg) orders for both cases. Closed form solutions are obtained for the first case, indicating only non- linearly induced self and cross-phase coupling. A simple experiment in- volving simultaneous recording and readout using photorefractive lithium niobate crystal indicates beam profile distortion, which may be expected in such 90-deg geometries. © 2004 Society of Photo-Optical Instrumentation Engi- neers. (DOI: 10.1117/1.1774195)

Multiport soliton devices with controllable transmission

We describe new planar multiport devices written by spatial solitons that are composed of several nonlinearly coupled components in Kerr-type media. Such devices have no radiation losses at a given wavelength. We demonstrate that, for the same relative angle between the input soliton-induced channels, one can vary the transmission coefficients into the output channels by adjusting the polarizations of multicomponent solitons. We determine analytically the transmission properties and discuss two types of experimental embodiment of the proposed device.

New Exact Jacobi Elliptic Function Solutions of Three-Dimensional Nonlinear Helmholtz Equation in a Nonlinear Kerr-Type Medium**The project supported by National Natural Science Foundation of China and National Key Basic Research Development Project Program under Grant No. G1 998 030 600

In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus or 0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodic solutions can be also found.

Self-guided waves and exact solutions of the nonlinear Helmholtz equation

The paraxial wave theory is known to lead to inaccurate predictions in self-focusing of optical beams. The nonlinear Helmholtz equation describes more accurately wave propagation in dispersive, spatially local, Kerr-type media. We derive rigorous bright and dark solutions to the nonlinear Helmholtz equation in a full three-dimensional form. These expressions are new and unique. The solutions are obtained with a multidimensional extension of the (paraxial) nonlinear Schrödinger equation. We also establish energy conservation laws for both nonlinear wave equations in terms of spatial currents. Our results give insight, for example, into the diffraction and breakup of tightly confined nonlinear fields.

Optical slab waveguides of Kerr material with linear profile

The problem of propagation of a TE wave in a three layers slab waveguide is discussed. The core material is a Kerr-type medium, and its profile of refractive index n 2 with x is a linear profile. The Helmholtz equation in the core region is reduced to Painlevé's equation. Its approximate analytic solution is obtained by using the Laurent series.

Internal reflection of one-dimensional bright spatial solitons

We study the reflection of one-dimensional spatial solitons at the non-linear interface between a Kerr-type medium and a linear medium. Our study places emphasis on determining the physical conditions under which the beam reflected by the non-linear interface is still a spatial soliton. We find that for small angles of incidence an elastic internal reflection takes place, in the sense that the reflected soliton is essentially the same as the incident one. For incidence angles near a critical angle, the reflected soliton becomes less intense and its reflection angle is smaller than the angle of incidence. Finally, for spatial solitons with input angles well above the critical angle, the main part of the energy is transmitted to the linear medium, and no soliton is internally reflected.

Amalgamation of interacting light beamlets in Kerr-type media

The interaction of optical filaments in bulk self-focusing media is investigated theoretically and numerically. The nature of this interaction is shown to vary with the incident individual powers and relative phases of the beamlets. By means of virial arguments supported by numerical results it is found that three distinct evolution regimes characterize two in-phase interacting filaments: (i) When each filament has a power below Nc/4, where Nc is the critical self-focusing threshold for a single wave, both filaments disperse along their propagation axis. (ii) When their respective powers lie between Nc/4 and Nc, they fuse into a single central lobe that may self-focus until collapse, depending on their initial separation distance. The critical distance below which a central lobe forms and collapses is estimated analytically. (iii) When their incident powers both exceed Nc, initially separated filaments individually self-focus without mutual interaction. In contrast to in-phase beamlets, two light cells with opposite phase are shown to never coalesce. The extension of the self-focusing dynamics to optical filaments in bulk media with anomalous group-velocity dispersion is discussed.

Polarized dark solitons in isotropic Kerr media

We characterize dark-type vector optical solitons of arbitrary polarization in isotropic, Kerr-type media by applying Hirota's method to the integrable Manakov model with a defocusing nonlinearity. We find that nonuniformly polarized solitons comprise a rich solution family that can be divided into two categories: dark-dark and dark-bright vector solitons. We consider the propagation dynamics and the interactions of these vector solitons by deriving multisoliton solutions, and show the existence of stationary bound states, a phenomenon not observed for scalar dark solitons.

Full wave vector Maxwell equation simulation of nonlinear self-focusing effects in three spatial dimensions

In our effort to meet an increasing demand for more accurate and realistic nonlinear optics simulations, we have developed a nonlinear hybrid vector finite element method (NL-HVFEM) to study different phenomena due to wave propagation in waveguides filled with nonlinear Kerr-type media. Contrary to the most existing scalar models, the NL-HVFEM approach is based upon the vector Helmholtz equation and thus can predict the vectorial properties of fields in nonlinear media. We describe the NL-HVFEM approach and apply it to study nonlinear self-focusing effects in nonlinear waveguides. The numerical results of the evolution of the beam self-focusing are also included. Also, we summarized conditions under which electromagnetic beam can produce its own dielectric waveguide and propagate without spreading.

Wigner distribution function in nonlinear optics

Transformation laws for the Wigner distribution function, the radiant intensity, the radiant emittance, and the first- and second-order moments of the Wigner distribution function through an inhomogeneous, Kerr-type medium have been derived as well as for the beam quality factor and the kurtosis parameter. It is shown that the inhomogeneous Kerr-type medium can be approximated from the Wigner-distribution-function transformation-law point of view with a symplectic ABCD matrix with elements depending on the field distribution.

Bosonic-degeneracy-induced quantum correlation in a nonlinear atomic beam splitter.

We employ a vector quantum field theory to describe the interaction of a coherent atomic beam with a standing-wave laser field. The coherent atomic beam is assumed to be composed of degenerate bosonic atoms. We derive a nonlinear Schr\"odinger equation to describe the diffraction of the coherent atomic beam through the standing-wave laser field in the adiabatic regime of interaction of atoms with a light wave. Under appropriate conditions, we find that the standing-wave laser field acts as a quantum nonlinear atomic beam splitter for a coherent atomic beam. The quantum correlations in the nonlinear atomic beam splitter are analyzed and the analogy to quantum correlations of nonclassical light in an optical Kerr-type medium is discussed.

A steady state solution to four-wave mixing utilising the SU(2,2) group symmetry with mixed gratings in a Kerr type media

Backward four-wave mixing in a Kerr type media with mixed refractive gratings of equal coupling strength are described by a set of nonlinear coupled wave equations. These are formulated into a compact matrix representation which then allows the identification of the four-dimensional symmetry group SU(2,2). When considering the two-point boundary value problem it is found that the mixed grating analysis reduces to the solution of a transmission only grating. This formulism is then used to find a solution for steady state phase conjugation and plots of reflectivity show the multiplicity of the solutions.

Excitation of nonlinear guided waves in Kerr-type media by use of chirped and tapered gratings

The canonical equations governing the excitation of nonlinear guided waves in Kerr-type nonlinear media with chirped and tapered gratings are obtained by a perturbation procedure. These canonical equations, made specific for uniform gratings, predict (1) decreases in the excitation efficiency when either the incident intensity or the nonlinearity is increased and (2) limitations on the propagation distance for which a nonlinear guided wave accumulates a π phase shift with respect to a linear guided wave. In the case of uniform gratings, this propagation distance cannot be reduced by increasing the nonlinearity or by increasing the incident intensity. The efficiency of excitation can be increased significantly by use of chirped or tapered gratings. The acceptance angle for efficient excitation is also increased. Moreover, a combination of chirping and tapering can be optimized so that the efficiency exceeds the maximum efficiency of excitation for linear guided waves.

Coupling between parallel dark spatial soliton waveguides

Dark spatial solitons are able to guide light in a self-defocusing Kerr-type medium by inducement of a refractive-index profile equivalent to a dielectric waveguide. We derive the coupling coefficients between two parallel dark soliton waveguides and investigate the coupling length as a function of various dark soliton and guided-wave parameters.

Modified theory of three-channel Kerr-type nonlinear directional coupler

We point out inconsistencies in previous analyses of multiple-channel nonlinear directional couplers based on Kerr-type media and present a modified set of coupled-mode equations for a three-channel nonlinear coupler that indicate a mode of power switching between channels with increased input power that is both qualitatively and quantitatively different from that predicted previously.

SELF-FOCUSING EFFECTS AND APPLICATIONS USING THIN NONLINEAR MEDIA

A model of the nonlinear optical effects attending the interaction of a laser beam with a thin Kerr-type medium has been analyzed in detail. The formalism developed is applicable to both near- and far-field situations. Some possible applications are discussed.