Kerr-like Nonlinearity Research Articles

Relationship between the atomic inversion and Wigner function for multimode multiphoton Jaynes–Cummings model

In this paper we consider the multimode multiphoton Jaynes–Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with N modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase-space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of initial atomic states as well as moving atoms. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for the Wigner function.

Vectorial spatial solitons in bulk periodic quadratically nonlinear media

We present a comprehensive analysis of the generation, propagation and characteristic properties of two-dimensional spatial solitons formed in quasi-phase-matched gratings through type-II vectorial interaction. By employing an averaging approach based on asymptotic expansion theory, we show that the dynamics of soliton propagation in the grating and their stability properties are strongly influenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we verify the validity of our theoretical predictions.

Optical bistability in semiconductor microcavities

We report the observation of polaritonic bistability in semiconductor microcavities in the strong-coupling regime. The origin of bistability is the polariton-polariton interaction, which gives rise to a Kerr-like nonlinearity. The experimental results are in good agreement with a simple model taking transverse effects into account.

A Coupled System for Nonlinear Wave Propagation Combining Wake Field Generation with a Kerr-Nonlinearity

Three cases of nonlinear wave propagation in plasmas are studied, involving different wave modes. In all cases a generic system of equations is found, combining a Kerr-like self nonlinearity with nonlocal effects due to the generation of low-frequency wake fields. Using the conservation laws of the system, explicit expressions for the soliton acceleration and frequency conversion rate are found.

NONLOCAL OPTICAL PROPAGATION IN NONLINEAR NEMATIC LIQUID CRYSTALS

Optical propagation in nematic liquid crystals is characterized by a large and highly-nonlocal Kerr-like nonlinearity. We investigate the fundamental role played by spatial nonlocality in nonlinear optical propagation, and develop a model able to predict the main features of spatial solitons and modulational instability in nematic liquid crystals. The model unifies solitons in physical systems exhibiting different degrees of nonlocality, disclosing a connection between nonlocal solitons and parametric solitons in quadratic media. Finally, soliton breathing as well as other characteristics of nonlocal propagation are experimentally demonstrated in a specifically-engineered liquid crystal cell.

Optical pulse propagation in an irregular waveguide with spatially distributed Kerr-like nonlinearity

A nonstationary two-dimensional problem of propagation of a femtosecond pulse in a planar waveguide comprised of linear and nonlinear sections connected in series is solved using the finite-difference method. The accuracy of the finite-difference techniques is analyzed as applied to solution of stationary and nonstationary two-dimensional quasi-linear equations of light propagation in step-index waveguides. The effects of wave instability on the dynamics of the spatiotemporal pulse distribution in a nonlinear waveguide are studied. It is shown that, due to the retarded nonlinear response of the medium and the dependence of the group velocity of the pulse on its intensity, radiation continuously leaks from the fiber core to the cladding as the pulse propagates along the fiber.

Shock-like optical modes trapped by the interface of cubic nonlinear media

We report the existence of new families of TE-polarized stationary waves propagating along the interface between two media with Kerr-like nonlinearity. The interfaces between two self-defocusing media and between self-focusing and self-defocusing media are considered. The eigenmodes found have one or two different nonzero backgrounds and represent (in the transverse direction) shock-like waves that are trapped by the interface. Upon constructing these eigenmodes the singular solutions of the corresponding nonlinear governing equations are utilized and the constraints for the modes existence are identified.

Polariton effect in nonlinear pulse propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside of the polariton gap exhibit different velocity and amplitude dependencies on their duration.

Asymmetrical transverse structures in nonlinear interferometers

The work presents a novel type of optical instability, which leads to the spontaneous formation of a stationary or pulsating asymmetrical structure in the problem of interaction between two counterpropagating waves in a ring cavity with Kerr-like nonlinearity. Linear stability analysis of interferometer transmission stationary states enabled: (1) to mark out typical bifurcations for this system: self- and cross-modulational instabilities, (2) to determine the range of parameters for which the symmetry breaking of transverse structures and complex temporal behaviour of the light field could be observed. The predictions of linear stability analysis have been verified with numerical modelling of coupled-modes equations.

Nonlinear optical characterization of cluster dynamic in water in oil microemulsion by a pump probe laser beam technique.

We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate) with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters, of the kind already reported with the application of strong electric field, could justify this result.

Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals.

A model is proposed to account for Kerr-like nonlinearity induced by femtosecond pulses via terahertz generation and electro-optical effect. This phenomenon, so far overlooked, is evidenced in a zinc blende single crystal with a heterodyne optical Kerr effect setup. The spectral evolution of this phenomenon as well as its noninstantaneous response character are reported. Its competition with a third-order optical Kerr effect is demonstrated.

Reflection and transmission of a plane TE-wave at a lossless nonlinear dielectric film

A general analytical solution of the Helmholtz equation describing the scattering of a plane, monochromatic, TE-polarized wave with a film exhibiting a local Kerr-like nonlinearity is presented. The film is situated between two semi-infinite media. All media are assumed to be non-absorbing, non-magnetic isotropic and homogeneous. The results derived contain conditions for unbounded field intensities expressed in terms of the imaginary half-period of Weierstrass’ elliptic function ℘. The reflectivity R is calculated as a function of the film thickness and the transmitted intensity. The critical values of R are determined. The results are a generalization of the linear optics results.

Multi-soliton complexes in a sea of radiation modes

We derive exact analytical solutions describing multi-soliton complexes and their interactions on top of a multi-component background in media with self-focusing or self-defocusing Kerr-like nonlinearities. These results are illustrated by numerical examples which demonstrate soliton collisions and field decomposition between localized and radiation modes.

Light guiding in optical fibers with Kerr‐like nonlinearity

AbstractGuiding properties of optical fiber with Kerr‐like nonlinearity are studied numerically using the finite‐difference beam‐propagation method to solve the scalar‐wave equation. The nonlinear fiber is shown to support fields with longitudinally invariant radial distributions having a mean‐squared beam width less than that of the linear fiber mode. The double‐mode propagation is shown to be unstable, and tends to convert into single‐mode propagation after some distance from the input endface of the fiber. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 212–216, 2001.

Photovoltaic saturable nonlinearity in 2D in photorefractive crystals

We formulate the equation describing the two-dimensional nonlinearity change in the refractive index induced by a focused beam under an incoherent uniform background illumination in photovoltaic photorefractive crystals. The analytical results indicate that under the appropriate condition the photovoltaic nonlinearity has a saturable Kerr-type form and uniform background illumination plays a role of the dark irradiance. Local saturable Kerr-like nonlinearity suggests the possibility of the existence of circular symmetric solitons in the crystals.

Spectral content of time resolved electronic and phonon induced non-linearities

We present an exhaustive description of the spectral content from the signal measured in a pump probe experiment devoted to Kerr-like third-order non-linearities. We demonstrate that encountered behavior depends on the experimental detection set-up, namely a transmission or a polarization measurement. Processes at the origin of the spectral changes are also linked to the specific non-linearities involved.

Scattering of the total field from the slow-tapered and step-like discontinuities of dielectric waveguides

The spatial transient regimes of the total field propagation in irregular optical fibers are considered. The propagation of a linearly polarized, axially symmetric mode through the cutoff cross section in a down-tapered fiber, as well as the scattering from the step-like and smooth discontinuities, are simulated by the finite-difference beam propagation method applied to solve the paraxial scalar wave equation. Kerr-like nonlinearity, as well as absorption losses of the fiber material, are shown to influence the transmittance of the structures. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 27–33, 2000.

Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions.

We carry out a theoretical investigation of the properties of partially coherent solitons for media which have a slow Kerr-like nonlinearity. We find exact solutions of the Nth-order Manakov equations in a general form. These describe partially coherent solitons (PCSs) and their collisions. In fact, the exact solutions allow us to analyze important properties of PCSs such as stationary profiles of the spatial beams and effects resulting from their collisions. In particular, we find, analytically, the number of parameters that control the soliton shape. We present profiles which are symmetric as well as those which are asymmetric. We also find that collisions allow the profiles to remain stationary but cause their shapes to change.

TE-polarized waves guided by a lossless nonlinear three-layer structure

We study TE-polarized electromagnetic waves guided by a three-layer structure consisting of a film surrounded by semi-infinite media. All three media are assumed to be lossless, nonmagnetic, isotropic, and exhibiting a local Kerr-like dielectric nonlinearity. We present general necessary and sufficient conditions for the existence of ``physical'' (real, nonnegative, bounded, and consistent with the dispersion relation) field intensities. As a physical consequence, the parameters ${a}_{\ensuremath{\nu}},{\overline{\ensuremath{\epsilon}}}_{\ensuremath{\nu}}{,n,E}_{0}^{2}{,k}_{0}d$ associated with realizable waves can be specified. To illustrate the procedure, analytical and numerical results for the allowed normalized thickness of the film and patterns of the field intensities as functions of the effective wave number and the intensity of the electric field at the lower surface of the nonlinear dielectric film are presented and the occurrence of singular field intensities is investigated. Finally, the particularization of the results to the three-layer structure containing a linear substrate and film and a nonlinear cladding is briefly discussed.

Analytical expressions of cut-off wavenumbers of TM modes in a Kerr-like nonlinear slab waveguide

A very simple analytical expression of cut-off wavenumbers for TM waves in a nonlinear MQW slab waveguide with Kerr-like nonlinearity is presented for the first time using a perturbation technique.