Nonlinear Kerr Medium Research Articles

Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium

We analytically and numerically find families of polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium and analyze their coherence properties. We find that the polychromatic incoherent solitons exist when higher temporal frequency constituents of the light are less spatially coherent than smaller temporal frequency constituents.

Modulation instability of non-paraxial beams for self-focusing Kerr media

Propagation stability of non-paraxial beam in nonlinear Kerr media is investigated by using the linear stability method.Both theoretical analysis and numerical simulation show that the modulation instability gain spectrum has three different distribution features, which are determined by ap0, where a and p0 represent the non-paraxial parameter and the incident power, respectively. Furthermore, the corresponding criterion is given to distinguish the three different distributions.

The influence of pulse width on transient thermally induced optical nonlinearities in a Kerr nonlinear medium

We report the experimental results on the effect of pulse width on transient thermally induced optical nonlinearities in the nanosecond r egime. We have obtained the Z_scan curves of the CS2 solutions of nigrosin e for different pulse widths, and analyzed the co_existence of third_order and transie n t thermally induced optical nonlinearities. The process of changing from transi ent state to steady_state thermal_induced optical nonlinearities was observed. M eanwhile, we have obtained the results of numerical simulation by solving simult aneously acoustic and electromagnetic wave equations, which agree well with the experimental results.

A comment on: “Superpositions of truncated phase states: generation and properties”: [Phys. Lett. A 309 (2003) 5

In a previous work [Phys. Lett. A 309 (2003) 5] an experimental proposal producing superpositions of truncated phase states in a high- Q microwave cavity was presented. In this Letter we employ a Mach–Zehnder interferometer including a nonlinear Kerr-medium to extend the previous result for traveling waves, appropriate for optical fields.

Bistable behaviour of a photonic crystal nonlinear cavity

A Fabry–Pérot cavity can be closed by reflecting slabs made with different types of materials. An interesting situation occurs when the slabs are constructed from a photonic crystal in the nonpropagating regime, i.e. with an incident frequency tuned to an evanescent mode. The situation is even more interesting when the cavity itself contains a nonlinear Kerr medium, i.e. a material which changes its refractive index with the transiting intensity. The response of this system to high-intensity incident waves is studied in detail. It is shown that (1) the refractive index of the material which fills the cavity changes in a significant way as a function of the incident power; (2) in specific intensity ranges, the refractive index in the cavity is multi-valued, leading to a bistable behaviour of the Fabry–Pérot filter. The hysteresis cycle of the refractive index and of the transmission coefficient is described.

Two-dimensional solitons and vortices in normal and anomalous dispersive media.

We study solitons and vortices described by the (2+1)-dimensional fourth-order generalized nonlinear Schrödinger equation with cubic-quintic nonlinearity. Necessary conditions for the existence of such structures are investigated analytically using conservation laws and asymptotic behavior of localized solutions. We derive the generalized virial relation, which describes the combined influence of linear and nonlinear effects on the evolution of the wave packet envelope. By means of refined variational analysis, we predict the main features of steady soliton solutions, which have been shown to be in good agreement with our numerical results. Soliton and vortex stability is investigated by linear analysis and direct numerical simulations. We show that stable bright solitons exist in nonlinear Kerr media both in anomalous and normal dispersive regimes, even if only the fourth-order dispersive effect is taken into account. Vortices occur robust with respect to symmetry-breaking azimuthal instability only in the presence of additional defocusing quintic nonlinearity in the strongly nonlinear regime. We apply our results to the theoretical explanation of whistler self-induced waveguide propagation in plasmas, and discuss possible applications to light beam propagation in cubic-quintic optical materials and to solitons in two-dimensional molecular systems.

Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions

Spatiotemporal instabilities in nonlinear Kerr media with arbitrary higher-order dispersions are studied by use of standard linear-stability analysis. A generic expression for instability growth rate that unifies and expands on previous results for temporal, spatial, and spatiotemporal instabilities is obtained. It is shown that all odd-order dispersions contribute nothing to instability, whereas all even-order dispersions not only affect the conventional instability regions but may also lead to the appearance of new instability regions. The role of fourth-order dispersion in spatiotemporal instabilities is studied exemplificatively to demonstrate the generic results. Numerical simulations confirm the obtained analytic results.

Low Threshold Bistable Switching by the NonlinearOne-Dimensional Photonic Crystal

In the approximation of the fast Debye relaxation of a nonlinear Kerr medium,the nonlinear finite-difference time-domain method is derived to simulatenumerically the one-dimensional nonlinear photonic crystal sandwiched bythe Kerr medium. Bistable switching with a low threshold intensity of0.01kW/cm2 is obtained, and the corresponding refractive index changeof the Kerr media is about 0.038.

Propagation properties of chirped soliton pulses in optical nonlinear Kerr media.

An investigation is made of the formation of a single soliton, or a pair of solitons, from initially nontransform limited pulses in a nonlinear Kerr medium having anomalous dispersion. A qualitative physical explanation is given for the formation of soliton pairs. Approximate solutions for the amplitudes and the velocities of the generated solitons are established and corroborated by numerical solutions of the Zakharov-Shabat eigenvalue problem.

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities.

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent x-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wave numbers can originate different structures, the detuning being a natural selection parameter.

Noncollinear interaction of optical vortices in Kerr nonlinear medium

The noncollinear interaction of singular light beams (degenerate four-wave mixing) in Kerr nonlinear medium is analyzed. It is demonstrated that vorticity of diffracted beams significantly depends on the topological charges of pump beams. The results of an experimental observation of the phenomenon are presented.

Nonlinear Aharonov-Bohm scattering by optical vortices.

We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wave packet) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wave-front splitting of the scattered wave develops into transverse modulational instability, "unzipping" the stripe into trains of vortices with opposite charges.

Modulational instability in nonlocal nonlinear Kerr media.

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.

Thermal and squeezed vacuum Jaynes–Cummings models with a Kerr medium

The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.

Interaction between multiple spatial solitons in the diffraction catastrophe region upon focusing a high-power laser beam in a nonlinear medium

When a high-power laser beam is focused in a nonlinear Kerr medium, beam self-diffraction by induced inhomogeneities of the refractive index is observed. A method for calculating the field amplitude and phase in the focal region with regard for self-diffraction by self-induced inhomogeneities is developed. Computer analysis of saturable Kerr media showed that the optical-field region with the least cross section of the focal pattern is followed by that of chaotically radiating “splashes” and long filaments. The latter radiate outward from the region of the caustic waist over long distances. They represent bright spatial solitons, which channel a significant portion of the primary beam energy. No less than 8–12 clear-cut solitons traveling in the positive z direction and moving apart in the transverse (x, y) plane are observed in the cross section. The field amplitude oscillates along each of the solitons. Various parameters of the saturable Kerr medium are taken into account.

Optical holonomic quantum computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a nonlinear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices, and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results in logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity, scalability, and reversibility are addressed and several steps are taken towards the physical implementation of this model.

A versatile method for analyzing paraxial optical propagation in dielectric structures

This paper presents a fast and accurate quasi-analytic model for studying optical field propagation in weakly guiding dielectric structures. The proposed efficient and versatile computational scheme is obtained by merging the Hermite-Gauss (HG) total field expansion with the numerical collocation method and is particularly suited for longitudinally nonuniform structures. By means of a quasilinearization scheme, the same procedure has also been successfully applied to the analysis of field propagation in Kerr-nonlinear media. The latter achievement gives an indication of the great potentialities offered by this straight forward method. Several examples are discussed in the paper and in all cases the results computed by the proposed method favorably compare with those from alternative methods.

Short laser pulse parameters in a nonlinear medium: different approximations of the ray-pulse matrix

The purpose of this paper is to find an expression to describe the evolution of the temporal parameters of a short laser pulse crossing a Kerr nonlinear medium, suitable to be recast in a form consistent with the standard formulas for Gaussian beam transformations, via 2×2 ray pulse matrices. The goal is to find a satisfactory compromise between accuracy and simplicity. Expressions with different degree of approximation are analyzed and their validity and accuracy are discussed.

Variational analysis and angular bistability in layered nonlinear Kerr media with phase conjugation

The calculus of variations is applied to electromagnetic fields in a layered nonlinear structure supporting a guided wave. The system also includes a phase-conjugate mirror (PCM). By introducing a ...

Cross Phase Modulation Induced Pulse Splitting – the Optical Axe

An analytical as well as numerical analysis is made of the dynamics induced on a weak signal wave pulse by a co-propagating strong pump wave pulse in a nonlinear Kerr medium. Emphasis is given to the situation where the group velocity dispersion and the non-linearity of the signal pulse have opposite signs. In this defocusing situation, it is demonstrated that the pump splits the signal pulse into two frequency shifted pulse fragments which separate in time, asymptotically with constant separation velocity. Explicit analytical predictions for the velocity of separation are obtained and corroborated by numerical simulations.