Nonlinear Kerr Medium Research Articles

Propagation of partially coherent light beams with parabolic intensity distribution in noninstantaneous nonlinear Kerr media

An exact solution describing the self-similar dynamics of partially coherent light beams in nonlinear and noninstantaneous Kerr media is presented and analyzed. The description is based on the Wigner formalism for analyzing the propagation of partially coherent light. The solution for the Wigner distribution corresponds to a transverse beam intensity profile of a parabolic form, and the effects of the partial coherence on the beam dynamics are analyzed. The presence of partial coherence in the parabolic beam is shown to increase the diffraction effect, thus weakening the nonlinear self-focusing and increasing the defocusing rate. In the case of an almost coherent beam and a strongly nonlinear situation in a defocusing medium, the new solution is shown to reduce to a previously given parabolic similarity solution for coherent high intensity beam-pulse propagation.

Strong influence of nonlinearity and surface plasmon excitations on the lateral shift

When surface plasmons are excited at a metal-dielectric interface, the electromagnetic field takes a very large value near the interface. If the dielectric is a nonlinear Kerr medium, then the effect of nonlinearity can be greatly amplified due to the field enhancement. In this paper, we calculate the lateral shift of p wave beams incident on metal-dielectric multilayer systems in the Otto configuration in a numerically exact manner, using the invariant imbedding method of wave propagation in nonlinear stratified media. In the linear case, we find that the lateral shift becomes very large at the incident angles where the surface plasmons are excited. As the nonlinearity is turned on, the value of the lateral shift changes rapidly. We find that even a small change of the intensity of the incident wave can cause a huge change of the lateral shift. We propose that this phenomenon can be applied to designing precise optical switches operating at small powers.

Generation of Four-Photon Cluster State with Coherent Light via Cross-Kerr Nonlinearity

We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.

Threshold of damped critical non-linear Schrödinger equation with fourth-order dispersion

This article is concerned with a damped critical non-linear Schrödinger equation with fourth-order dispersion which models propagation of fibre arrays in non-linear Kerr media. We analyse the effect of the damping force on the solution for the system and prove that there exists a threshold value of the damping parameter for global existence and blowup of the system. Furthermore, we estimate the threshold value.

Interaction between two partially incoherent soliton stripes

A detailed analysis is made of the mutual interaction of two, initially well separated, partially incoherent solitons in a nonlinear Kerr medium. Explicit expressions are obtained describing the influence of partial incoherence on the subsequent dynamics of the solitons. In particular it is shown that as the degree of incoherence increases, the character of the interaction may change between attractive and repulsive behavior (or vice versa). Furthermore, it is found that this dependence is not always monotonous.

Induced modulation instability and recurrence in nonlocal nonlinear media

The long-term behaviour of spatial modulation instability in nonlocal nonlinear Kerr media is studied theoretically and numerically. Seeding the modulation instability with a periodic modulation leads to an energy transfer to higher-order modes and the long-term behaviour of the system shows the Fermi–Pasta–Ulam recurrence. For large spatial frequencies, close to the cut-off frequency, the stable solution can be found analytically. The propagation with an initial state different from the stable solution results in a propagation circling around the stable point. For general frequencies, the calculation of the stable point is performed numerically. Comparison of the calculations with earlier reported experimental results in nematic liquid crystals shows a satisfactory agreement.

Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium

The change in nature of light in propagation through a lossless isotropic nonlinear Kerr medium is studied. Considering a monochromatic unidirectional light beam, we see that coherent light remains coherent but the polarization state changes in general, and completely unpolarized light retains its nature in all respects. For a light beam having a coherent signal and unpolarized noise, a change in polarization state of the signal and depolarization occurs in general. For circular and plane polarized signals, the polarization states of the signal do not change and depolarization is absent for the former and maximum for the latter. Numerical calculations for a practical case indicate that these effects are observable.

Nonlinear Coherent Transport of Waves in Disordered Media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.

Mode interaction in few-mode optical fibres with Kerr effect

We generalize the method of projection to orthogonal basis functions of transverse coordinates for a nonlinear (Kerr medium) fibre and apply this method in the case of a two-mode waveguide (each with two polarization modes). We use orthogonal Bessel functions that fit the choice of the cylindrical geometry of a fibre. The coupled nonlinear Schrödinger equations are derived for the envelopes of electromagnetic field wave trains in each mode. Analytic expressions and numerical results for coupling coefficients are given; the nonlinearity parameters' dependence on fibre radius is illustrated by plots and compared with results of other authors.

Nonlinearity management in optics

AbstractWe study nonlinearity management in optics by investigating the propagation of localized pulses and plane waves in a layered, cubically nonlinear (Kerr) medium that consists of alternating layers of glass and air. We show that such nonlinearity management delays the blow‐up/collapse of pulses and leads to a band structure of modulationally unstable regions for plane waves. We find excellent agreement between experiments, numerical simulations, and theory. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Photonic Crystal Waveguide Weakly Interacting with Multiple Off-Channel Resonant Features Formed of Kerr Nonlinear Dielectric Media

A theoretical study is presented of guided modes of a photonic crystal waveguide for cases in which they interact with multiple bound electromagnetic modes localized on off-channel impurity features of Kerr nonlinear media. The interest is on the properties of resonant scattering and optical bistability exhibited by the system and the coherent scattering of the guided modes due to their simultaneous resonant interactions with multiple bound modes. In first study, two off-channel features on opposite sides of a photonic crystal waveguide are made of different Kerr nonlinear dielectric media. In second study, an off-channel feature is composed of two neighboring sites having different Kerr dielectric properties. In addition to numerical results a number of analytical results are presented providing simple explanations of the quantitative behaviors of the systems. A relationship of these systems to forms of electromagnetic-induced transparency and modifications of waveguide dispersion relations is discussed.

Near-complete teleportation of two-mode four-component entangled coherent states

In this paper, we propose an optical scheme to almost completely teleport a two-mode four-component entangled coherent state in terms of optical devices such as nonlinear Kerr media, beam splitters, phase shifters and photon detectors. Different from those previous schemes in which exact photon number discrimination is needed, in our scheme one only needs to make ‘yes’ and ‘no’ measurements upon the photon numbers in related modes. This scheme can also be understood as an entanglement swapping protocol.

Observation of Temporal Vector Soliton Propagation and Collision in Birefringent Fiber

We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schrödinger equation.

Excitability Mediated by Localized Structures in Kerr Cavities

We characterize a scenario where localized structures in nonlinear optical cavities display an oscillatory behavior which becomes unstable leading to an excitable regime. Ex- citability emerges from spatial dependence since the system locally is not excitable. We show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. DOI: 10.2529/PIERS060907134206 Localized structures (LS) in dissipative optical cavities arise as a consequence of the interplay between difiraction, nonlinearity, driving, and dissipation (1). These structures, also known as cavity solitons, are unique once the parameters of the system have been flxed. This fact makes this structures potentially useful in optical storage and processing of information (2,3). LS may develop a number of instabilities, for instance their amplitude can oscillate in time while remaining static in space. Here we report on a novel regime of excitability associated to the existence of localized structures in a nonlinear optical system (4,5). Excitability has been found in a variety of systems (6), including optical systems (7), and is characterized by a nonlinear response under applied external perturbation. Perturbations exceeding a certain threshold are able to elicit in the system a full and well deflned response. Furthermore after one perturbation the system cannot be excited again within a refractory period of time. Excitability is behind excitation waves in heart tissue and the existence of action potentials in neurons, and, so, may confer new computational capabilities to optical systems beyond information storage. In this paper we show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. For a homogeneous pump the mechanism leading to excitable behavior is a saddle-loop bifurcation through which an stable oscillating LS collides with an unstable LS (4). For a system pumped by a localized Gaussian beam on top of homogeneous background the scenario is richer and one flnds two difierent mechanisms leading to excitability. One is based on a saddle- loop bifurcation as above while the other takes place through a saddle-node in the invariant circle (SNIC) bifurcation. This second mechanism has excitability threshold which can be much lower. We consider a ring cavity fllled with a nonlinear self-focusing Kerr medium pumped by an external fleld. In the mean fleld approximation, the dynamics of the electric fleld inside the cavity can be described by a single partial difierential equation for the scaled slowly varying amplitude E(~) (8) @tE = i(1 + iµ)E + ir 2 E + E0 + ijEj 2 E;

Long-distance propagation of periodic patterns in weakly nonlinear Kerr medium

We investigate the propagation of periodic patterns in one and two dimensions for weak Kerr-type nonlinearity. Nonlinear amplitudes are introduced, which are related to the Fourier harmonics of a wave by polynomials of third and fifth degree. These amplitudes evolve in a particularly simple way and permit easy reconstruction of waveform after propagation. For the one-dimensional case, solutions are quasiperiodic, and solitonlike structures can be identified. For the two-dimensional case, recurrent and chaotic regimes exist depending on lattice type.

Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials

We study a ring cavity filled with a slab of a right-handed material and a slab of a left-handed material. Both layers are assumed to be nonlinear Kerr media. First, we derive a model for the propagation of light in a left-handed material. By constructing a mean-field model, we show that the sign of diffraction can be made either positive or negative in this resonator, depending on the thicknesses of the layers. Subsequently, we demonstrate that the dynamical behavior of the modulation instability is strongly affected by the sign of the diffraction coefficient. Finally, we study the dissipative structures in this resonator and reveal the predominance of a two-dimensional up-switching process over the formation of spatially periodic structures, leading to the truncation of the homogeneous hysteresis cycle.

A new optical scheme for teleportation of entangled coherent state

We propose a nearly perfect optical scheme for the quantum teleportation of entangled coherent states using optical devices such as nonlinear Kerr media, beam splitters, phase shifters, and photon detectors. Different from those previous schemes, our scheme needs only ``yes'' or `no' measurements of the photon number of the related modes, i.e. nonzero- and zero-photon measurements, while in previous schemes one has to exactly identify the even or odd parity character of the photon numbers detected by detectors.

Effect of a thin optical Kerr medium on a Laguerre-Gaussian beam

Using a generalized Gaussian beam decomposition method the authors determine the propagation of a Laguerre-Gaussian (LG) beam that has passed through a thin nonlinear optical Kerr medium. The orbital angular momentum per photon of the beam is found to be conserved while the component beams change. As an illustration of applications, the authors propose and demonstrate a Z-scan experiment using a LG01 beam and a dye-doped polymer film.

Interaction of two different frequency photonic crystal waveguide modes through the resonant excitation of modes on off-channel Kerr nonlinear media

The properties of two photonic crystal waveguide modes at different frequencies that propagate down a straight photonic crystal waveguide are studied for cases in which the two modes interact with off-channel structures composed of Kerr nonlinear dielectric media. The optical nonlinearity of the off-channel structures mediates an interaction between the two modes that allows the modes to modulate the transmission of each other down the waveguide channel. This interaction and mutual modulation is shown to be pronounced in the case when either of the two waveguide modes resonantly excites a localized mode on the off-channel features formed of Kerr nonlinear media. Cases that are considered are a straight linear dielectric media waveguide with off-channel structures formed as: (a) a single off-channel Kerr site that supports a bound localized electromagnetic mode, (b) multiple off-channel Kerr sites that support a bound intrinsic localized electromagnetic mode, and (c) multiple off-channel Kerr sites that support an intrinsic localized mode that in turn interacts with a semi-infinite waveguide of linear dielectric media. In cases (a) and (b) the effects of resonant excitation of single site and intrinsic localized modes in the Kerr medium on the transmission characteristics are determined. In case (c) the effects of resonant excitation of intrinsic localized modes in the Kerr medium on the transmission characteristics of the two waveguide modes into the infinite and semi-infinite waveguides are studied.

Azimuthal modulation instability for a cylindrically polarized wave in a nonlinear Kerr medium

Inhomogeneously polarized optical waves form a class of nonlinear vector wave propagation that has not been widely studied in the literature. We find a modulation instability only when the wave has nonzero ellipticity in a medium where the Kerr nonlinearity possesses opposite handness. Under the modulation instability the wave develops an azimuthally periodic shape with two or four peaks.