Focusing Kerr Media Research Articles

Collisions of Light Bullets with Different Circular Polarizations

Collisions of left- and right-polarized spatiotemporal optical solitons have been numerically simulated for a locally isotropic focusing Kerr medium with anomalous chromatic dispersion. The stable propagation of such “light bullets” in a moderate nonlinear regime is ensured by a transverse parabolic profile of the refraction index in a multimode waveguide. The transverse motion of centers of mass of wave packets in such systems occurs on classical trajectories of a harmonic oscillator, whereas the motion in the longitudinal direction is uniform. Therefore, collisions of two solitons can be not only head-on but also tangential. An inelastic collision of two solitons with opposite circular polarizations can result either in two binary light bullets combining the left and right polarization or in more complex bound systems.

Appendix I to the paper published in transactions of Scientific Journal Physics, 2011 355(16), pages 133 138.

A solution of initial value problem for finding amplitude of every field component in arbitrary polarized light waves in totally reflected from self focusing kerr media, as function of dielectric function. is given by power series accurate to the 6th order.

Dissipative solitons supported by transversal single- or three-channel amplifying chirped lattices.

We study the properties of dissipative solitons supported by a chirped lattice in a focusing Kerr medium with nonlinear loss and a transversal linear gain landscape consisting of single or three amplifying channels. The existence and stability of two types of dissipative solitons, including fundamental and three-peaked twisted solitons, have been explored. Stable fundamental solitons can only be found in a single-channel gain chirped lattice, and stable three-peaked twisted solitons can only be obtained in a three-channel gain chirped lattice. The instability of two types of dissipative solitons can be suppressed at a high chirp rate. Also, robust fundamental and three-peaked twisted nonlinear states can be obtained by excitation of Gaussian beams of arbitrary width in corresponding characteristic structures.

Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice.

We predict the existence of gap solitons in the nonlinear fractional Schrödinger equation (NLFSE) with an imprinted optically harmonic lattice. Symmetric/antisymmetric nonlinear localized modes bifurcate from the lower/upper edge of the first/second band in defocusing/focusing Kerr media. A unique feature we revealed is that, in focusing Kerr media, stable solitons appear in the finite bandgaps with the decrease of the Lévy index, which is in sharp contrast to the standard NLSE with a focusing nonlinearity. Nonlinear bound states composed by in-phase and out-of-phase soliton units supported by the NLFSE are also uncovered. Our work may pave the way for the study of spatial lattice solitons in fractional dimensions.

Extended Propagation of Powerful Laser Pulses in Focusing Kerr Media.

Powerful incoherent laser pulses can propagate in focusing Kerr media much longer distances than can coherent pulses, due to the fast phase mixing that prevents transverse filamentation. This distance is limited by 4-wave scattering, which accumulates waves at small transverse wave numbers, where phase mixing is too slow to retain the incoherence and thus prevent the filamentation. However, we identify how this theoretical limit can be overcome by countering this accumulation through transverse heating of the pulse by random fluctuations of the refractive index. Thus, the laser pulse propagation distances are significantly extended, making feasible, in particular, the generation of unprecedentedly intense and powerful short laser pulses in a plasma by means of backward Raman amplification in new random laser regimes.

Solitons stabilization in PT symmetric potentials through modulation the shape of imaginary component

Stability and dynamics of PT symmetric fundamental bright solitons supported by localized potentials in a focusing Kerr medium are investigated numerically. How the shape and magnitude of the imaginary component affect soliton stability is addressed when fixed real part of the potentials. The unbroken PT symmetry in linear case and stable region in nonlinear case are discussed. Numerical simulations proved that solitons can propagate stably when the loss or gain distribution become narrower. So we can stabilize the solitons through modulation the shape of imaginary component, and can use the method for solitons formation and control in other nonlinear media with PT potentials.

Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium.

We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z3/2 up to ten times the power threshold for solitary wave generation.

Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium.

We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z3/2 up to ten times the power threshold for solitary wave generation.

Improving the quality of filament-impaired images in Kerr media by statistical averaging.

In focusing Kerr media, small-scale filamentation is the major obstacle to imaging at high light intensities. In this article, we experimentally and numerically demonstrate a method based on statistical averaging to reduce the detrimental effects of filamentation on the reconstructed images. The experiments are performed with femtosecond optical pulses propagating through a nonlinear liquid (toluene). We use digital holography to capture the transmitted optical image. The reverse propagation of the captured field is numerically performed using a numerical solution of the nonlinear Schrödinger equation. Because of their intrinsic sensitivity to measurement noise, filaments fail to propagate back on their initial trajectories and parasitic filaments form. The principle of the method is the introduction of artificial perturbations on the measurement, which spatially displace the parasitic filaments. By averaging the reconstruction over many realizations of the artificial perturbation, we show that the reconstruction improves the quality of the images. Finally, in order to identify the different regimes of optical power for which the filaments are time reversible, we also derive an analytical estimate for the condition number of the nonlinear propagator.

Influence of the imaginary component of the photonic potential on the properties of solitons inPT-symmetric systems

Existence, stability, and dynamics of $\mathcal{PT}$-symmetric fundamental bright solitons supported by localized super-Gaussian potentials in a focusing Kerr medium are investigated theoretically. We address how the shape and the magnitude of the transverse profile of the loss-gain distribution affect soliton stability. We find the stability region for nonlinear wave packets via a linear stability analysis, interpreting the insurgence of instability as an unbalanced flow of energy on the transverse plane. We confirm our results via numerical simulations, showing that an unstable soliton first undergoes longitudinal oscillations in propagation due to the interference between the soliton and the exponentially growing perturbation modes, eventually forming a highly localized single peak in the gain region.

Imaging in focusing Kerr media using reverse propagation [Invited

We present imaging experiments in focusing Kerr media using digital holography and digital reverse propagation (DRP) of the wave. For moderate power, the nonlinear DRP algorithm can be used to improve the quality of images over the linear DRP. We discuss the limits of the method at high power, the role of small-scale filaments, and the problem of time-dependent self-phase modulation.

Giant Goos–Hänchen shifts and radiation-induced trapping of Helmholtz solitons at nonlinear interfaces

Giant Goos-Hänchen shifts and radiation-induced trapping are studied at the planar boundary separating two focusing Kerr media within the framework of the Helmholtz theory. The analysis, valid for all angles of incidence, reveals that interfaces exhibiting linear external refraction can also accommodate both phenomena. Numerical evidence of these effects is provided, based on analytical predictions derived from a generalized Snell's law.

Digital reverse propagation in focusing Kerr media

Lenses allow the formation of clear images in homogeneous linear media. Holography is an alternative imaging method, but its use is limited to cases in which it provides an advantage, such as three-dimensional imaging. In nonlinear media, lenses no longer work. The light produces intensity-dependent aberrations. The reverse propagation method used in digital holography to form images from recorded holograms works even in Kerr media [M. Tsang, D. Psaltis, and F. G. Omenetto, Opt. Lett. 28, 1873 (2003).]. The principle has been experimentally demonstrated recently in defocusing media [C. Barsi, W.Wan, and J.W. Fleischer, Nat. Photonics 3, 211 (2009).]. Here, we report experimental results in focusing media.

Effect of oblique incidence on bistability of nonlinear microcavity

Based on the nonlinear medium transfer theory, optical bistability of nonlinear microcavity is investigated at oblique incidence. It is found that the critical frequency of incident light inducing bistability phenomenon is related to the polarization and incident angle. The critical frequency increases with the incident angle. Increasing the incident angle can make bistability happen easier for focusing Kerr medium, but will hinder bistability for defocusing Kerr medium. The bistability switch threshold of TE mode is significantly lower than that of TM mode at a large incident angle.

Coupling the symmetrical pair of temporary pulses propagating in the focusing Kerr media.

Coupling the symmetrical pair of temporary pulses propagating in the focusing Kerr media.

Feshbach-resonance-induced atomic filamentation and quantum pair correlation in atom-laser-beam propagation.

We study the propagation of an atom laser beam through a spatial region with a magnetic field tuned around a Feshbach resonance. Magnetic fields below the resonance produce an effective focusing Kerr medium that causes a modulational instability of the atomic beam. Under appropriate circumstances, this results in beam breakup and filamentation seeded by quasiparticle fluctuations and in the generation of correlated atomic pairs.

Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states

The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed.

Influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot cavity

An analysis of the influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot resonator with a self- focusing and self-defocusing Kerr medium is presented. The case is considered of two plane waves with different wavelengths incident on a non-linear Fabry–Pe´rot cavity. It is shown that the polarization states of the transmitted waves change bistably or multistably and depend on the parameters of incident waves and the resonator.

Rotating ring-shaped bright solitons

We show that ring-shaped bright soliton structures can exist in focusing Kerr media. Ring-shaped bright solitons, being initially at rest, demonstrate the inherent tendency to shrink. However, the ring axial rotation makes it possible to stabilize the soliton radius. The analytical results are confirmed by numerical calculations.