Photorefractive phase conjugation of pulses: A numerical and analytical comparison

We study numerically the temporal behavior of the phase conjugation of a pulse, by a single four-wave mixing grating, in photorefractive media. We solve numerically the time-dependent coupled-wave equations obtained from a currently used generalization of the Khuktarev model, under the standard restriction of undepleted pump and slowly varying envelope approximations. The fully numerical solutions presented here are terminal solutions that do not require solving any intermediate steps such as the reflectivity. However, we compare the numerical reflectivity with its analytical counterpart, when available, and discuss the differences on their predictions of the phase conjugate pulse.Current permanent position at INAOE and on a Sabbatical leave from the Centro de Investigaciones en Optica, Apdo. Postal 948, Leon, Gto. 37000. Mexico.     

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.     

Phase conjugation of gap solitons: A numerical study

We study the effect of a nearby phase-conjugate mirror (PCM) on the gap soliton of a Kerr non-linear periodic structure. We show that phase conjugation of the gap soliton (in the sense of replication of the amplitude profile in the reverse direction) is possible under the condition of PCM reflectivity approaching unity. This is in contrast with the results for linear structures, where the wave profiles can be conjugated for arbitrary values of the PCM reflectivity. The sensitivity of the conjugation of the gap solitons to PCM reflectivity is ascribed to the fine balance of non-linearity with dispersion, necessary for their existence.     

Optical phase conjugation in laser dyes

The nonlinear optical response of four laser-active dyes (Pyridine 1, DCM, Pyridine 2 and Styryl 9) is reported at a wavelength of 532 nm. The dyes show phase conjugate reflectivities in the 5 to 85% range. Polarization discrimination experiments and comparison with the Caro-Gower model suggests thermal origin of the nonlinearity.     

Quality of phase conjugation in silicon

The quality of phase conjugates generated by real-time holography in silicon is assessed interferometrically. The conjugate phase is found to be degraded by about a half wave distortion due to self-defocussing. We infer that the nonlinearly- induced gratings decay at a rate much faster than the value suggested previously.     

Optical phase conjugation in semiconductor-doped glasses

We have studied optical phase conjugation in two types of semiconductor-doped glasses. Corning 3.68 and Schott OG 530 at λ = 0.532 μm using picosecond pulses. We observe a slow nonlinearity in agreement with the slow decay of luminescence. The saturation of the reflectivity is strongly correlated with the absorption saturation of these glasses and may be interpreted in terms of a three-level system model.     

Nonequilibrium phase transitions and chemical instabilities

The effect of inhomogeneous fluctuations on instabilities in various nonlinear chemical models is studied in terms of concepts developed in the theory of equilibrium phase transitions.Chercheur qualifié au Fonds National de la Recherche Scientifique.     

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.     

Transparency in Bragg scattering and phase conjugation

Reflectionless transmission of light waves with unitary transmittance is shown to occur in a certain class of gain-grating structures and phase-conjugation mirrors in the unstable (above-threshold) regime. Such structures are synthesized by means of the Darboux method developed in the context of supersymmetric relativistic quantum mechanics. Transparency is associated to superluminal pulse transmission.     

Chaos in symmetric phase oscillator networks

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities.     

复摆振动中的混沌现象

利用组合物理实验仪,研究了复摆振动中的混沌现象,分析了产生混沌的物理条件,并给出不同条件下的混沌图形.     

Interactions and disorder in quantum dots: instabilities and phase transitions

Using a fermionic renormalization group approach, we analyze a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by random matrix theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.     

Chaos in numerical analysis of ordinary differential equations

The discretisation of the ordinary nonlinear differential equation $\text{d}\text{y}\text{d}\text{t}\text{= y(1?y)}$ by the entral difference scheme is studied for fixed mesh size. In the usual numerical computation, this method produces some “ghost solution” for the long range calculation. Regarding this discretisation as a dynamical system in R², these pathological behaviors are shown to be a kind of “chaos” in the dynamical system for any mesh size. Moreover, some combination of the central difference scheme and the Euler's scheme is studied for the above equation. It gives some motivation for Hénon's model. The usual discretisation of a second order differential equation are studied also. It gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by Hénon-Heiles.     

Reduction of soliton phase jitter by in-line phase conjugation

The main impairment of differential-phase-shift-keyed communication systems is phase jitter. Noise-induced phase jitter, which is mediated by self-phase modulation, can be reduced significantly by a small number of in-line phase conjugators.     

Optical phase conjugation and pseudolinear transmission

We describe the use of optical phase conjugation (OPC) to suppress intrachannel nonlinearities that limit pseudolinear transmission. We show that OPC combined with appropriate dispersion mapping is effective in suppressing intrachannel nonlinearities, even in the absence of signal-power evolution symmetry that is generally required by OPC to compensate fiber nonlinearity. An increase in signal power by 5.5 dB is observed when a single OPC is used for 40-Gbit/s pseudolinear transmission over 32 x 100 km of passive-fiber spans.     

RF stabilization of plasma instabilities: a note on physical mechanism

In a series of recent works, we have developed models including realistic spatial profiles of both flow and radio-frequency-induced ponderomotive force. With these inclusions, the picture of stability of various plasma and fluid instabilities is expected to be changed drastically with ground-breaking consequences. The inhomogeneous parallel flow and the radio-frequency waves can actually stabilize turbulence. This is different from the prevalent notion that both parallel flow shear and radio-frequency waves are responsible for the excitation (destabilization) of plasma turbulence. This model thus aims to open-up new channels and provide a major breakthrough in our knowledge of plasma and fluid turbulence and its consequent roles in energy, space and processing technology. In this short note, we elucidate the physical mechanism behind this novel observation.     

Effect of phase noise on parametric instabilities

We report an experimental study on the effect of an external phase noise on the parametric amplification of surface waves. We observe that both the instability growth rate and the wave amplitude above the instability onset are decreased in the presence of noise. We show that all the results can be understood with a deterministic amplitude equation for the wave in which the effect of noise is just to change the forcing term. All the data for the growth rate (respectively the wave amplitude), obtained for different forcing amplitudes and different intensities of the noise, can be collapsed on a single curve using this renormalized forcing in the presence of noise.     

Multiple-conjugation expansion in distortion elimination by phase conjugation

The multiple-conjugation expansion results from a method of phase-conjugate scattering analysis that is convenient in connection with strong aberrators and weak phase conjugators. Based on this expansion, a new proof is obtained of a recently established theorem according to which a complete cancellation of distortion is possible in the absence of gains or losses. The proof makes use of the reciprocity property and of the generalized optical theorem of potential scattering.