Analytic structure of the four-wave mixing model in photorefractive materials

In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise, to that of the cubic complex Ginzburg-Landau equation. The main result is that, in order to be single valued, time-dependent solutions should depend on the space-time coordinates through the reduced variable xi=\sqrt{z} exp(-t / tau), in which tau is the relaxation time.Comment: 5 pages, Waves and stability in continuous media, 30 June-7 July 2007, Scicli (Rg), Ital

Explicit solutions of the four-wave mixing model

The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lower-dimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painleve' test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time tau, the complex response constant gamma. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (Real(gamma)=0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (Re(gamma) not=0), we display strong similarities with the cubic complex Ginzburg-Landau equation.Comment: 16 pages, J Phys A Fast track communication, to appear 200

Вплив напівпровідникових та металевих наночастинок на діелектричні властивості іонної матриці октаноата кадмію

Dielectric properties of ionic composites consisted of cadmium octanoate matrix and semiconductor or metal nanoparticles have been investigated. The nanoparticles of different nature (semiconductor CdS, metal Au, and metal core-semiconductor shell Au-CdS) were chemically synthesized in the smectic A phase of (Cd+2(C7H15COO)−2, CdC8) that was used as a nanoreactor. These nanocomposites are very stable and well ordered; the size and shape of the nanoparticles (NPs) are well controlled during the synthesis. The main aim of the research was to examine the influence of nanoparticles on the dielectric properties of ionic matrix, which has smectic A ordered structure. Electrical characteristics were investigated at different temperatures, which correspond to different phases of the material. The conductivity of nanocomposites has an activation nature. The electrical conductivity anisotropy confirms the structural anisotropy of the nanocomposites. The conductivity of the nanocomposite along the cation-anion layers is higher by 2 orders of magnitude than that across the cation-anion layers. Basing on the experimental data, we proposed the simple model of the charge carriage process

Structural characteristics of different types of nanoparticles synthesised in mesomorphic metal alkanoates

The class of thermotropic ionic liquid crystals (LCs) of the metal alkanoates possesses a number of unique properties, such as intrinsic ionic conductivity, high dissolving ability and ability to form time-stable mesomorphic glasses. These ionic LCs can be used as nanoreactors for the synthesis and stabilisation of different types of nanoparticles (NPs). Thus, some semiconductors, metals and core/shell NPs were chemically synthesised in the thermotropic ionic liquid crystalline phase (smectic A) of the cadmium octanoate (CdC8) and of the cobalt octanoate (CoC8). By applying the scanning electron microscopy, the cadmium and cobalt octanoate composites containing CdS, Au, Ag and core/shell Au/CdS NPs have been studied. NPs’ sizes and dispersion distribution of the NPs’ size in the nanocomposites have been obtained