Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras

In 1951, Diliberto and Straus [5] proposed a levelling algorithm for the uniform approximation of a bivariate function, defined on a rectangle with sides parallel to the coordinate axes, by sums of univariate functions. In the current paper, we consider the problem of approximation of a continuous function defined on a compact Hausdorff space by a sum of two closed algebras containing constants. Under reasonable assumptions, we show the convergence of the Diliberto–Straus algorithm. For the approximation by sums of univariate functions, it follows that Diliberto–Straus’s original result holds for a large class of compact convex sets.     

The Inclusion Properties of a New Watersoluble Sulfonated Calix[4]resorcinarene towards Alkylammonium and N-Methylpyridinium Cations

The inclusion behaviour of a new water-soluble sulfonated calix[4]resorcinarene towards alkylammonium and N-methylpyridinium cations has been investigated on the basis of ¹H NMR spectroscopy and pH-potentiometry data. The inclusion of the N-methylpyridinium cation has been found to be dependent on pH with the preferable inclusion of the methyl substituent in alkaline and the aromatic ring in neutral aqueous media.     

On some contact problems for composite half-spaces PMM vol. 31, no. 6, 1967, pp. 1001–1008

Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.

1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.

2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.

In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.

Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.

The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].

The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials.     

Phase conjugation by reflection gratings in electrooptic crystals

Phase conjugation by reflection gratings in electrooptic crystals in investigated in a nonlinear model proposed by Kukhtarev and Semenets [1] which takes into account not only photoconductivity but also dark conductivity. The coupled-wave equations of the model can be solved analytically. To take the boundary conditions into account, numerical calculations are unavoidable. These can be performed, however, without any approximation. Phase mismatch and self-oscillation effects are dealt with in the undepleted pump approximation.Two of us (KHR and GT) would like to dedicate this paper to Prof. Dr. H. Salecker on the occasion of his 65^th birthday     

Space charge field limitations in photorefractive LiNbO3:Fe crystals

We use holographic techniques for the investigation of strongly oxidized LiNbO₃:Fe crystals with small Fe²⁺ concentrations and compare the results with theoretical predictions. Experimental evidence is presented for enhanced phase shifts between light intensity pattern and refractive index grating and for limitations of optically induced space charge fields in photovoltaic crystals due to the low concentration of filled traps. Our findings do not support the model of a nonlocal photovoltaic effect in LiNbO₃.     

Magneto-transport properties of La0.7Ca0.3MnO3/SrTiO3/La0.7Ce0.3MnO3 tunnel junction

Hole-doped rare-earth manganite La_0.7Ca_0.3MnO₃ and the electron-doped manganite La_0.7Ce_0.3MnO₃ both show a metal-insulator transition around 250 K associated with a ferromagnetic transition and colossal magnetoresistance. In an earlier publication we have reported the rectifying characteristic of La_0.7Ca_0.3MnO₃/SrTiO₃/La_0.7Ce_0.3MnO₃ tunnel junction at room temperature, showing that it is possible to fabricate a diode out of the polaronic insulator regime of doped manganites. Here we report the magneto-transport properties of such a tunnel junction above and below the metal-insulator transition. We show, from the large positive magnetoresistance of the tunnel junction at low temperature, that La_0.7Ce_0.3MnO₃ could be a minority spin carrier ferromagnet. The implication of this observation is discussed.     

Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002     

Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003