Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KNbO(3)

We demonstrate self-trapping of one-dimensional and two-dimensional optical beams in a photorefractive KNbO(3) crystal. We study the waveguides induced by the self-trapped beams for prospective applications of tunable nonlinear frequency conversion in soliton-induced waveguides.     

Stable observer-based trajectory controller for asymptotic model matching of a rigid robot

This paper considers a control problem that requires the design of an observed-based compensator in order to guarantee the asymptotic convergence of the output (namely, the joint generalized coordinates of ann-degree of freedom robot) to a corresponding output produced by a linear reference model. It is shown that, for a model having a relative degree vector {r ₁, ...,r _n}, withr _i 2, it is possible to determine a controller-observer yielding a robot output that converges exponentially to the desired model output. Moreover, the combined system comprising the plant and the controller is internally stable in the semiglobal sense. The solution to the standard trajectory-following problem in robotics is obtained as a simplified case of the underlying model matching problem. While the controller-observer is nonlinear, its dynamic part is linear time-varying; in addition, the construction does not assume a priori the knowledge or even the existence of an upper bound to the model state vector.This research was supported in part by the Paul Ivanier Center for Robotics Research and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel.The authors wish to thank Evgany Landau from the Department of Electrical and Computer Engineering, Ben Gurion Univeersity of the Negev, for designing and performing the computer simulation.     

The Geometry of Cauchy's Fluxes

A formulation of the Cauchy theory for balance laws of scalar valued quantities is considered from a general geometric point of view. It is assumed only that the ambient space is an orientable m-dimensional manifold. The analog of the usual flux vector field is an (m−1)-differential form. Both the Cauchy theorem and differential version of the balance laws are formulated in this context. Accepted December 9, 1999?Published online July 12, 2000     

Holographic solitons

We propose a new kind of an optical spatial soliton: the holographic soliton. This soliton consists of two mutually coherent field components that interfere, induce a periodic change in the refractive index, and simultaneously are Bragg diffracted from the grating. Holographic solitons are formed when the broadening tendency of diffraction is balanced by phase modulation that is due to Bragg diffraction from the induced grating. Holographic solitons are solely supported by cross-phase modulation arising from the induced grating, not involving self-phase modulation at all.     

Modeling of high-frequency propagation in inhomogeneous background random media

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.     

Optical parametric oscillation in soliton-induced waveguides

We demonstrate experimentally an optical parametric oscillator constructed in a waveguide induced by a photorefractive spatial soliton and show that the pumping threshold is reduced considerably.     

Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe

We demonstrate the formation of (1+1) - and (2+1) -dimensional solitons in photorefractive CdZnTe:V, exploiting the intensity-resonant behavior of the space-charge field. We control the resonance optically, facilitating a 10-mus soliton formation times with very low optical power.