Bounds on the extensional strains in elastic homogeneous crystals under simple tension

Within the context of the linearized theory of elasticity, weconsider homogeneous crystals, which have orthorhombic, tetragonal,hexagonal symmetry or cubic symmetry (‘RTHC’ crystals).When such a crystal is subjected to a simple tension (or compression)of amount T in the direction n, there will be three, generallydifferent, extensional strains along the three mutually perpendiculardirections corresponding to the principal axes of strain. Thepurpose of this paper is to present a simple procedure to placebounds, upper and lower, on the possible extensional strainsin the crystal, both in the case when n is fixed in directionand in the case when n is arbitrary. The procedure allows usto determine whether the bounds are attained or not.     

The effect of a high external electric field on a photorefractive ring phase conjugator

It is shown that a high external electric field often used to enhance the efficiency of photorefractive beam coupling and to decrease the photorefractive response time, may cause mode switching in photorefractive ring phase conjugator leading to a significant drop in the phase conjugate reflectivity.     

Tailoring Čerenkov second-harmonic generation in bulk nonlinear photonic crystal

We investigate theoretically the ?erenkov-type second-harmonic generation in two-dimensional bulk nonlinear photonic crystal with longitudinal modulation of the χ((2)) nonlinearity. We show that in this scheme the ?erenkov radiation can be achieved simultaneously at multiple directions with comparable intensities. The angles of emission are controllable by the spatial modulation of the nonlinearity. We propose a design of the periodically poled domain pattern, which maximizes the efficiency of the second-harmonic emission.     

Third-harmonic generation via nonlinear Raman-Nath diffraction in nonlinear photonic crystal

We report on the observation of multiple third-harmonic conical waves generated in an annular periodically poled nonlinear photonic crystal. We show that the conical beams are formed as a result of the cascading effect involving two parametric processes that satisfy either the transverse and/or longitudinal phase-patching conditions. This is the first experimental observation of third-harmonic generation based on nonlinear Raman-Nath diffraction.     

Broadband third-harmonic generation in two-dimensional short-range ordered nonlinear photonic structure

We study parametric frequency conversion in two-dimensional nonlinear photonic crystal with short-range ordered ferroelectric domains. We demonstrate that the short-range order enables broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We obtain conversion efficiencies that are much higher than those achieved from a randomized medium, owing to the unique distribution of reciprocal lattice vectors in the short-range ordered structure.     

Stable rotating dipole solitons in nonlocal optical media

We reveal that nonlocality can provide a simple physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which are known to be unstable in all types of realistic nonlinear media with a local response.     

Mapping phases of singular scalar light fields

We implement experimentally a simple method for accurate measurements of phase distributions of scalar light fields. The method is based on the polarimetric technique for recording the polarization maps of vector fields, where coaxial superposition of orthogonally polarized reference and signal beams allows the signal phase to be reconstructed from the polarization map of the total field. We demonstrate this method by resolving topologically neutral pairs of closely positioned vortices in a speckle field and recovering the positions of vortices within a Laguerre-Gaussian beam with the topological charge three.     

Multipole spatial vector solitons

We introduce the concept of multipole spatial optical vector solitons associated with higher-order guided modes trapped by a soliton-induced waveguide in a bulk medium. Such stationary localized waves include previously predicted vortex- and dipole-mode vector solitons and also describe new higher-order vector solitons and necklace-type beams. We present the theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons.     

The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices

Two recent methods (Shanno, 1978; Toint, 1980) for revisingestimates of sparse second derivative matrices in quasi-Newtonoptimization algorithms reduce to variable metric formulae whenthere are no sparsity conditions. It is proved that these methodsare equivalent. Further, some examples are given to show thatthe procedure may make the second derivative approximationsworse when the objective function is quadratic. Therefore theconvergence properties of the procedure are sometimes less goodthan the convergence properties of other published methods forrevising sparse second derivative approximations.     

Transverse second-harmonic generation from disordered nonlinear crystals

We investigate the transverse second-harmonic generation in as grown strontium barium niobate (SBN) crystals with a random structure of anti-parallel ferroelectric domains. We consider both, single and counter-propagating pulse geometries. We investigate polarization properties of the second harmonic signal and discuss applications of this process for short pulses characterization. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland