We discuss a nonlinear beam obstacle model defined by inequality constraints and differential equations with highly nonlinear and fourth order operators. An appropriate discrete approximation by the finite element method leads to a large finite-dimensional mixed nonlinear complementarity problem. We propose an interior-point algorithm for the solution of this complementarity problem. Some compu...

We propose and experimentally demonstrate a colorful nonlinear Raman-Nath second-harmonic generation by engineering the quadratic nonlinearity χ((2)) in an aperiodically poled lithium tantalite. The engineered nonlinear structure allows multicolored Raman-Nath second-harmonic signal outputs along a uniform direction, which cannot be achieved in a uniform nonlinear grating. The diffraction angle...

The authors theoretically and numerically investigate the beam propagation near the supercollimation frequency s 0 in a photonic crystal made of nonlinear material. Since the value and sign of the equal-frequency-contour curvature which dominates the beam behaviors can be nonlinearly tuned near s , a kind of nonlinear effect is generated. The envelope equation with unique form is also obtained....

In recent experiments investigating the nonlinear interaction between light and nematic liquid crystals, Braun et al. (1993) observed complex optical beam structures that were generated by the strong self-focussing of laser light. For a simplified partial differential equation (PDE) model which captures the essential coupling between optical refraction and nematic deformation, we demonstrate tw...

We report on a new optical device allowing to efficiently add desired functionalities to a nonlinear interaction. This is achieved by focused ion beam patterning of a nano-layer of gold sputtered at the exit facet of a nonlinear crystal. The functionality is experimentally demonstrated with three examples: spatial filtering where a fundamental beam with a poor mode quality and its' frequency-do...

We demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double-resonant system with quadratic nonlinear response. We use an array of periodically poled coupled optical waveguides and observe inhibition of the nonlinear beam self-action independent on power. This inhibition is demonstrated in both regimes of normal and anomalous beam diffraction.

We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in ...

Remote sensing applications often require high energy laser-like beams with narrow bandwidth and low divergence at wavelengths that cannot be reached directly with ordinary laser materials. The common way of generating such wavelengths is through optical parametric oscillators (OPOs), sumor difference frequency generators, or a combination of these. For the new beam to be generated with high co...

The static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. Two engineering cases including cantilever and double cantilever micro-beam are considered. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, c...

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group ...