Deeply sub-wavelength two-dimensional films may exhibit extraordinarily strong nonlinear effects. Here we show that 2D films exhibit the remarkable property of a phase-controllable nonlinearity, i.e., the amplitude of the nonlinear polarisation wave in the medium can be controlled via the pump beam phase and determines whether a probe beam will "feel" or not the nonlinearity. This is in stark c...

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler– Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler–Bernoulli beam theory. The Ritz–Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlin...

Recent developments in the study of integrable Hamiltonian systems have led to nonlinear accelerator lattice designs with two transverse invariants. These lattices may drastically improve the performance of high-power machines, providing wide tune spreads and Landau damping to protect the beam from instabilities, while preserving dynamic aperture. To test the feasibility of these concepts, the ...

Nonlinear beam resting on linear elastic foundation and subjected to harmonic excitation is investigated. The beam is simply supported at both ends. Both linear and nonlinear analyses are carried out. Hamilton’s principle is utilized in deriv ing the governing equations. Well known forced duffing oscillator equation is obtained. The equation is analyzed numerically using Runk-Kutta technique. T...

LETER A R IC LE Abstract A method is proposed for nonlinear beam shaping, employing a non-collinear quasi phase-matched interaction in a crystal whose nonlinear coefficient is encoded by a computer generated hologram pattern. In this method the same axis is used for both satisfying the phase-matching requirements and encoding the holographic information, the result is a single shaped beam in th...

Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST) code is used to simulate the linear and nonlinear properties of the electron-proton (e-p) two-stream instability observ...

We demonstrate control of the nonlinear conversion across a beam profile by using periodically poled lithium niobate with a laterally nonuniform quasi-phase-matching grating. As a representative experiment, generation of a flat-top second-harmonic beam is demonstrated.

In this paper a novel all-optical logic NAND, NOR and XOR gate based on nonlinear directional coupler theory is demonstrated. We use the identical structure which contains three waveguides, for designing these gates; the only difference however, is the power of inputs light beam. In other words, while a beam with 4 W/μm in power considered as logical one, the output is NAND gate and if a beam w...

In this paper a novel all-optical logic NAND, NOR and XOR gate based on nonlinear directional coupler theory is demonstrated. We use the identical structure which contains three waveguides, for designing these gates; the only difference however, is the power of inputs light beam. In other words, while a beam with 4 W/μm in power considered as logical one, the output is NAND gate and if a beam w...

In this paper the problems of state estimation, tracking control and shape control in a micro-cantilever beam with nonlinear electrostatic actuation are investigated. The system’s partial differential equation of motion is converted into a set of ordinary differential equations by projection method. Observabillity of the system is proven and a state estimation system is designed using extended ...