Physically intuitive coupled-mode and equivalent electrical-circuit theories are described for synthesis of nanophotonic resonator/interferometer circuits, including a new phase law for general 4-ports. Synthesis of self-adaptive (highly-nonlinear) optomechanical systems based on light forces is introduced. ©2008 Optical Society of America OCIS codes: (230.5750) Resonators; (120.2440) Filters; ...

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservative equation. In particular, entropy satisfying convergence follows for E schemes—those containing more numerical viscosity tha...

In this expository paper, we discuss the use of the Evans function in finding resonances, which are poles of the analytic continuation of the resolvent. We illustrate the utility of the general theory developed in [13, 14] by applying it to two physically interesting test cases: the linear Schrödinger operator and the linearization associated with the integrable nonlinear Schrödinger equation.

A nonlinear first-order boundary value problem with discontinuous solutions is considered. It arises in the study of gasflow through a duct and allows, in general, for multiple solutions. New convergence results for three difference schemes are presented and the sharpness of numerical layers is established. For the EO-scheme, stability of a physically correct solution with respect to time evolu...

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model transformed to the reaction-diffusion analog of the NLS equation for which the bilinear repres...

Losses during the operation of electrical machines heat up permanent magnets which in turn changes their demagnetization behavior. An elevation magnet’s temperature usually correlates to a decreasing remanence and coercivity. The relation between them may become nonlinear. Existing material models either lack accuracy or are parameterized with high number variables. This paper presents novel se...

We revisit the problem of the optimization of a silicon-nanocrystal (Si-NC) waveguide, aiming to attain the maximum field confinement inside its nonlinear core and to ensure optimal waveguide performance for a given mode power. Using a Si-NC/SiO2 slot waveguide as an example, we show that the common definition of the effective mode area may lead to significant errors in estimation of optical in...

In earlier work we proposed a family of nonlinear time-evolution equations for quantum mechanics associated with certain unitary group representations. Such nonlinear Schrr odinger equations are expected to describe irreversible and dissipative quantum systems. Here we introduce and justify physically the group of nonlinear gauge transformations necessary to interpret our equations. We determin...

We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( PT-) and non- PT-symmetric potentials. We find that the constant momentum coefficient Γ can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Γ...