In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the re...

We have expressed the nonlinear optical absorption of a semiconductor in terms of its linear spectrum. We determined that the two-photon absorption coefficient in a strong DCelectric field of a direct gap semiconductor can be expressed as the product of a differential operator times the convolution integral of the linear absorption without a DC-electric field and an Airy function. We have appli...

Ferroelectric crystals are important materials in many kinds of applications. Since the invention of so called quasi-phase matching technique, periodically domain-inverted ferroelectrics crystals with modulated second order nonlinear susceptibility are widely used in frequency conversion application. In periodically domain-inverted ferroelectrics crystals, besides the nonlinear optical coeffici...

In this paper, we propose an algorithm for numerical solving an inverse nonlinear diffusion problem. The algorithm is based on the linearized nonlinear terms by Taylor ́s series expansion, removed the time-dependent terms by Laplace transform, and so, the results at a specific time can be calculated without step-by-step computations in the time domain. Finite difference technique used for discre...

Single-mode Ge₂₈Sb₁₂Se₆₀ strip waveguides, fabricated with thermal evaporation and lift-off, were demonstrated at 1.03 µm. The linear and nonlinear optical properties of these waveguides were shown to be similar to bulk samples, with differences attributed to small variations in composition of ~4 atomic % or less. From z-scan measurements at 1.03 µm using circularly polarized, ~200 fs pulses at...

By employing the Gaussian decomposition method, the analytical formulas of the Gaussian-beam Z-scan traces have been derived for an optically thin material exhibiting both refractive and absorptive parts of third-order nonlinearity, with Gaussian or hyperbolic secant squared laser pulses of femtosecond duration. The formulas have been verified experimentally with femtosecond-pulsed Z scans on a...

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the f...