We use pump-probe spectroscopy and continuous wave cross-phase and cross-amplitude modulation measurements to study the optical nonlinearity of a hydrogenated amorphous silicon (a-Si:H) nanowire waveguide, and we compare the results to those of a crystalline silicon waveguide of similar dimensions. The a-Si:H nanowire shows essentially zero instantaneous two-photon absorption, but it displays a...

In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF (2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlineari...

The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schrödinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical propert...

A Wiener system is composed of a linear dynamic subsystem followed by a static nonlinearity. It is well known in the literature that the identi cation of the linear subsystem of a Wiener system can be separated from that of the output nonlinearity, if the input signal is Gaussian. In order to deal with non Gaussian inputs, two new algorithms are proposed in this paper for direct identi cation o...

Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the si...

We propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as separate innovation-like variables. Common nonlinearity can then be easily defined as the presence of common inn...

Bistable responses of Fabry–Pérot cavities and all-optical arrays, in the presence of weak diffraction and strong diffusion, are studied both analytically and numerically. The model is a pair of nonlinear Schrödinger equations coupled through a diffusion equation. The numerical computations are based on a split-step method with three distinct characteristics. This bistable nonlinear system, wit...