We present an analysis and simulation of the non-paraxial nonlinear SchroÈ dinger equation. Exact general relations describing energy ̄ ow conservation and transformation invariance are reported, and then explained on physical grounds. New instabilities of fundamental and higher-order paraxial solitons are discovered in regimes where exact analytical non-paraxial solitons are found to be robust...

Using the integrable nonlinear Schrödinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called "eigenvalue communication" idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol....

The NLSE soliton scattering by impurities is considered in the framework of the one-dimensional model. The scattering intensity is characterized by the reflection coefficient. The reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory for the following cases: (i) and isolated impurity, (ii) two point impurities, and (iii) a regular or random sys...

We consider the reconstruction of a spatially-dependent scattering coefficient in a linear transport equation from diffusion-type measurements. In this setup, the contribution to the measurement is an integral of the scattering kernel against a product of harmonic functions, plus an additional term that is small when absorption and scattering are small. The linearized problem is severely ill-po...

We present sum-frequency-scattering experiments on colloidal dispersions with various concentrations and in different scattering geometries. At small scattering angles, large fluctuations are observed in the intensity of the scattered sum-frequency photons. By considering the angular dependence of the signal, the particle concentration dependence, and the surface vibrational spectra of the part...

The extended Born technique is an approximate nonlinear method for analyzing scattering from a weak discontinuity. Moreover, when applied to the low-frequency (electromagnetic induction) applications for which it was developed originally, extended Born has accurately modeled scattering from inhomogeneities considerably larger than those appropriate for the standard linear Born technique. In thi...

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low-coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation r...

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the...

We have recently developed a spectral re-shaping technique to simultaneously measure nonlinear refractive index and nonlinear absorption. In this technique, the information about the nonlinearities is encoded in the frequency domain, rather than in the spatial domain as in the conventional Z-scan method. Here we show that frequency encoding is much more robust with respect to scattering. We com...