Related papers: Information Transmission using the Nonlinear Fouri…
We describe a self calibrating optical technique that allows to perform absolute measurements of scattering cross sections for the light scattered at extremely small angles. Very good performances are obtained by using a very simple optical…
We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…
In this research, numerical analysis of nonlinear pulse propagation is carried out. This is done mainly by solving the nonlinear Schrodinger equation using the split step algorithm. In a nonlinear media, dispersive effects exist…
Experimental Stokes vector spectroscopy characterizes polarization state noise in nonlinear fiber transmission. Noise bandwidths of a few MHz are observed from XPM-blurred receive SOPs using a polarization scrambling interferometer. This…
We expose a functional integration method for the averaging of continuous products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This problem is…
We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral…
A new method to calculate the spectrum using cascaded open systems and master equations is presented. The method uses two state analyzer atoms which are coupled to the system of interest, whose spectrum of radiation is read from the…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or,…
We study active array imaging of small but strong scatterers in homogeneous media when multiple scattering between them is important. We use the Foldy-Lax equations to model wave propagation with multiple scattering when the scatterers are…
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography and telecommunications. A key paradigm for devices based on this…
The use of ultra-massive multiple-input multiple-output and high-frequency large bandwidth systems is likely in the next-generation wireless communication systems. In such systems, the user moves between near- and far-field regions, and…
The Optical Darboux Transformer is introduced as a photonic device which performs the Darboux transformation directly in the optical domain. This enables two major advances for signal processing based on the nonlinear Fourier transform: (i)…
We report a simple and efficient all-optical polarization scrambler based on the nonlinear interaction in an optical fiber between a signal beam and its backward replica which is generated and amplified by a reflective loop. When the…
A lower bound on the capacity of the split-step Fourier channel is derived. The channel under study is a concatenation of smaller segments, within which three operations are performed on the signal, namely, nonlinearity, linearity, and…
We outline a novel numerical method, called Ultrafast Ultrafast (UF$^2$), for calculating the $n^\text{th}$-order wavepackets required for calculating n-wave mixing signals. The method is simple to implement, and we demonstrate that it is…