Related papers: Numerical Method for Nonlinear Optical Spectroscop…
Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments…
This paper provides a mathematical analysis of ultrafast ultrasound imaging. This newly emerging modality for biomedical imaging uses plane waves instead of focused waves in order to achieve very high frame rates. We derive the point spread…
Convolutional neural networks (CNNs) have attracted a rapidly growing interest in a variety of different processing tasks in the medical ultrasound community. However, the performance of CNNs is highly reliant on both the amount and…
We propose a numerical interferometry method for identification of optical multiply-scattering systems when only intensity can be measured. Our method simplifies the calibration of optical transmission matrices from a quadratic to a linear…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…
This paper is concerned with the fast computation of Fourier integral operators of the general form $\int_{\R^d} e^{2\pi\i \Phi(x,k)} f(k) d k$, where $k$ is a frequency variable, $\Phi(x,k)$ is a phase function obeying a standard…
We show, for the first time, how to calculate photonic band structures for metals and other dispersive systems using an efficient Order N scheme. The method is applied to two simple periodic metallic systems where it gives results in close…
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using…
In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effective implementation. In constant-order cases, our methods can…
We present ultra-fast quantum chemical methods for the calculation of infrared and ultraviolet-visible spectra designed to provide fingerprint information during autonomous and interactive explorations of molecular structures.…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
In this work we numerically analyze a photonic unconventional accelerator based on the four-wave mixing effect in highly nonlinear waveguides. The proposed scheme can act as a fully analogue system for nonlinear signal processing directly…
Ultrafast nonlinear photonics enables a host of applications in advanced on-chip spectroscopy and information processing. These rely on a strong intensity dependent (nonlinear) refractive index capable of modulating optical pulses on…
The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
Extreme ultraviolet pulses as generated by high harmonic generation (HHG) are a powerful tool for both time-resolved spectroscopy and coherent diffractive imaging. However, the integration of spectroscopy and microscopy to harness the…