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Recent differentiable rendering techniques have become key tools to tackle many inverse problems in graphics and vision. Existing models, however, assume steady-state light transport, i.e., infinite speed of light. While this is a safe…

Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume of…

Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many…

Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…

We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

The guiding and transport of energy, for example of electromagnetic waves underpins many technologies that have shaped modern society, ranging from long distance optical fibre telecommunications to on-chip optical processors. Traditionally,…

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…

Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…

A novel approach to study transmission through waveguides in terms of optical streamlines is presented. This theoretical framework combines the computational performance of beam propagation methods with the possibility to monitor the…

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…

Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive…

Relying on Feynman-Kac path-integral methodology, we present a new statistical perspective on wave single-scattering by complex three-dimensional objects. The approach is implemented on three models -- Schiff approximation, Born…

Wave-particle duality finds a natural application for electrons or light propagating in disordered media where coherent corrections to transport are given by two-wave interference. For scatterers with internal degrees of freedom, these…

Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves.…

We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where…

We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…

Eikonal, or ray tracing, methods are commonly used to estimate the propagation of radio frequency fields in plasmas. While the information gained from the rays is quite useful, an approximate solution for the fields would also be valuable,…

We present a method based on a time domain simulation of wave propagation that allows studying the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological…