Created by sebastien.popoff on 16/09/2020

## Langevin Institute, Paris

We propose a 2 years postdoctoral position in the Waves Theory and Mesoscopic Physics group of the Langevin Institute under the supervision of Arthur Goetschy. The goal of the project is to provide a theory for the scattering matrix of strongly scattering media made of resonant units for wavefront shaping applications. Applicants should have a Ph.D. in wave physics with a solid background on wave propagation in complex systems.
Contact: arthur.goetschy@espci.psl.eu

Created by sebastien.popoff on 23/06/2020

## DMD diffraction tool

I presented in this tutorial the diffraction effects occurring in a DMD setup. It corresponds to a blazed grating effect and depends on the wavelength $$\lambda$$, the pixel pitch $$d$$, the incident angle $$\alpha$$, and the angle of the micro-mirrors $$\theta$$. Here is a simple app (see source code on Github) to calculate the criterion for optimal diffraction efficiency and the aspect of the diffraction pattern in the far-field when illuminating the DMD with a plane wave of incident angle $$\alpha$$ with respect to the normal of the surface.

Created by sebastien.popoff on 22/05/2019

## Semidefinite Programming for Intensity Only Estimation of the Transmission Matrix

The possibility of measuring the transmission matrix using intensity only measurements is a much sought-after feature as it allows us not to rely on interferometry. Interferometry usually requires laboratory-grade stability difficult to obtain for real-world applications. Typically, we want to be able to retrieve the transmission matrix from a set of pairs composed of input masks and output intensity patterns. However, this problem, which corresponds to a phase-retrieval problem, is not convex, hence difficult to solve using standard techniques. The idea proposed in [I. Waldspurger et al., Math. Program (2015)] is to relax some constraints to approximate the problem to a convex one that can be solved using the semidefinite programming approach. I briefly detail the approach and provide an example of the procedure to reconstruct the transmission matrix using Python. A Jupyter notebook can be found on my Github account: semidefiniteTM_example.ipynb.

Created by sebastien.popoff on 13/12/2018

## Part 1: Straight Fibers

Under the weakly guided approximation, analytical solutions for the mode profiles of step-index (SI) and graded-index (GRIN) multimode fibers (MMF) can be found [1]. It also gives a semi-analytical solution for the dispersion relation in SI MMFs, and, by adding stronger approximations, an analytical solution for the parabolic profile GRIN MMFs [2] (note that those approximations do fail for lower order modes). An arbitrary index profile requires numerical simulations to estimate the mode profiles and the corresponding propagation constants of the modes. I present in this tutorial how to numerically estimate the scalar solution for the profiles and propagation constants of guides modes in multimode circular waveguide with arbitrary index profile and in the presence of bending. I released a beta version of the Python module pyMMF based on such an approach [3]. It relies on expressing the transverse Helmholtz equation as an eigenvalue problem. Solutions are found by finding the eigenvectors of a large but sparse matrix representing the equation on the discretized space.