Transfer-matrix method (optics)

The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors. The reflection of light from a single interface between two media is described by the Fresnel equations. However, when there are multiple interfaces, such as in the figure, the reflections themselves are also partially transmitted and then partially reflected. Depending on the exact path length, these reflections can interfere destructively or constructively. The overall reflection of a layer structure is the sum of an infinite number of reflections. The transfer-matrix method is based on the fact that, according to Maxwell's equations, there are simple continuity conditions for the electric field across boundaries from one medium to the next. If the field is known at the beginning of a layer, the field at the end of the layer

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (8)

Related publications

Related people (1)

Related people

Related units (2)

Related units

Related concepts (4)

Related concepts

Related courses (1)

Related courses

Related lectures (4)

Related lectures

Additive manufacturing of ceramics by two-photon lithography, volumetric 3D printing and high-resolution endo-printing.

Georgia Konstantinou

Additive manufacturing is a growing sector of industrial production that allows the fabrication of parts with complex geometries and reduced waste. The context of this thesis is light-based additive manufacturing technologies. In the first part of the thesis, we explore the micro-fabrication of a highly viscous, preceramic resin with a commercially available two-photon 3D-printer. The micro-additive manufacturing of ceramics with a preceramic polymer formulation was successfully achieved. We report on the printing parameters of the preceramic polymer and pyrolysis conditions that ensured a ceramic conversion with minimum deformation and shrinkage without cracks and porosity. In the second part of the thesis, a complete set-up of a fiber endo-printer is presented that yields smooth objects with submicrometer lateral resolution. We introduce a transmission matrix method for scanning and tuning the size of the focused spot and adjust the fabrication speed. We include an exposure dose correction, which significantly improves the surface quality of the print. In the third part of the thesis, we explore centimeter scale fabrication of a preceramic resin formulation with a volumetric tomographic printing technology that allows to produce support-free, complex shapes, more challenging to produce with a conventional layer-by-layer printing technology. We report on the details of the pre-processing and post-processing steps, including formulation protocol, printing parameters and pyrolysis step that produces a high-fidelity ceramic object.

EPFL2022

Wave dispersion in periodic post-buckled structures

Florian Paul Robert Maurin, Alessandro Spadoni

Wave propagation in pinned-supported, post-buckled beams can be described with the Korteweg de Vries (KdV) equation. Finite-element simulations however show that the KdV is applicable only to post-buckled beams with strong pre-compression. For weak and moderate pre-stress, a dispersive front is present and it is the aim of the current paper to analyze sources of dispersion beyond periodicity given three support types: guided, pinned, and free. Bloch theorem and a transfer-matrix method are employed to obtain numerical dispersion relations and characteristic wave modes, which are used to analyze the effects of pre-stress, initial curvature, and the influence of support types. Additionally, a new method is proposed to obtain a semi-analytical dispersion equation for the acoustic branch. Powers of frequency and the propagation constant are explicitly expressed and their coefficients are based on stiffness and mass-matrix components obtained from finite elements. This allows a physical interpretation of the dispersion sources, based on which, equivalent mass-spring models of post-buckled beam are proposed. It is found that mass and stiffness coupling are significant dispersion sources. In the present paper, a reduced form of Bloch theorem is presented exploiting glide-reflection symmetries, reducing the size of the unit cell and allowing an easier representation and interpretation of results.

Elsevier2014

Transmission in Multimode fiber with deep learning

Georgia Konstantinou, Damien Claude-Marie Loterie, Christophe Moser, Demetri Psaltis, Babak Rahmani

Spatio-temporal control of femtosecond pulse-delivery through multimode fibers (MMF) can be used to achieve two photon photo-polymerization. Transmission-matrix method is used in linear domain to solve the scrambling effect at the fiber output and generate focused spots. However, multimode fibers suffer from non-linear effects at high peak intensities. The method is not effective to describe light propagation in the nonlinear regime. Here we propose a deep learning network which can learn the relationship between inputs and outputs of the MMF. We show that once the network is properly trained, it can directly calculate the inverse of the transmission matrix.

IEEE2018

Fabry–Pérot interferometer

In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces (i.e.: thin mirrors). Optical waves can pass through the optical cavity only wh

Dielectric mirror

A dielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical mate

Optics

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually

MICRO-561: Biomicroscopy I

Introduction to geometrical and wave optics for understanding the principles of optical microscopes, their advantages and limitations. Describing the basic microscopy components and the commonly used biomicrocopy methods such as widefield and fluorescence.