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Lecture

Maxwell's Equations in Vacuum

In course

MICRO-420: Selected topics in advanced optics

This course proposes a selection of different facets of modern optics and photonics. ...

Description

This lecture covers Maxwell's equations in vacuum, including the constitutive relations, boundary conditions, and the wave equation for each field component. It also discusses the photon scanning near-field optical microscope, light confinement in near-field optics, and experimental proof of light confinement effects.

Instructor

Olivier Martin

Olivier J.F. Martin received the M.Sc. and Ph.D. degrees in physics in 1989 and 1994, respectively, from the Swiss Federal Institute of Technology, Lausanne (EPFL), Switzerland. In 1989, he joined IBM Zurich Research Laboratory, where he investigated thermal and optical properties of semiconductor laser diodes. Between 1994 and 1997 he was a research staff member at the Swiss Federal Institute of Technology, Zurich (ETHZ). In 1997 he received a Lecturer fellowship from the Swiss National Science Foundation (SNSF). During the period 1996-1999, he spent a year and a half in the U.S.A., as invited scientist at the University of California in San Diego (UCSD). In 2001 he received a Professorship grant from the SNSF and became Professor of Nano-Optics at the ETHZ. In 2003, he was appointed Professor of Nanophotonics and Optical Signal Processing at the Swiss Federal Institute of Technology, Lausanne (EPFL), where he is currently head of the Nanophotonics and Metrology Laboratory and Director of the Microengineering Section.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Discrete exterior calculus

Related concepts (24)

Cauchy boundary condition

In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

Mixed boundary condition

In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Boundary value problem

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

Neumann boundary condition

In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.

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