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Maxwell overview

Tutorial for Maxwell propagation and its coupling with TDDFT in Octopus

Authors: Rene Jestädt, Franco Bonafé and Heiko Appel

Max Planck Institute for the Structure and Dynamics of Matter - Theory Department

This tutorial is based on the following publication:

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications René Jestädt, Michael Ruggenthaler, Micael J. T. Oliveira, Angel Rubio, and Heiko Appel https://doi.org/10.1080/00018732.2019.1695875

Slides of Heiko Appel’s talk

Using the Riemann-Silberstein representation for the Maxwell’s equations, the corresponding time-evolution of Maxwell fields is implemented as quantum mechanical like propagation in the TDDFT code Octopus.

The program can be run in a free Maxwell propagation mode where the electromagnetic fields are calculated inside a simulation box. This box can include various shapes for linear media. An initial electromagnetic field can be set up in the box as well as an external current density or incoming plane waves at the box boundaries. The simulation box boundaries can be selected as zero boundaries, perfectly electric conductor (PEC mirror), perfectly magnetic conductor (PMC) or absorbing boundaries with different methods.

Combining all features of a free Maxwell propagation with the normal TDDFT matter propagation in Octopus, the code can solve fully coupled Maxwell-Kohn-Sham systems by propagating both systems on two separated grids. In this case, the Kohn-Sham system gives rise to an internal current density that influences the Maxwell field propagation, and in turn the electromagnetic field is part of the Kohn-Sham Hamiltonian. Both coupled systems are propagated self-consistently, but the code can also be used for only forward or only backward coupling.

In the following we introduce the different input options for the free Maxwell propagation and the fully coupled Maxwell-Kohn-Sham propagation, and different examples to show the various features.

Simulation box and relevant input file variables

Examples of electromagnetic field propagation without coupling to TDDFT