# Resources: Mathematical and Numerical Modelling

This page contains an overview of the mathematical models and numerical models added to this
site.

Simulation results (animations, graphs) related to quantum dot lasers and amplifiers can be viewed here.

Hint: Click on one of the following links for a brief introduction to mathematical modelling or numerical modelling.

Simulation results (animations, graphs) related to quantum dot lasers and amplifiers can be viewed here.

Hint: Click on one of the following links for a brief introduction to mathematical modelling or numerical modelling.

## Mathematical Models

- 2-D Waveguide

Model of a semiconductor double hetero-structure wave-guide describing counter-propagating optical fields. - QD Active Medium

Model describing the active area in a semiconductor medium containing nano-scale quantum dots (QDs). The model is based on Maxwell-Bloch equations. - QD Ensemble

How to describe an ensemble of inhomogeneously broadened quantum dots using a statistical approach. - QWell States

Description of electrons and holes confined to a 2-D Quantum Well. Expressions for the chemical potential are derived. - Theoretical Model: QDSOA, QDL

Model describing an edge-emitting quantum dot semiconductor optical amplifier (QDSOA) or laser (QDL) with ridge geometry.

## Numerical Models

The numerical integration techniques presented in this section
are related to the modelling of opto-electronic device but
can be adapted to solve equations encountered in other
areas of science.

## Numerical Simulation Results

- Simulating a QDSOA

Simulation results showing a QDSOA at steady state and during excitation by an injected optical pulse. The effect of inhomogeneous broadening on the QD gain medium is visualised. - Simulating a QDL

Simulation results showing a QDL at during the build-up of the lasing field. The internal dynamics of the optical fields and the gain medium is visualised.