  We report a new computational model for simulations of electromagnetic
interactions with semiconductor quantum well(s) (SQW) in complex
electromagnetic geometries using the finite difference time domain (FDTD)
method. The presented model is based on an approach of spanning a large number
of electron transverse momentum states in each SQW sub-band (multi-band) with a
small number of discrete multi-electron states (multi-level, multi-electron).
This enables accurate and efficient two dimensional (2-D) and 3-D simulations
of nanophotonic devices with SQW active media. The model includes the following
features: (1) Optically induced interband transitions between various SQW
conduction and heavy-hole or light-hole sub-bands are considered. (2) Novel
intra sub-band and inter sub-band transition terms are derived to thermalize
the electron and hole occupational distributions to the correct Fermi-Dirac
distributions. (3) The terms in (2) result in an explicit update scheme which
circumvents numerically cumbersome iterative procedures. This significantly
augments computational efficiency. (4) Explicit update terms to account for
carrier leakage to unconfined states are derived which thermalize the bulk and
SQW populations to a common quasi-equilibrium Fermi-Dirac distribution. (5)
Auger recombination and intervalence band absorption are included. The model is
validated by comparisons to analytic band filling calculations, simulations of
SQW optical gain spectra and photonic crystal lasers.
