  Complex envelope and reduced phase simulation models describing the dynamical
behavior of an optoelectronic oscillator (OEO) under injection by an external
source are described. The models are built on the foundations of a previously
reported delay integral differential equation (DDE) theory of injection locking
of time delay oscillators (TDO) such as the OEO. The DDE formulation is
particularly amenable to high precision simulation using the Simulink block
diagram environment. The correspondence between the blocks and the oscillator
components offers intuition and considerable freedom to explore different
circuit architectures and design variations with minimal coding effort. The
simulations facilitate the study of the profound effect the multimode nature of
a TDO has on its dynamical behavior. The reduced phase models that make use of
the Leeson approximation are generally successful in reproducing the results of
complex envelope models for established oscillations except for spiking
phenomena for which the Leeson approximation fails. Simulation results
demonstrating phenomena not captured by classical injection theory are
presented, including multimode oscillation, the appearance of sidemodes in the
RF and phase noise spectrum, and persistent spike trains redolent of recent
experimental observations of 2pi phase pulse trains in a broadband OEO under
injection.
