Simulation of optoelectronic oscillator injection locking, pulling and spiking phenomena

TL;DR

This paper develops and utilizes advanced simulation models to analyze the complex dynamical behaviors of optoelectronic oscillators under external injection, revealing phenomena like multimode oscillations and spiking that extend classical theory.

Contribution

It introduces high-precision delay differential equation models and reduced phase models for simulating OEO injection phenomena, capturing behaviors beyond classical theories.

Findings

Demonstrates multimode oscillations and sidemodes in RF spectra.

Shows persistent spike trains similar to recent experimental observations.

Reveals limitations of Leeson approximation for spiking phenomena.

Abstract

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.