Dynamics of Time-Delay Coupled Opto-Electronic Oscillators

Abstract

This thesis describes the theory, design, and testing of solitary and coupled optoelectronic oscillators (OEO). It includes the work of four papers: two on solitary OEOs, one on coupled OEOs, and one on noise characterizations of general OEO systems. The goal is to derive analytic characterizations then experimentally leverage predictions for amplification and sensing applications in radio frequency (RF) integrated photonic platforms. For the single OEO case we experimentally characterize and numerically model the amplification of RF signals injected into a sub-threshold optoelectronic oscillator. Further, we characterize the transient temporal characteristics when subject to a pulse square wave and derive a recursion relationship between the steps of the transient response. In injected single OEO experiments, a radio frequency gain of 27.5 dB is demonstrated at an optical power of 0.989 times the threshold optical power. The transient behavior shows signatures of both the intrinsic time-delay of the optoelectronic oscillator and the finite bandwidth of the electronic radio frequency filter. Approximating higher-order group delay contributions of the experimental band-pass filter as an external time-delay allows the system to be modeled with a well-known optoelectronic oscillator rate equation model. The solitary rate equation model is generalized to numerically model coupled OEOs. Linearization, stability analysis, and a modified slowly varying envelope technique are utilized to derive novel analytic predictions. A second attractor is identified above the critical point that overlaps the threshold with an exceptional point. Experiments show that the coupled OEO’s second attractor may be triggered from the off state with a relative » 78 dB RF injected signal.