This paper presents a detailed study of injection-locking characteristics of a single-loop optoelectronic oscillator (OEO) under strong radio frequency (RF) signal injection. We provide formulas for the steady-state phase-angle after locking, and the locking time for a higher level of a locking signal and considering only the phase perturbation. We also provide a compact expression for the main spectrum components of the pulled OEO in terms of the beat frequency, which is useful to evaluate and quantify the injection-pulling effects in the OEO. The experimental results provide partial support to the conclusion of the analysis. The analytical and experimental results are presented in design curves, which can be used to determine the required properties of an injection-locked OEO required for a specific performance of the oscillator.

In this paper, we analyze the phase-locking phenomenon in a single-loop optoelectronic microwave oscillators when subjected to the influence of small radio frequency (RF) signal. We derive the differential equations for the amplitude and phase variations in the oscillator. Using quasi-linear approximation, analytical expressions for the lock range and phase-shift after phase-locking are presented. In addition, beat frequency of the unlocked-driven optoelectronic oscillator (OEO) is obtained and the phase-locking dynamics of the driven oscillator is discussed. Also, the spectrum components of the pulled OEO is derived as a function of the frequency detuning, lock range, beat-frequency and frequency-shift induced by the phase perturbation of the injection signal. It is shown that all the analytical closed-form expressions clearly demonstrate the phase-locking mechanism starting from the fast-beat state through the quasi-locked state to the locked state of the pulled OEO. Finally, the simulation results are given to validate the analytical results.

The optoelectronic oscillator is a delay line oscillator that leverages optical fibre technology to realize the large delay required for low phase noise systems. Spurious sidemodes are an artefact of the delay line oscillator, yet treatments of injection locking of optoelectronic oscillators have relied on the application of classical injection locking theory valid only for single mode oscillators. The large delay contributed by the optical fibre delay line is accounted for by the classical theory only in part through the quality factor Q that captures the round-trip group delay in a neighborhood of the oscillation frequency. This paper presents a new formulation of time delay oscillators subject to injection that describes all the essential features of their dynamics and phase noise. The common assumptions of a single mode oscillator and weak injection are removed. This is important to correctly predict the lock-in range, the suppression of sidemodes and the phase noise spectrum. The findings of the analysis are validated by experimental measurements provided by an optoelectronic oscillator under injection by an external source.

A study on the transient behavior of a single-loop optoelectronic oscillator (OEO) under a single sinusoidal radio frequency (RF) signal injection is presented. Considering only the phase perturbation imposed by the external RF signal, the phase-dynamic equation is solved to analyze the frequency settling behavior of the loop. A closed form expression for the required time of an OEO under RF injection-locking, reaching the steady state condition, is derived in terms of the initial phase difference, beat frequency and injection signal strength. The phase modulated signal, which is responsible for the perturbation of the free running oscillation, is expanded in a Fourier series and the expression for the output RF spectrum of the injection pulled OEO is derived. The injection-pulling dynamics approach is used to describe the phase noise of the OEO and also, the influence of the phase settling time constant on the phase noise of the injection-locked OEO is studied. The experimental results corroborating the theoretical findings are given.

Complex envelope and reduced phase simulation models describing the dynamical behaviour of an optoelectronic oscillator (OEO) under injection by an external source are described. The models build 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 $$2\pi $$2 π phase pulse trains in a broadband OEO under injection.