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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 …