Synchronization between two weakly coupled delay-line oscillators

We study theoretically the generation of a continuous-wave signal by two weakly coupled delay-line oscillators. In such oscillators, the cavity length is longer than the wavelength of the signal. We show by using an analytical solution and comprehensive numerical simulations that in delay-line oscillators, the dynamics of the amplitude response cannot be neglected even when the coupling between the oscillators is weak. Therefore, weakly coupled delay-line oscillators cannot be accurately modeled by using coupled phase-oscillator models. In particular, we show that synchronization between the oscillators can be obtained in cases that are not allowed by coupled phase-oscillator models. We study the stability of the continuous-wave solutions. In delay-line oscillators, several cavity modes can potentially oscillate. To ensure stability, the bandwidth of the delay-line oscillator should be limited. We show that the weakly coupled delay-line oscillator model that is described in this paper can be used to accurately model the synchronization between two weakly coupled optoelectronic oscillators. A very good quantitative agreement is obtained between a comprehensive numerical model to study optoelectronic oscillators and the model results given in this paper.