Determination of Phase Noise Spectra in Optoelectronic Microwave Oscillators: A Langevin Approach

Abstract

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case of optoelectronic oscillators where the microwave is a limit-cycle originated from a bifurcation induced by nonlinearity and time-delay. This Langevin approach based on stochastic calculus is also successfully confronted with experimental measurements.

Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems

“…While the analytical mathematical treatment presented here has been done for identical systems in the ideal case without noise, we expect the results to be relevant for real systems. The effect of noise in the periodic regime of OEOs is small [31] and we have shown that the periodic square-wave solutions are robust to mismatches in the delay times of the order of a few percent. The rich dynamics of the system allows for the coexistence of many in-or out-of-phase stable periodic orbits with different periods for the same values of the fixed parameters.…”

“…These devices have also been proposed and studied to produce efficient ultrapure microwaves in the periodic regime [27][28][29][30]. In particular, their robustness to noise has been studied both theoretically and experimentally [31]. Finally, OEOs operating in the steady-state regime have recently been implemented in an experimental demonstration of a photonic liquid-state machine performing as a kind of neuromorphic computer [32].…”

Time-Domain Dynamics and Stability Analysis of Optoelectronic Oscillators Based on Whispering-Gallery Mode Resonators

“…The same approach also enabled us to show that under certain conditions, the abrupt switch-on behavior of the fiber-based OEOs leads to robust multimode oscillations instead of an ultrastable single-tone microwave [23]. The timedomain deterministic model was also an essential prerequisite that enabled us to perform a phase noise analysis based on stochastic differential equations (or Langevin equations) and which enabled us to predict phase noise characteristics with remarkable precision [24], [25]. The same formalism also enabled us to analyze more complex OEO architectures, like dual-loop OEOs [26], or hybrid configurations whose outputs are an ultrastable microwave in the RF domain and an ultralow jitter picosecond pulse train in the optical domain [27].…”

A Review of Optoelectronic Oscillators for High Speed Signal Processing Applications

“…By operating in a multimode configuration just below oscillation threshold, the MM-OEO can be used to selectively amplify low power RF signals in a cluttered environment. The OEO continues to be investigated theoretically [95][96][97] to better understand the sources of noise as well as to improve their performance. Demonstrations of the OEO continue to explore new applications, from generating broadband chaos [98], use in sensors [99], and as a measurement of the refractive index of optical fibers [100].…”