Phase noise performance of double-loop optoelectronic microwave oscillators

Summary form only given. Optoelectronic oscillators (OEOs) are useful for applications such as radar, time-frequency metrology and lightwave technology, where microwaves with exceptional purity are needed [1]. The purity of microwave signals is achieved thanks to an optical fiber delay-line inserted into the feedback loop providing a quality factor equal to Q = 2π f_mT, where f_m is the microwave frequency and T the delay. Microwaves with frequencies as large as 75 GHz, and a phase noise lower than -160 dBc/Hz at 10 kHz has been achieved [2]. As Q increases with T, a long delay should improve the performance. However strong parasite ring-cavity peaks at the integer multiples of the round-trip frequency Ω_T = 2π/T limiting the region of low phase noise. Alternatives consisting in adding the output of two loops with different delay time has been proposed to lower the phase noise or to reduce the level of parasite ring-cavity peaks [3]. Single-loop OEOs suffer from another severe limitation: increasing the gain the system becomes unstable leading to a modulation of the microwave amplitude and thus to a degradation of the spectral purity [4].Here, we consider a double-loop optoelectronic delay system in which the output of one of the loops is used to modulate the other (Fig. 1) [5]. Besides reducing the phase noise spurious peaks as linearly coupled dual-loop OEOs, this system allows for stable microwave emission with larger amplitude. A semiconductor laser (SL) injects light into a Mach-Zehnder (MZM1). One part of the optical output is delayed by T2 , detected by photodiode PD2, fed to a narrow-band filter with a central frequency Ω0 and bandwidth ΔΩ2, amplified, and used to modulate MZM2. The other part is delayed by T1, optically fed to MZM2, detected by PD1, filtered by an RF filter of central frequency Ω0 and bandwidth ΔΩ1, amplified and finally used to drive the - F electrode of MZM1 closing the loop. The system can be described by the dimensionless amplifier outputs x(t) and y(t) [5] where xt0 = x(t - t0), F(x,φ) = cos[2x(t) + 2φ], du1/dt = x(t), du2/dt = y(t) and G1 and G2 are the overall loop gains. We derive an amplitude equation and determine the parameter region where stable pure microwaves are generated. By including suitable stochastic terms we determine the phase noise performance. As shown in Fig. 1 by appropriately setting the parameters of the second loop, a significant improvement of performance can be achieved comparatively to the single-loop configuration, as the detrimental effect of the multiplicative phase noise can be reduced up to about 18 dB close to the carrier, while delay-induced spurious peaks can be strongly damped.