Noise and stability analysis of coupled oscillators

Power combining by using coupled oscillators (either phase-locked, or mode-locked) is a promising technique for overcoming the inherent power limitations of solid state devices. For the case of phase-locking, all the oscillators axe synchronized to a common fundamental frequency. For the case of mode-locking, the frequency components are separated evenly with fixed phase relationship. In this work, the analytical technique can be applied to any type of the oscillator with some modification. Here we use the microwave and laser oscillators as the illustrations.;We analyze the noise properties of coupled oscillators in phase-locked states. The total phase (PM) or FM noise of the total combined signal is reduced for the whole spectra. The noise reduction of the individual oscillators in the array are also found to be reduced near the common locked frequency. For the case of a 2-element array of semiconductor lasers, the noise spectra of the individual elements are found to have a new relaxation resonance oscillation frequencies due to the nearest neighbor coupling. For the case when reciprocal of the coupling time (1/ tk ) is greater than the original laser relaxation resonance frequency ( wR ), the new relaxation resonance frequency is at about 2/ tk from the lasing frequency.;The locking stability of coupled phase locked oscillators is an important issue. We apply the averaged potential theory of circuits to analyze the coupled phase-locked lasers. The results are in agreement with the supermode analysis and provide new insight into the stable modes.;The coupled oscillators in mode locked states can be used as the pulse generator or the automatic beam scanning if the oscillators are separated in space. By using the Krylov-Bogoliubov averaging method, we prove the existence of the mode-locked states in coupled lasers. The coupled lasers in stable mode-locked states can also be used as the robust optical FDM (or WDM) transmitters for the optical fiber communication systems.