Nonlinear analysis of phase relationships in quasi-optical oscillator arrays

A dynamic theory of coupled oscillators is developed and applied to the class of loosely coupled quasi-optical oscillator arrays. This theory permits the calculation of stable, steady-state phase relationships between the oscillators. The distribution of free-running frequencies and the coupling parameters are most important in determining the behavior of the arrays. It is found that free-running frequencies of the peripheral elements have the strongest influence on the steady-state phase relationships. The influence of randomness in the frequency distribution is considered for the case of broadside beamforming, establishing a critical value for the coupling strength in order to maintain mutual synchronization with a specified maximum beam deviation. Techniques for simplifying the calculation of phase relationships for some common coupling parameters are also developed