Locking of microwave oscillators on the interharmonics of mode-locked laser signals

In this paper, the theory of phase-locking of a microwave oscillator on the interharmonics, i.e. non-integer harmonics, of the repetition rate of the optical pulse train of a mode-locked laser (MLL) is developed. A balanced optical microwave phase detector (BOMPD) is implemented using a balanced Mach-Zehnder modulator and is employed to discriminate the phase difference between the envelope of the optical pulses and the microwave oscillator. It is shown mathematically that the inherent nonlinear properties of BOMPD with respect to the microwave excitation amplitude can be used for interharmonic locking. The characteristic functions of the phase detector for interharmonic locking are derived analytically and are compared with the measurement results. An opto-electronic phase-locked loop (OEPLL) is demonstrated whose output frequency locks on interharmonics of the MLL repetition rate when an appropriate modulator bias and sufficient RF amplitude are applied. Thus, for the first time theory and experiment of reliable locking on interharmonics of the repetition rate of a MLL are presented.