No abstract

In this article, we develop the theory of a special type of optoelectronic phase-locked loop (PLL). The output signal of this type of PLL is in the electrical domain and its reference oscillator, typically a mode-locked laser, operates in the optical domain. The PLL uses a balanced optical microwave phase detector (BOMPD). In order to model the optoelectronic PLL, the nonlinear characteristic function and the gain of the BOMPD are derived analytically. Using the results of the phase detector analysis, the theory of an optoelectronic PLL using such a phase detector is developed. Based on the theoretical analysis, a broadband optoelectronic frequency synthesizer with a programmable frequency range from 2 to 20 GHz is designed and implemented. Phase noise measurements show that the optoelectronic PLL frequency synthesizer achieves an integrated rms-jitter (1 kHz-100 MHz) of less than 4 fs in the frequency range from 5 to 20 GHz with a typical value of 4 fs and a minimum of 3 fs. This is the first reported wideband PLL frequency synthesizer achieving sub-10-fs integrated rms-jitter (1 kHz-100 MHz) in the frequency range from 3 to 20 GHz. A comparison with best-in-class laboratory-grade frequency synthesizers in this frequency range shows that this synthesizer achieves lower phase noise than any electronic frequency synthesizer for offset frequencies larger than 2 kHz.

No abstract

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.

An analysis of an optical Nyquist pulse synthesizer using Mach-Zehnder modulators is presented. The analysis allows to predict the upper limit of the effective number of bits of this type of photonic digital-to-analog converter. The analytical solution has been verified by means of electro-optic simulations. With this analysis the limiting factor for certain scenarios: relative intensity noise, distortions by driving the Mach-Zehnder modulator, or the signal generator phase noise can quickly be identified.