Bahmanian Meysam, Kress Christian, Scheytt J Christoph
Opt Express. 2022 Feb 28;30(5):7763-7771. doi: 10.1364/OE.451894.
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.
本文阐述了微波振荡器锁相在锁模激光器（MLL）光脉冲序列重复率的间谐波（即非整数谐波）上的理论。利用平衡马赫曾德尔调制器实现了一种平衡光微波鉴相器（BOMPD），并用于判别光脉冲包络与微波振荡器之间的相位差。从数学上证明，BOMPD相对于微波激励幅度的固有非线性特性可用于间谐波锁定。解析推导了用于间谐波锁定的鉴相器的特征函数，并与测量结果进行了比较。展示了一种光电锁相环（OEPLL），当施加适当的调制器偏置和足够的射频幅度时，其输出频率锁定在MLL重复率的间谐波上。因此，首次提出了在MLL重复率间谐波上可靠锁定的理论和实验。
