Methods of conversion of stability of femtosecond stabilized mode-locked laser to optical resonator

In this work we propose three methods of a conversion of RF clock stability to the length precision using fs stabilized laser via Fabry-Perot by three proven conversion techniques. One mode stabilized lasers could provide optical frequency reference. Stability of such a laser could be transferred to length etalon represented by optical interferometer.We present using of Fabry-Perot interferometer as a length etalon referenced to fs stabilized optical comb. The train of femtosecond pulses produces equidistant optical frequencies separated by repetition frequency and shifted by an offset frequency. Both frequencies are stabilized according to widely used f-to-2f stabilization method to RF frequency standard, i.e. atomic clocks represented by GPS controlled signal with relative stability down to 10^-15. First method of conversion is based on a simple assumption that the femtosecond laser light is transmitted only when a free spectral range (FSR) of Fabry-Perot cavity (FP) is a multiple of the repetition frequency of the laser. Precise length is inversely proportional to the repetition frequency and fixed to the position of pulse to pulse interferogram´s centroid. In the second method FP length is chosen arbitrary to increase the FSR of the FP and only few frequencies of optical laser are transmitted and detected. FP length could be stabilized to any transmitted laser line. The third method is based on the frequency lock of DFB laser line to one of the frequency lines of femtosecond laser and by fixing the beat frequency between the DFB laser and the frequency synthesizeraAZs line. Length of FP is stabilized to DFB laser line.