Transfer of laser frequency from 729 nm to 1.5 mu m with precision at the level of 10(-20)

By using a self-reference transfer oscillator method, two individual 1560 nm lasers with about 1.2 GHz frequency difference were phase locked to a 729 nm ultra-stable laser at two preset ratios. By measuring the beat frequency of the two 1560 nm lasers, fractional instabilities of 2 x 10(-17) at 1 s and 2 x 10(-20) at 10,000 s averaging time were obtained, and the relative offset compared with the theoretical value was 4.2 x 10(-21) +/- 4.5 x 10(-20). The frequency ratio of them was evaluated to a level of 1.3 x 10(-20) in one day's data acquisition. This work was a preparation for remote comparison of optical clocks through optical fiber links. The technique can also be used to synthesize ultra-stable lasers at other wavelengths.