Determination of mode number using two laser combs with large difference in repetition rate

Two Er-fiber laser combs with repetition frequency of 500 MHz and 400 MHz are used to measure the frequency of a free-running external cavity diode laser. The mode number is determined by operating the 500 MHz comb at two different repetition rates while keeping the repetition rate of the 400 MHz comb unchanged. A monochromator measures the wavelength of the ECDL to offers an approximate mode number to help determining the mode number shift between the two repetition rates of the 500 MHz comb. The mode number of the beating comb line can be determined with short average time of 1 s.