Optical frequency metrology with an Rb-stabilized ring-cavity resonator-study of cavity-dispersion errors

We have developed a technique to measure the absolute frequencies of optical transitions by using an evacuated Rb-stabilized ring-cavity resonator as a transfer cavity. The absolute frequency of the Rb D-2 line (at 780 nm) used to stabilize the cavity is known and allows us to determine the absolute value of the unknown frequency. We study wavelength-dependent errors due to dispersion at the cavity mirrors by measuring the frequency of the same transition in the Cs D-2 line (at 852 nm) at three cavity lengths. The spread in the values shows that dispersion errors are below 30 kHz, corresponding to a relative precision of 10(-10). We give an explanation for reduced dispersion errors in the ring-cavity geometry by calculating errors due to the lateral shift and the phase shift at the mirrors, and show that they are roughly equal but occur with opposite signs. We have earlier shown that diffraction errors (due to Guoy phase) are negligible in the ring-cavity geometry compared to a linear cavity; the reduced dispersion error is another advantage. Our values are consistent with measurements of the same transition using the more expensive frequency-comb technique. Our simpler method is ideally suited for measuring hyperfine structure, fine structure, and isotope shifts, up to several hundreds of gigahertz.