Cavity Pulling in Passive Frequency Standards

Assuming a Lorentzian shape for the atomic line, we calculate the cavity-pulling factors of passive frequency standards, taking into account the modification of the applied electromagnetic field by the atomic radiation. The calculation is therefore valid for all values of the gain of the atomic medium and gives, in particular, the cavity-pulling factor when the oscillation threshold is approached. The effect of saturation of the line by the field is included. Two expressions of the cavity-pulling factor are derived. One applies when the electromagnetic field level in the cavity is measured, and the other when the population of the atomic levels is analyzed. Consequences of these results are discussed. An experimental verification of the theoretical results is given, when the resonance of the field level in a hydrogen maser cavity is monitored in conditions where the oscillation threshold is approached.