The Line Shape of Optical Ramsey Resonances

The optical Ramsey resonances (ORR) need additional inventions for possibility of registration, because the simplest one (in two separated in space fields) is vanishing due to averaging over transverse velocity distribution. There is a lot of realizations of ORR. In all of them there is quite necessary to take correctly into account the transverse velocity distribution and real (Gaussian) shape of laser fields. In this work we suggest a way of describing the Ramsey resonance for arbitrary saturation and arbitrary transverse laser field shape, which takes into account the first order term correction to resonance approximation (zero pulse width) of the order of a/L (a is the width of the laser beam, L is a distance between laser beams). Additional rather interesting phenomenon consists in non-trivial performance of the recoil effect in case of ORR, different for each variant. In this respect the most interesting of them are the ORR in 3 standing waves and so called linear ORR (in two standing waves separated by λ/2 grating), where we have a few (more than 2) recoil components: in first case with different shapes, in second one of the same shape but with different intensities.