Probing a laser field by measuring photon replica transitions

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Abstract
How much information about a laser field can be reconstructed is considered if multiphoton transitions have been measured but if the laser-flux distribution in the experiment is unknown. It is shown how this reconstruction is done in detail if the relative strengths of the photon replicas of some atomic or molecular transitions are given. The resulting information about the laser field turns out to be the power moments of a weight function which indicates the relative weight with which a particular laser-flux value has contributed to the observed multiphoton transitions. Some analytically soluble examples are presented for the connection between the laser-flux distribution in space and time, the resulting moments of the weight function, and the weight function itself.