Bi-chromatic paraxial beam as a model of spatio-temporal light fields

Optical fields with rich and well-developed spatio-temporal structure, including ultra-short structured light pulses, are essentially non-monochromatic and contain a continuous spectrum of monochromatic constituents. However, some substantial features of such fields and physical mechanisms determining their behavior can be understood based on simplified models including only two monochromatic paraxial components. We consider examples of such model beams, their specific spatial and temporal properties as well as their descriptive abilities for the meaningful characterization of realistic spatio-temporal light fields. In particular, the proposed model enables an explicit consistent analysis of the photon-probability distributions in non-monochromatic fields, which confirms a high degree of coincidence between the "energy center" and "probability center" of the field. Simultaneously, particular features of the two-component bi-chromatic paraxial fields (periodic and rotational character of the longitudinal and temporal evolution, specific deformations of the propagating-beam transverse intensity profile, etc.) are inspected using numerical examples.