Partially coherent and partially incoherent full Gaussian wave

Abstract

Wolf et al. [5-7] introduced the idea of planar secondary sources for the treatment of partially coherent light beams. For the extended full Gaussian waves, only the fully coherent waves in which the wave amplitude remains a constant in time were considered [3]. For the partially coherent beams, the wave period is the same, namely Tw, but the source amplitude is essentially a constant on the time scale of Tw; but on a longer time scale Tf , on the order of nearly thousands of Tw, the amplitude changes in a random manner [8]. A majority of treatments of the partially coherent beams are restricted to the paraxial beams for which the beam waist is large compared to the wavelength. There is a need for the treatment of partially coherent, spatially localized electromagnetic waves extended beyond the paraxial approximation to the full waves governed by Maxwell's equations. An analysis of the partially coherent, spatially localized electromagnetic waves was presented for the fundamental Gaussian wave [9,10]. This is a special case (bt/b 1/4 0) for which the virtual source becomes identical to the actual secondary source in the physical space. In this chapter, the treatment of partially coherent, spatially localized electromagnetic waves is enlarged in scope to include the extended full Gaussian waves for which the virtual source is in the complex space requiring a different formulation.