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 T_w, but the source amplitude is essentially a constant on the time scale of T_w; but on a longer time scale T_f , on the order of nearly thousands of T_w, 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 (b_t/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.

Chapter Contents:

• 1 Extended full-wave generalization of the paraxial beam
• 2 Cross-spectral density
• 3 Radiation intensity for the partially coherent source
• 4 Time-averaged power for the partially coherent source
• 5 Radiation intensity for the partially incoherent source
• 6 Time-averaged power for the partially incoherent source
• 7 General remarks
• References

Inspec keywords: Gaussian processes; electromagnetic wave propagation; approximation theory; integral equations

Other keywords: partially coherent light beams; spatially localized electromagnetic waves; wave period; extended full Gaussian waves; paraxial approximation; Maxwell's equations; wave amplitude; complex space; source amplitude; virtual source; paraxial beams; planar secondary sources; physical space; fundamental Gaussian wave

Subjects: Mathematical analysis; Electromagnetic wave propagation; Interpolation and function approximation (numerical analysis); Function theory, analysis; Numerical approximation and analysis; Other topics in statistics; Fluctuation phenomena, random processes, and Brownian motion; Electromagnetic waves: theory