We report a general framework capable of describing the focusing of electromagnetic waves with spatially varying coherence and polarization properties in optical systems of arbitrary numerical aperture and Fresnel number. We also investigate the reduction of the dimensionality of the requisite integrals by use of a coherent mode expansion. We find that coherent mode expansions treating each component of the electric field vector individually are unsuitable for describing focusing systems because of the inter-component mixing that can occur in high numerical aperture systems. In addition, we show that the assumption of harmonic angular dependence allows the azimuthal integration to be performed analytically, providing further simplification of the analysis. We also find that the effective degree of spectral coherence of an electromagnetic beam is unchanged upon focusing. Finally, as an illustration of the developed framework, we calculate the transverse and axial focal distributions for a partially coherent source formed by incoherent superposition of radially and azimuthally polarized Laguerre–Gauss modes.
© 2009 Optical Society of America
Coherence and Statistical Optics
Original Manuscript: July 17, 2009
Revised Manuscript: September 21, 2009
Manuscript Accepted: September 22, 2009
Published: October 30, 2009
Matthew R. Foreman and Peter Török, "Focusing of spatially inhomogeneous partially coherent, partially polarized electromagnetic fields," J. Opt. Soc. Am. A 26, 2470-2479 (2009)