First- and second-order statistics of partially coherent, high-numerical-aperture optical fields

Abstract

The intensity probability distribution as well as the cross-spectral density of partially coherent optical fields generated through high-numerical-aperture illuminations are analyzed, and novel effects, not apparent in paraxial optical fields, are described. It is shown that the intensity probability distribution significantly differs from what can be expected from a small-angle analysis, and the number of degrees of freedom for the distribution is higher. It is further shown that the cross-spectral density of a high-angle optical field is a function of the coordinate difference along the propagation direction of the field.

Focusing of spatially inhomogeneous partially coherent, partially polarized electromagnetic fields

“…(8) In some applications it may be more useful to define the focused CSDM in terms of the CSDM in the back focal plane of the lens, which we denote…”

“…Focusing of coherent light under a scalar approximation has been well understood for many years (see, for example, [1]), while even as early as 1919 focusing of coherent, fully polarized electromagnetic waves could be described by what is now known as the Debye-Wolf diffraction integral [2][3][4][5]. In more recent years attention has slowly turned toward focusing of partially coherent light in both scalar [6][7][8][9] and vectorial [10,11] regimes due to its potential use in lithography, laser fusion, and microscopy [12][13][14][15]. Consideration of the full electromagnetic problem has, however, been limited to homogeneous (partial) polarization across the pupil of the focusing lens.…”

Focus shaping of linearly polarized pseudo-nondiffracting beam using a radial shift and a large numerical aperture

“…In recent years, the properties of beams focused by an NA lens system have attracted more attention and extensive investigation, because of their fascinating features and wide potential applications in modern micro-lithography optical data storage, microscopy, material processing, and manipulation of particles (Rydberg 2008, Foreman and Torok 2009, Bokor and Davidson 2007, Walker and Milster 2001, Helseth 2002. Moreover, the properties of optical vortex beams have received substantial interest from many researchers (Zhan and Leger 2002, Hricha et al 20021a, Hricha et al 2021b, Hricha et al 20021c, Hricha et al 2021d, El Halba et al 2021, Milster 2001, Rao et al 2009.…”

Tight focusing of partially coherent, partially polarized vortex beams

“…Vortex beams can be used in optical spanners, micromanipulation, and quantum information, etc. Meanwhile, the study of focusing of vortex beams has also started [11][12][13], and later further developed into partially coherent beams [14], partially coherent partially polarized beams [15,16] and partially coherent light vortex beams [1,[17][18][19]. These researches show that the topological charge, degree of correlation and degree of polarization of the incident beam could influence the intensity and degree of polarization of the light beam on propagation.…”