Tight focusing of partially coherent and circularly polarized vortex beams

Abstract

Based on the vectorial Debye theory, the tight focusing properties of partially coherent and circularly polarized vortex beams are investigated. The focused characteristics of right-circular and left-circular polarized partially coherent vortex beams in the focal region are presented and compared by some numerical calculation results. Furthermore, the influences of the source coherence and the numerical aperture of the focusing objective on the tight focusing properties are studied in great detail. It is shown that the coherence and polarization properties of the focused left-circular polarized beam is less influenced by the source coherence and the numerical aperture of the focusing objective than that of the focused right-circular polarized beam. By selecting certain parameters, the widely used flat top beam can be obtained.

Degree of polarization of a tightly focused, partially coherent anomalous hollow beam

“…(7), we can obtain the total intensity distribution of the tightly focused, partially coherent AHB in the focal region as follows [24][25][26]:…”

“…Ir; ϕ; z I x r; ϕ; z I y r; ϕ; z I z r; ϕ; z W xx r; ϕ; z W yy r; ϕ; z W zz r; ϕ; z: (12) The degree of polarization of the tightly focused, partially coherent AHB in the focal region is given by [24][25][26] Pr;ϕ;z 3 2 I x r;ϕ;z 2 I y r;ϕ;z 2 I z r;ϕ;z 2 I x r;ϕ;z I y r;ϕ;z I z r;ϕ;z 2 − …”

“…The spectral degree of coherence of the tightly focused, partially coherent AHB in the focal region is expressed as [24][25][26] μ ij r; ϕ; z W ij r; ϕ; z W ii r; ϕ; zW jj r; ϕ; z p ; i; j x; y; z:…”

“…A fractional Fourier transform for an AHB is proposed in [11,13]. In the past decade, because of important applications in optical trapping, laser machining, and highresolution imaging, the tightly focused properties of various beams have been widely studied [14][15][16][17][18][19][20]. In this paper, we will study the focusing properties of a partially coherent AHB focused by an aplanatic high numerical aperture (NA) focusing system and find some interesting results.…”

Tight Focusing of Partially Coherent Vortex Beams

“…Detailed study on the tight focusing of uniformly partially polarized radiation has been carried out in the past [30]. Such investigations for partially coherent vortex beams have been carried out recently [32,33]. With increasing importance of polarized vortex beams in several applications and in physical optics, it is also important to carry out such investigations.…”