Analytical vectorial structure of hollow Gaussian beams in the far field

Abstract

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation.

Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam

“…Up to now, much work has been done on HGBs because it is a convenient and powerful tool to describe and treat dark hollow beams with circular symmetry. The propagation properties of HGBs have been studied in detail [14][15][16][17][18]. However, all previous theoretical models of HGBs are related to the fully coherent case.…”

Tight focusing of phase modulated radially polarized hollow Gaussian beam using complex phase filter

“…It is reported that radial polarization to be the preferred approach for pupil masks for super resolution and apodization at high NA [7]. Recently, hollow Gaussian beam (HGB) has attracted much attention due to its properties and applications [8][9][10][11][12][13][14][15][16][17][18][19]. It was found that the area of the dark region across the HGBs can be easily controlled by proper choice of the beam parameters [11].…”

“…The propagation, farfield intensity distribution, and M2 factor of HGB through paraxial systems have been investigated in detailed [12][13][14][15]. In addition, the nonparaxial propagation of vectorial HGBs in free space is also studied based on the vectorial Raleigh-Summerfield diffraction integral [16], and the analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase [17]. On the other hand, singular optics studying optical vortices, or phase singularities, has grown rapidly recently because optical vortices have some interesting properties [18][19][20] and promising applications [21][22][23][24], for instance, optical vortices can be used to construct highly versatile optical tweezers.…”

Analytical vectorial structure of an apertured hollow Gaussian beam in the far field

“…Followed by the advent of HGB, a rich amount of investigations about HGB have been increasingly presented. For example, the propagation properties of HGB through apertured paraxial optical systems [10] and a turbulent atmosphere [11] have been studied, radiation forces produced by highly focused HGB have also been discussed, and the analytical vectorial structure of HGB in the far field has been studied by Wu et al [12] more recently.…”