Sharper Focal Spot for a Radially Polarized Beam Using Ring Aperture with Phase Jump

Svetlana N Khonina,Andrei V Ustinov

doi:10.1155/2013/512971

Abstract

We study analytically and numerically in which way the width of ring aperture containing a phase jump affects the size and intensity of the focal spot generated with a radially polarized beam. It is shown that by means of destructive interference of beams coming from the different-phase rings it becomes possible to overcome the scalar diffraction limit corresponding to the first zero of the zero-order Bessel function. The minimal focal spot size (FWHM=0.33λ) is found to be attained when the annular aperture width amounts to 20% of the full-aperture radius. In this case, the side-lobe intensity is not larger than 30% of the central peak. A wider annular aperture with the phase jump introduced is also shown to form a focal spot not exceeding the diffraction limit for a narrow annular aperture, simultaneously providing a nearly six times higher intensity. In this case, the side lobes amount to 35% of the central peak.

Highlights

A narrow annular pupil that blocks the light from propagating practically through the entire central part of the lens [1,2,3] is a simple, albeit low-efficiency technique to generate narrowextended beams in the focal plane.More complicated techniques for the full-aperture apodization of the pupil’s function that employ both purely phase and amplitude-phase distributions have been reported [4,5,6,7,8,9]
The focal spot size can be further decreased without an essential side-lobe increase based on the destructive interference if a π-radian phase jump is introduced along the central radius of the narrow annular aperture (16)
We understand that the radius of phase jump is additional parameter for optimization of the focal distribution; experience of other researchers [4, 6,7,8, 19,20,21] shows that even a plenty of free parameters does not allow to reduce the focal spot simultaneously keeping energy

Summary

Introduction

A narrow annular pupil that blocks the light from propagating practically through the entire central part of the lens [1,2,3] is a simple, albeit low-efficiency technique to generate narrowextended beams in the focal plane. More complicated techniques for the full-aperture apodization of the pupil’s function that employ both purely phase and amplitude-phase distributions have been reported [4,5,6,7,8,9] In this case, a tighter focal spot is normally obtained at a sacrifice of the energy redistribution from the central peak to the side lobes. The analysis of the sharp focusing based on the RichardsWolf integrals [23] has shown that the dependence of the focal spot size on the width of the narrow annular pupil is different for the scalar and vector models In the former case, the diffraction-limited focal spot size is attained when the width of the ring that transmits the peripheral rays tends to zero, while the focal intensity drops quadratically with decreasing width. The numerical simulation has shown that notwithstanding the destructive interference, by choosing a fairly wide annular pupil, the focal point intensity can be essentially increased without exceeding the limit corresponding to the narrow annular pupil

Analysis of Generating a Sharper Focal Spot

Numerical Results

Conclusions