Focusing properties of a 4Pi configuration system under the illumination of double ring shaped $$\hbox {LG}_{11}$$ LG 11 beam

Abstract

Based on the vectorial Debye theory, the tight focusing properties of a 4Pi configuration system under the illumination of double ring shaped \(\hbox {LG}_{11}\) beam through a high numerical aperture objective are investigated numerically. The result shows that a spherical focal is generated by tightly focused azimuthally polarized \(\hbox {LG}_{11}\) beams in a 4Pi focusing system configuration. The numerical simulation result shows that it is possible to trap particle or to scan a specimen without moving the source (lenses or laser beams), we also generated multiple focal spot by changing the beam parameter (\(\beta \)) which is suitable for many optical applications.