Focal depth and focal splitting of truncated hyperbolic-cosine-Gaussian beam induced by phase plate

Focal depth and focal splitting of hyperbolic-cosine-Gaussian beams induced by a phase plate were investigated. The pure phase plate consists of three concentric zones: a center circle zone, an inner annular zone and an outer annular zone. The phase variance of the inner annular zone is adjustable. Simulation results show that the focal depth can be adjusted by changing the radii of zones. With the increase of the inner radius of the outer annular zone, the focal spot broadens along the optical axis and splits into two peaks. Then the two peaks combine back into one peak. There are two critical values for the inner radius of the outer annular zone, at which focal spot changes sharply. The tunable range of the focal depth varies considerably. The phase variance of the inner annular zone affects focal depth also; when the phase variance is π, the effect attains maximum. The parameters of cosh parts of the beam affect both focal splitting and focal depth evidently; focal splitting disappears with increasing parameters of cosh parts, and focal depth increases with increasing the parameters of cosh parts in both the low and the high numerical-aperture optical systems.