ABSTRACT
This chapter derives analytical relations for the Fresnel and Fraunhofer diffraction of a plane wave with circular and ring-like cross-section by an spiral phase plate (SPP) of arbitrary integer order. An accurate formula for the intensity on the vortex's first ring and an approximate formula for the radius of the vortex's first ring are derived. The high-quality, 32-level SPPs are fabricated using direct e-beam writing in resist. It is shown that the experimental and theoretical diffraction patterns are in good agreement. The chapter also derives an analytical expression to describe the paraxial diffraction of a finite with circular and ring-like diaphragms plane wave by an SPP and formulae for the radius and intensity of the vortex first ring. The SPP can be used as a spatial filter to implement the generalized Hilbert transform and to increase contrast when viewing phase objects under microscope. The chapter conducts experimental studies on SPP-aided generation of a high-quality tube-shaped beam with ring-like intensity distribution.
