Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate

TLDR

The study derives an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate to generate arbitrary‑order phase singularities. Analytical Fresnel diffraction of Gaussian beams by SPPs of arbitrary order is developed, with detailed analysis of the n = 2 case and experimental generation of first‑ and second‑order singularities using a 32‑level SPP fabricated by electron‑beam lithography. The work provides vortex‑radius estimates and shows that near‑zero vortex intensity scales as ρ^(2n), derives far‑field intensity distributions, and confirms that numerical simulations agree with the analytical predictions.

Abstract

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity’s integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to ρ2n, where ρ is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n=2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.