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

Area of Science:

• Optics and Photonics
• Diffraction Theory
• Light Field Manipulation

Background:

• Spiral phase plates (SPPs) are crucial for imparting phase singularities onto light fields.
• Understanding Fresnel diffraction is key to predicting light behavior after passing through optical elements.
• Optical vortices, characterized by phase singularities, have applications in various scientific fields.

Purpose of the Study:

• To derive and analyze analytical expressions for Fresnel diffraction of plane and Gaussian waves by SPPs.
• To determine the relationship between singularity order and optical vortex radius and intensity.
• To experimentally validate the analytical models through fabrication and characterization of SPPs.

Main Methods:

• Analytical derivation of Fresnel diffraction formulas for SPPs with arbitrary-order phase singularities.
• Mathematical analysis of optical vortex radius and intensity dependence on topological charge (n).
• Numerical simulations using Fresnel transforms and experimental generation of light fields using fabricated SPPs.

Main Results:

• An analytical expression for Fresnel diffraction by SPPs was deduced.
• Optical vortex radius was shown to depend on the singularity order (n).
• Near-zero vortex intensity was found to be proportional to rho^(2n), and far-field intensity distribution depends on singularity number.

Conclusions:

• The study provides a comprehensive analytical framework for understanding Fresnel diffraction by SPPs.
• Experimental results align well with theoretical predictions, validating the derived formulas.
• The work facilitates the controlled generation of optical vortices for advanced applications.