Wigner functions for paraxial and nonparaxial fields

Abstract

The Wigner function gives an intuitive representation of coherent and partially coherent wave fields in the frequency domain, which takes the form a ray weight distribution. However, this weight distribution is conserved along rays only for paraxial or significantly incoherent fields. Generalizations of the Wigner function have been defined for propagation through transparent homogeneous media that are exactly conserved along rays for any angular spread and state of coherence. A series expression is derived here for calculating these nonparaxial generalizations starting from the standard Wigner function.

Keywords:

• Wigner function
• nonparaxial fields
• coherence theory
• Gaussian Schell-model

Acknowledgement

The authors acknowledge support from the National Science Foundation through award number PHY-0449708.