Ray-based propagation of the cross-spectral density

Area of Science:

• Optics and Photonics
• Wave Propagation
• Electromagnetism

Background:

• Cross-spectral density (CSD) is crucial for characterizing partially coherent fields.
• Generalized radiance offers a framework for analyzing wave propagation.
• Existing methods for CSD calculation can be computationally intensive.

Purpose of the Study:

• To develop novel formulas for calculating the cross-spectral density of optical fields.
• To investigate the propagation of generalized radiance along rays.
• To explore new cross-spectral correlations related to flux and energy density.

Main Methods:

• Derivation of two exact formulas for cross-spectral density.
• Development of an infinite series expression for CSD using a subset of rays.
• Numerical evaluation of truncated series for various field properties (coherence, angular width).

Main Results:

• The first formula provides an exact CSD calculation using all rays.
• The second formula, an infinite series, shows improved convergence with specific ray choices (centroid), reduced field coherence, and increased paraxiality.
• Two novel cross-spectral correlations associated with flux and energy density were identified.

Conclusions:

• The derived formulas offer efficient and accurate methods for CSD calculation.
• Understanding convergence factors provides insights into optimizing CSD computations.
• The new correlations expand the toolkit for analyzing partially coherent fields.