Independent-elementary-field model for three-dimensional spatially partially coherent sources

Area of Science:

• Optics and Photonics
• Electromagnetics
• Mathematical Physics

Background:

• The independent-elementary-source model was previously developed for planar sources.
• Extending this model to three-dimensional (3D) volume sources is crucial for broader applications in optical engineering.

Purpose of the Study:

• To generalize the independent-elementary-source model to handle volume source distributions.
• To analyze the impact of 3D source distribution on far-field radiation and spectral coherence.
• To outline methods for determining effective 3D source distributions with specific coherence properties.

Main Methods:

• Extension of the existing planar source model to accommodate 3D volume source distributions.
• Mathematical analysis of the far-field radiation pattern and the complex degree of spectral coherence.
• Application of the 3D Fourier transform to the weight function of elementary fields.

Main Results:

• The far-field radiation pattern is demonstrated to be independent of the specific 3D distribution of coherent elementary sources.
• The absolute value of the complex degree of spectral coherence is determined by the 3D Fourier transform of the elementary field weight function.
• Effective 3D source distributions can be determined, which may differ significantly from the primary emitting volume, especially in the longitudinal dimension.

Conclusions:

• The generalized model provides a robust framework for analyzing partially coherent fields from volume sources.
• The findings offer insights into controlling and predicting the spatial coherence of light emitted from complex sources.
• The model facilitates efficient numerical propagation of partially coherent fields, aiding in optical system design and simulation.