Random sources for beams with azimuthal intensity variation

Area of Science:

• * Optics
• * Statistical Optics
• * Radiometry

Background:

• * Understanding the coherence properties of light sources is crucial for various optical applications.
• * Previous research has primarily focused on sources with simpler intensity distributions.
• * Characterizing sources with complex azimuthal intensity patterns presents a significant challenge.

Purpose of the Study:

• * To determine the degree of coherence structure for wide-sense statistically stationary planar sources radiating far fields with azimuthal intensity dependence.
• * To establish a link between the azimuthal modes of far-field intensity and the spatial frequency components of the source's degree of coherence.
• * To provide a foundational understanding for generating and controlling light fields with specific azimuthal structures.

Main Methods:

• * Employed Fourier series decomposition to analyze the azimuthal dependence of far-field intensity patterns.
• * Utilized the relationship between far-field properties and source coherence.
• * Leveraged the concept of spatial frequency components within the source's degree of coherence.

Main Results:

• * Successfully determined the structure of the degree of coherence for planar sources with azimuthal intensity dependence.
• * Demonstrated that azimuthal modes in the far field are direct representations of the source's spatial frequency components.
• * Established a novel method for characterizing coherence in complex optical fields.

Conclusions:

• * The study provides the first determination of the coherence structure for sources with azimuthal far-field intensity dependence.
• * The findings offer a new perspective on the relationship between source coherence and far-field characteristics.
• * The developed methodology paves the way for experimental realization using spatial light modulators.