Higher-order twisted/astigmatic Gaussian Schell-model cross-spectral densities and their separability features

Area of Science:

• Optical physics
• Classical optics
• Mathematical physics

Background:

• Partially coherent sources are crucial in various optical applications.
• Adding twist phase terms to cross-spectral density (CSD) functions requires maintaining non-negative definiteness.
• Existing constraints for valid twisted CSDs were limited to standard Twisted Gaussian Schell-model (TGSM) sources.

Purpose of the Study:

• To introduce an infinite family of higher-order TGSM sources.
• To enable the construction of a wider range of valid twisted CSDs with tunable parameters.
• To explore the properties and separability of these higher-order sources and their Astigmatic Gaussian Schell-model (AGSM) counterparts.

Main Methods:

• Defined higher-order TGSM sources using products of standard TGSM CSDs and Hermite polynomials.
• Investigated the twist-coherence constraints for the new sources.
• Utilized partial transposition to convert higher-order TGSM CSDs into higher-order AGSM CSDs.
• Analyzed the separability conditions for both higher-order TGSM and AGSM CSDs.

Main Results:

• Successfully introduced higher-order TGSM sources that maintain the validity of the twist-coherence constraint.
• Demonstrated that these higher-order sources can serve as building blocks for numerous valid twisted CSDs.
• Showcased the ability to achieve diverse intensity and coherence features distinct from standard TGSM sources.
• Derived conditions for the separability of higher-order TGSM and AGSM CSDs.

Conclusions:

• The proposed higher-order TGSM sources significantly expand the toolkit for generating complex optical field correlations.
• These sources provide a flexible framework for designing optical beams with tailored properties.
• The findings contribute to a deeper understanding of the mathematical framework governing partially coherent light.