Three modal decompositions of Gaussian Schell-model sources: comparative analysis.

Area of Science:

• * Optics and Photonics
• * Statistical Optics
• * Optical Communication Systems

Background:

• * Modal representations simplify cross-spectral density (CSD) analysis in optical systems.
• * Gaussian Schell-model (GSM) sources are crucial in various imaging and communication applications.
• * Comparing coherent-mode representation (CMR), pseudo-mode representation (PMR), and random mode representation (RMR) is essential for accurate modeling.

Purpose of the Study:

• * To investigate the equivalence and differences between CMR, PMR, and RMR for GSM sources.
• * To determine the efficiency of each method in reconstructing CSD.
• * To analyze the impact of these representations on second- and fourth-order statistics during propagation.

Main Methods:

• * Theoretical analysis of three modal representation methods (CMR, PMR, RMR).
• * Examination of Gaussian Schell-model (GSM) source class.
• * Numerical simulations of beam propagation through deterministic and dynamic random screens.

Main Results:

• * CMR requires the fewest modes for accurate CSD reconstruction, followed by PMR and RMR.
• * Methods become equivalent for second-order statistics (intensity, degree of coherence) with sufficient modes.
• * Fourth-order statistics (intensity-intensity correlations) differ significantly among methods, even with many modes.
• * Second-order statistics remain consistent across methods after screen propagation, unlike fourth-order statistics.

Conclusions:

• * CMR offers the most efficient modal representation for GSM sources.
• * While second-order statistics are robust across methods, fourth-order statistics highlight fundamental differences.
• * Propagation through screens does not reconcile the differing fourth-order statistics derived from the three methods.