Elementary-field analysis of partially coherent beam shaping

Area of Science:

• Optics and Photonics
• Wave Propagation
• Coherent and Partially Coherent Fields

Background:

• Spatial shaping of partially coherent fields is crucial for various optical applications.
• Understanding the propagation of partially coherent light through optical systems is complex.
• Existing methods for analyzing partially coherent fields can be computationally intensive.

Purpose of the Study:

• To investigate and compare different representations of partially coherent fields for spatial beam shaping.
• To determine the most computationally efficient representations for specific optical system architectures (2F and 4F systems).
• To introduce generalized concepts for analyzing optical systems with partially coherent fields.

Main Methods:

• Analysis of spatial beam shaping in 2F Fourier-transforming and 4F imaging systems.
• Comparison of Mercer-type coherent-mode representation with spatially and angularly shifted elementary field mode expansions.
• Dimensionality reduction of propagation integrals using different field representations.

Main Results:

• The angular elementary-field representation is computationally superior for Fourier-transforming systems.
• The spatially shifted elementary-field expansion is optimal for imaging systems.
• Generalized amplitude and transfer functions are derived for imaging systems, reducing to standard metrics for incoherent light.

Conclusions:

• The choice of field representation significantly impacts computational efficiency in spatial beam shaping of partially coherent fields.
• Optimized representations enable more effective analysis and design of optical systems dealing with partial coherence.
• The study provides a framework for understanding generalized system descriptions in the context of partial coherence.