Partially coherent vectorial nonparaxial beams.

Area of Science:

• Optics and Photonics
• Electromagnetism
• Mathematical Physics

Background:

• Partially coherent beams are crucial in various optical applications.
• Vectorial nature and nonparaxial propagation effects are often significant.
• Existing theories may not fully capture the complexity of these beams.

Purpose of the Study:

• To develop generalized vectorial Rayleigh-Sommerfeld diffraction integrals.
• To accurately describe the propagation of cross-spectral-density matrices for partially coherent beams.
• To analyze nonparaxial Gaussian Schell-model (GSM) beams beyond the paraxial approximation.

Main Methods:

• Development of generalized vectorial Rayleigh-Sommerfeld diffraction integrals.
• Derivation of propagation expressions for cross-spectral-density matrices and intensity.
• Analysis of vectorial nonparaxial Gaussian Schell-model beams.
• Evaluation of far-field asymptotic forms.

Main Results:

• Generalized integrals are derived for cross-spectral-density matrices of partially coherent beams.
• Expressions for propagation of vectorial nonparaxial GSM beams and their far-field forms are obtained.
• The necessity of a 3x3 cross-spectral-density matrix for exact description is demonstrated.

Conclusions:

• A 3x3 cross-spectral-density matrix or vector theory is required for exact description of nonparaxial GSM beams.
• The developed integrals provide a more complete framework for analyzing partially coherent vectorial beams.
• This work advances the understanding of nonparaxial beam propagation.