Fundamental electromagnetic Gaussian beam beyond the paraxial approximation

Area of Science:

• Electromagnetism
• Optics
• Mathematical Physics

Background:

• The fundamental electromagnetic Gaussian beam is a key concept in optics.
• Existing models often rely on paraxial approximations, limiting accuracy for certain applications.

Purpose of the Study:

• To develop a more accurate model for electromagnetic Gaussian beams beyond the paraxial approximation.
• To investigate the electrodynamics of nonparaxial Gaussian beams and their properties.

Main Methods:

• Constructing the beam from a single electric vector potential component with cylindrical symmetry.
• Solving the inhomogeneous paraxial wave equation, including particular and complementary functions.
• Determining amplitude coefficients for Laguerre-Gauss beams based on asymptotic behavior.

Main Results:

• The paraxial and first-order nonparaxial beams were obtained.
• A procedure for deducing the asymptotic state of nonparaxial beams was established.
• Electromagnetic fields and beam characteristics were analyzed beyond the paraxial limit.

Conclusions:

• The study provides a comprehensive framework for understanding nonparaxial electromagnetic Gaussian beams.
• The first-order nonparaxial beam plays a significant role in defining average beam characteristics.
• This work advances the theoretical understanding of light propagation in optical systems.