Nonparaxial elegant Laguerre-Gaussian beams

Area of Science:

• * Optics and Photonics
• * Mathematical Physics

Background:

• * Calculating optical fields from tightly focused laser beams requires accurate mathematical expressions.
• * Existing models often rely on paraxial approximations, limiting their applicability for highly focused beams.
• * Elegant Laguerre-Gaussian (eLG) beams are exact solutions to the Helmholtz equation, but nonparaxial expressions are needed.

Purpose of the Study:

• * To introduce novel closed-form nonparaxial expressions for elegant Laguerre-Gaussian (eLG) beams.
• * To provide exact analytical solutions for the electromagnetic fields of tightly focused eLG beams.
• * To ensure these new expressions reduce to known eLG beams in the paraxial limit.

Main Methods:

• * Derivation of closed-form nonparaxial expressions.
• * Utilization of spherical Bessel functions and associated Legendre functions with complex arguments.
• * Expressing solutions as linear combinations of analytic functions.

Main Results:

• * Introduced exact, closed-form nonparaxial expressions for eLG beams.
• * Demonstrated that these expressions are linear combinations of analytic functions.
• * Verified that the derived expressions simplify to standard eLG beams under paraxial conditions.

Conclusions:

• * The new nonparaxial expressions offer a more accurate description of tightly focused eLG beams.
• * These analytical solutions facilitate precise calculations in optical beam propagation and manipulation.
• * The findings extend the utility of eLG beams to nonparaxial regimes.