Generalized Bessel beams in modified axially symmetric graded index structures

Area of Science:

• Optics and Photonics
• Wave Propagation

Background:

• Bessel beams are non-diffracting beams with unique propagation characteristics.
• Graded index media offer tunable optical properties for beam manipulation.

Purpose of the Study:

• To explore stable Bessel beams in a general class of graded index media.
• To derive explicit solutions for Bessel beam envelopes in media with an
• α
• index profile.

Main Methods:

• Analytical derivation of radial field envelopes using generalized Bessel functions.
• Mathematical analysis to identify conditions for retaining Bessel functions of the first kind.
• Numerical simulations to validate theoretical predictions.

Main Results:

• Explicit solutions for stable Bessel beams in graded index media derived.
• Demonstrated unique retention of Bessel functions of the first kind under specific conditions.
• Numerical examples illustrate beam stability, propagation, and diffraction characteristics.

Conclusions:

• The proposed graded index medium supports stable Bessel beams.
• The derived solutions provide a theoretical framework for designing and analyzing such beams.
• The study highlights the interplay between medium properties and beam behavior.