Bessel-like beams modulated by arbitrary radial functions

Area of Science:

• Optics and Photonics
• Beam Propagation
• Mathematical Physics

Background:

• Bessel beams and their modified versions (Bessel-Gauss, generalized Bessel-Gauss, Bessel-super-Gauss) are crucial in various optical applications due to their self-reconstruction properties.
• Accurate determination of their radial and axial intensity profiles is essential for understanding and optimizing their behavior.
• Existing methods for calculating these profiles can be computationally intensive or limited in scope.

Purpose of the Study:

• To present a novel, approximate method for calculating the radial and axial intensity of general Bessel-like beams.
• To validate the accuracy of this approximation for various modified Bessel beams.
• To demonstrate the method's applicability to practically generated optical beams.

Main Methods:

• Development of a simplified analytical approximation for Bessel-like beam intensity.
• Comparison of approximate results with exact solutions for Bessel beams.
• Evaluation of the approximation's accuracy for Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams.
• Analysis of a practically generated Bessel-like beam using the proposed method.

Main Results:

• The approximate method provides highly accurate results for Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, closely matching exact values.
• The approximation yields exact results for standard Bessel beams.
• The method is demonstrated to be effective for analyzing practically generated beams, such as those created with simple lenses.

Conclusions:

• The proposed approximate method offers a computationally efficient and accurate tool for analyzing the intensity profiles of a wide range of Bessel-like beams.
• This simplification facilitates the design and analysis of optical systems employing these beams.
• The method's applicability to practical beam generation highlights its potential for real-world optical engineering.