Generalized Airy derivative transform of a Gaussian beam

Area of Science:

• Optics and Photonics
• Beam Shaping and Transformation

Background:

• The conventional Airy transform converts Gaussian beams into Airy beams.
• The need exists for generating a broader range of specific beams.

Purpose of the Study:

• To propose a generalized Airy derivative transform.
• To extend the functionality of Airy transforms for generating diverse beams.

Main Methods:

• Derivation of analytical expressions for beam characteristics (center of mass, spot dimension, divergence, M-square factor) using light intensity moments.
• Investigation of transformed Gaussian beam propagation in free space.
• Experimental demonstration of the first-order Airy derivative transform.

Main Results:

• The generalized Airy derivative transform includes the conventional Airy transform as a zeroth-order case.
• Transformed Gaussian beams exhibit ballistic trajectories during free-space propagation.
• The light field during propagation is a sum of Airy function derivatives with modified weighting factors.

Conclusions:

• The generalized Airy derivative transform provides a versatile method for generating specific beams.
• Experimental realization is straightforward and generalizable.
• This broadens the applicability of Airy transforms in optics.