Hyperbolic accelerating beams and their relation with Hermite-Gaussian beams.

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Hermite-Gaussian beams are fundamental in optics, but their complex amplitude expressions offer limited geometrical insight.
• Designing beams with specific trajectories, like hyperbolic paths, is crucial for advanced optical applications.

Purpose of the Study:

• To derive initial distributions for accelerating beams with hyperbolic trajectories.
• To explore the relationship between these novel beams and established Hermite-Gaussian beams.
• To gain clearer geometrical insights into beam propagation and structure.

Main Methods:

• Utilizing the caustic-design method to determine phase and complex amplitude distributions.
• Analyzing the ray-based method to understand beam propagation characteristics.
• Deriving approximate expressions for the initial complex amplitude of Hermite-Gaussian beams.

Main Results:

• Hyperbolic accelerating beams represent a more extensive class than Hermite-Gaussian beams.
• When the bending parameter is an integer, these beams exhibit similar initial distributions and propagation to Hermite-Gaussian beams.
• Approximate complex amplitude expressions reveal local amplitude, wave vector, and ray structure, including caustics.

Conclusions:

• Hyperbolic accelerating beams offer a generalized framework for understanding beam behavior.
• The derived expressions enhance geometrical interpretation of beam properties.
• This work expands the understanding of optical beam characteristics and design possibilities.