Generation of high-dimensional caustic beams via phase holograms using angular spectral representation.

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Holography

Background:

• Umbilic caustics are complex wave structures with unique geometric properties.
• Diffraction catastrophe theory provides a framework for understanding wave propagation and caustic formation.
• Generating and controlling high-dimensional umbilic beams presents significant challenges.

Purpose of the Study:

• To develop a generalized approach for generating high-dimensional elliptic and hyperbolic umbilic caustic beams.
• To investigate the wavefront properties and propagation dynamics of these novel beams.
• To explore potential applications of these beams in optical technologies.

Main Methods:

• Utilizing angular spectral representation for beam generation via phase holograms.
• Applying diffraction catastrophe theory to analyze wavefronts and potential functions.
• Conducting numerical simulations and experimental verification of beam generation and properties.

Main Results:

• Successfully generated high-dimensional elliptic and hyperbolic umbilic caustic beams.
• Elliptic umbilic beams demonstrated autofocusing, while hyperbolic umbilic beams degenerated into Airy beams under specific conditions.
• Both beam types exhibited robust self-healing properties and unique 3D caustic structures.
• Hyperbolic umbilic beams showed trajectory following during propagation.

Conclusions:

• The developed phase hologram method is effective for generating complex umbilic beams.
• These beams possess intriguing properties like self-healing and autofocusing, suitable for advanced applications.
• The findings advance the understanding and control of structured light beams for optical manipulation and micromachining.