Airy pulsed beams

Area of Science:

• Optics and Photonics
• Wave Propagation
• Nonlinear Optics

Background:

• Airy beams (AiBs) exhibit unique properties like curved trajectories and weak diffraction.
• AiBs are understood as caustics of rays originating from an Airy function aperture distribution.
• Extending these properties into the time domain presents challenges in dispersion and trajectory maintenance.

Purpose of the Study:

• To derive ultra wideband Airy pulsed beams (AiPBs) as a time-domain extension of Airy beams.
• To ensure all frequency components propagate along the same curved trajectory, preventing pulse dispersion.
• To provide exact and approximate analytical solutions for AiPBs.

Main Methods:

• Introduction of a frequency scaling technique for the initial aperture field.
• Application of the spectral theory of transients for an exact closed-form solution.
• Derivation of uniform geometrical optics-based wavefront approximations for the time domain.

Main Results:

• Successfully derived a class of ultra wideband Airy pulsed beams (AiPBs).
• Demonstrated that frequency scaling ensures a frequency-independent ray skeleton and curved trajectory for all components.
• Obtained an exact solution and valid uniform approximations for AiPBs, preserving AiB characteristics.
• Confirmed that AiPBs do not disperse, maintaining their unique propagation features.

Conclusions:

• Ultra wideband Airy pulsed beams (AiPBs) are successfully derived, extending Airy beam properties into the time domain.
• The proposed frequency scaling method effectively prevents pulse dispersion and ensures consistent curved trajectory propagation.
• The derived analytical solutions and approximations provide valuable tools for understanding and utilizing AiPBs in various applications.