Propagating analysis of Airy beams via complex phase space and ray method

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Airy beams exhibit unique non-diffracting and self-healing properties.
• Understanding their complex propagation dynamics, including intensity profiles and phase shifts, is crucial.

Purpose of the Study:

• To propose a novel phase space and ray method for interpreting Airy beam characteristics.
• To provide an intuitive understanding of Airy beams and finite-energy Airy beams without solving wave equations.

Main Methods:

• Development of a complex phase space and ray tracing approach.
• Analysis of parabolic phase space curves (PSC) and light ray clusters.
• Mapping ray evolution to caustic curves in complex coordinate space.

Main Results:

• Finite-energy Airy beams represented as complex PSCs converging to complex parabolic caustics.
• Infinite-energy Airy beams correspond to real-valued phase space elements.
• Paraxial Airy beams maintain PSC parabolicity and constant ray density, ensuring non-diffraction.

Conclusions:

• The phase space and ray method provides intuitive comprehension of Airy beam propagation.
• This method simplifies the derivation of phase and decay factors.
• It offers an alternative to solving wave equations or diffraction integrals for understanding Airy beam behavior.