Theoretical Simulation of Airy Beams

An Airy beam is a non-diffracting beam with unique propagation characteristics, exhibiting an intensity distribution that follows the Airy function pattern. This beam demonstrates self-accelerating behavior during propagation in free space, attracting significant attention in optical research domains.

In theoretical simulations, constructing a mathematical model of Airy beams typically involves mathematical descriptions of the Airy function, including its amplitude and phase distributions. The initial field distribution of Airy beams can be achieved through cubic phase modulation, which can be implemented using spatial light modulators (SLMs) or specially designed phase plates. From a code implementation perspective, this typically involves defining the phase mask using array operations and applying complex exponential functions to generate the beam profile.

The simulation process generally consists of two main components: phase plate design and propagation simulation. The phase plate design phase requires calculating the phase distribution necessary for generating Airy beams, typically employing cubic phase modulation functions. Propagation simulation is based on wave equations or angular spectrum theory to compute the evolution characteristics of the beam at different propagation distances. In computational implementations, this often utilizes Fourier transform algorithms and propagation kernels to model beam diffraction and evolution.

Notably, Airy beams exhibit distinctive characteristics during propagation: maintaining invariant transverse profiles while following parabolic trajectories. These properties make them valuable for applications in optical manipulation, particle trapping, and optical communications. Through theoretical simulations, researchers can deeply investigate these characteristics and provide guidance for experimental studies. Simulation codes typically include parameter studies to analyze beam behavior under different conditions and optimization algorithms for phase mask design.