Study of the origin of the complex beam profile of a hole-coupled free electron laser oscillator

Hole coupling is a way to extract laser beams from an optical cavity through a hole on a cavity mirror. Hole coupling is often used in free electron laser oscillators and inherently causes a non-Gaussian beam profile at user stations, which are more than 10 m apart from the coupling hole. The laser beam extracted from a coupling hole has a bright central region (Airy disk) surrounded by a series of concentric rings (Airy pattern). The existence of an Airy pattern results in a non-Gaussian beam profile. It was demonstrated that the beam profile can be changed from a non-Gaussian to a nearly Gaussian distribution by removing the Airy pattern in the experiments and physical optics calculations.