Laser beams in Fabry–Perot cavities with circular apertures

This study investigates the propagation of laser beams within Fabry–Perot resonators bounded by circular apertures. We present two independent analytical methods that can be shared with students for determining the transverse eigenmodes of such resonators, one based on the solution of the paraxial Helmholtz equation and the other employing the Huygens–Fresnel integral formulation. Complementing the theoretical analysis, we designed an undergraduate-level experiment using a half-symmetric plano-concave Fabry–Perot resonator. In this setup, Laguerre–Gaussian mode patterns were generated and compared with the theoretical predictions. The approach enhances students' understanding of resonator optics and fosters deeper engagement with experimental physics.