Azimuthal mode discrimination of annular resonators

Abstract

A diffraction formula for annular beam propagation is suggested. Significant computational savings are obtained without restriction to low azimuthal mode orders. Azimuthal mode discrimination is shown to exist in stable annular resonators. High-order azimuthal modes can suffer low diffraction losses with certain mirror parameters. These high-order modes are identified with azimuthal revolving rays that satisfy known geometric relations for multipass resonators.

Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser

“…where M is the free-space propagation matrix, M is the aperture matrix, M is the thermal lensing matrix, and M is the rear concave mirror matrix (all 2-D matrices). The propagation matrix M for each azimuthal order could be determined from the radial Kirchhoff-Fresnel diffraction kernel for long distances [9], given by (4) where is the propagation distance, k=2 , and and are the radial coordinates at and , respectively. Alternatively, M could equally be determined from the angular spectrum propagation for short distances [10].…”

Numerical simulation of the w-axicon type optical resonator for coaxial slab CO2lasers

“…It should be noted that according to a more exact analysis [16], annular stable resonators have azimuthal mode discrimination. However, the effect becomes apparent in the range of n ∼ 100, and this is beyond our scope of interest.…”

Coupling efficiencies and mode discrimination in coaxial waveguide laser resonators

“…where the highly oscillatory term has been dropped due to its much smaller contribution to the integral [7][8]. For d = R, the Fourier optical transform gives [11]…”

“…Abrams [2], Degnan and Hall [3], Avrillier and Verdonck [5] and Boulnois [6] have studied the single mode losses of resonators in the hollow circular waveguide and rectangular waveguide (including square waveguide), respectively, and report that there exist three special geometries to provide the lowest coupling losses, corresponding to plane-parallel, half-concentric and semiconfocal configurations. In recent years coaxial waveguides have been increasingly used for gas lasers operating with RF transverse excitation and diffusion cooling [7,8]. However, there is no published report on the coupling losses of annular waveguide resonators.…”