An optical resonator supporting two sets of simultaneously co-existent oscillation modes (30 and 31), having polarizations orthogonal to each other. Mode control elements (28 and 29), such as apertures and phase elements, are introduced into the resonator to allow only preferred modes to exist. The placement and orientation of the sets are designed such that the high intensity zones of one set fall on the nodes or low intensity zones of the other set in an interlaced pattern. Thus, in a laser resonator, better utilization of the gain medium (24) is achieved and the beam quality and brightness over multimode lasing are improved. This configuration improves the performance of high Fresnel number resonators, in both pulsed and continuous lasers, for applications such as scribing, drilling, cutting, target designation and rangefinding. An application of the intra-cavity coherent summation of orthogonally polarized modes is described, whereby azimuthally or radially polarized beams may be obtained.