Simplified intracavity phase plates for increasing modal discrimination in a laser cavity

Recently, a new class of laser resonators was introduced by one of the authors (J. Leger) that utilizes diffractive mirrors and an additional intracavity diffractive phase element. High modal discrimination and low fundamental mode loss were achieved simultaneously using sinusoidal and pseudo-random diffractive phase elements. In this paper, an analytical approach is developed to study a simplified diffractive mirror resonator for producing Gaussian-shaped beams. Explicit expressions are obtained for the fundamental mode loss and modal discrimination by assuming a Gaussian-shaped reflectivity for the output mirror. An intracavity phase element consisting of a simple single-step phase modulation was approximated by a Gaussian with small radius. Explicit expressions are obtained for the modal discrimination factor as a function of resonator parameters with a Gaussian output mirror. Analytical results demonstrate that simple single-step phase elements can enhance cavity performance. Numerical simulations were performed for a phase element with a step singularity in the phase function. This element was found to increase the modal discrimination of the cavity, while simplifying element fabrication and cavity alignment.