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Computing unstable resonator modes

Abstract The potential of the so-called ‘eigenvector method’ (here called the direct eigenvector method (DEM)) for computing the modes of unstable resonators in two transverse dimensions is examined, and a detailed comparison with the traditional Fox–Li approach undertaken. The memory requirements of the DEM are potentially enormous and, if high-resolution patterns are needed, the Fox–Li approach must remain the method of choice. However, the DEM has the important advantage that higher order modes can be generated as easily as the fundamental mode, and this provides an incentive for exploring its capabilities. With the help of some simple devices for limiting the memory requirements, we have obtained DEM results in hexagonal geometry that display an impressive level of detail.