Three-dimensional (3D) fabrication by direct laser writing opens new perspectives in resonator design and laser applications. We fabricated various shapes and sizes of microlasers of nanoscale quality: pyramids, tetrahedra, and 3D plano-concave cavities. The lasing thresholds depend on the resonator shapes and are lower than those of equivalent two-dimensional microlasers. The experimental spectra and the directions of emission may be predicted via a semiclassical analysis using periodic orbits, in good agreement with experiments. The screw angle is a key quantity to characterize a periodic orbit in 3D resonators. In this proceeding, we present different methods to calculate the screw angle in polyhedra, based on the example of the folded diamond periodic orbit in the square pyramid. Preliminary experimental results on the regular tetrahedron are also reported.
We investigate in detail the resonant properties of a two-dimensional dielectric cavity with an equilateral triangle shape, using a numerical integral equations approach and a semiclassical approach. The homogeneous Müller boundary equations are used to calculate the resonant modes of a dielectric triangle in a wide range of frequencies. It is shown that the modes of dielectric triangles localized on families of periodic orbits can be well described in terms of a semiclassical superscar model. Special attention is given to the families of resonances based on the inscribed triangle periodic orbit.
We investigate in detail the resonant properties of a 2D dielectric cavity with an equilateral triangle shape, using a numerical integral equations approach and a semiclassical approach. The homogeneous Müller boundary equations are used to calculate the resonant modes of a dielectric triangle in a wide range of frequencies. It is shown that the modes of dielectric triangles localized on families of periodic orbits can be well described in terms of a semiclassical superscar model. Special attention is given to the families of resonances based on the inscribed triangle periodic orbit.
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