Large-aperture vertical-cavity surface-emitting lasers with an equilateral triangular lateral confinement are fabricated to investigate the formation of high-order resonant modes. The experimental lasing patterns are composed of the superscar mode, honeycomb eigenstate, and chaotic mode. Experimental results confirm the theoretical predictions that tiny symmetry breaking can cause the high-orde...

Let P(t) denote an infinitely long right triangular prism whose base is an equilateral triangle of edge length t. Let F (t) be the family of those subsets of P(t) that are congruent to a regular tetrahedron of unit edge. We present complete classification of the members of F (t) modulo rigid motions within the prism P(t), for every t > 0.

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues.

The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a Wigner-molecule in the form of equilateral triangular configuration for electrons is observed as the size of the dot is increased. PACS Numbers: 73.20.Dx, 73.61.-r

The classification of all dihedral triangular f-tilings of the Riemannian sphere S 2 whose prototiles are an equilateral triangle and an isosceles triangle and the identification of their symmetry groups are given. We also determine their classes of isogonality and isohedrality.