Manifestation of quantum-billiard eigenvalue statistics from subthreshold emission of vertical-cavity surface-emitting lasers

Abstract

We report that the subthreshold emission spectra of vertical-cavity surface-emitting lasers (VCSELs) can be analogously used to manifest the quantum-billiard energy spectra. The Fourier-transformed distributions of the subthreshold emission spectra are demonstrated to display various peak structures that are in good agreement with the results of the quantum-billiard model. We also verify that the statistical analyses of the nearest-neighbor eigenvalue spacing distributions obey a Poisson distribution for an equilateral-triangular device and a Wigner distribution for a stadium-shaped device.