Extracting photon periodic orbits from spontaneous emission spectra in laterally confined vertically emitted cavities

We report our observation of the signature of photon periodic orbits in the spontaneous emission spectra of largeaperture vertical-cavity surface-emitting lasers (VCSELs). The high-resolution measurement clearly demonstrates that over a thousand cavity modes with a narrow linewidth can be perfectly exhibited in the spontaneous emission spectrum just below the lasing threshold. The Fourier-transformed spectrum is analyzed to confirm that the spontaneous emission spectra of large-aperture VCSELs can be exploited to analogously investigate the energy spectra of the 2D quantum billiards.