Density of states of slab photonic crystals and the laser oscillation in photonic crystals

A treatment of the density of states of electromagnetic normal modes of slab photonic crystals is given to illustrate the thickness dependence of the Q values of the slab modes of arrayed dielectric spheres. The onset of the laser oscillation is then examined for a slab photonic crystal of arrayed cylinders by simulating active cylinders as having a complex dielectric constant of negative imaginary part γ. It is shown that the divergence of the transmittivity of light occurs as an indication of the onset of lasing, when the slab is thick enough to give high Q values to the slab modes. The threshold value of γ is discussed in comparison with a one dimensional (1-D) multilayer stack of thin film,