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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 /spl gamma/. 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 /spl gamma/ is discussed in comparison with a one dimensional (1-D) multilayer stack of thin film,.
K. Ohtaka (1999) studied this question.