Natural modes of an active slab microcavity with air-filled periodic inclusions

Scattering of a normally incident plane wave by a dielectric slab with air-filled periodic inclusions of circular cylinder form is investigated. Comparison with the related homogeneous slab problem shows the presence of modes associated with the periodic inclusions. The corresponding resonances are sharp. Lasing threshold and the real-valued lasing frequency are then sought by introducing a negative imaginary part into the slab refractive index to develop a laser eigenvalue problem (LEP). The dependencies of lasing threshold and frequency on geometrical parameters are found, and indicate that the periodic modes have high lasing efficiency.