PHOTONIC BAND STRUCTURES OF 2-DIMENSIONAL SYSTEMS FABRICATED FROM RODS OF A CUBIC POLAR CRYSTAL

By the use of the plane-wave method, we calculate the photonic band st ructure for electromagnetic waves of E and H polarization propagating in a system consisting of an infinite array of identical, infinitely l ong, parallel cylinders of circular cross section, embedded in vacuum, whose intersections with a perpendicular plane form a square or trian gular lattice. The cylinders are fabricated from GaAs, which represent s a cubic, polar crystal material, containing two atoms ina primitive unit cell, for which the dielectric function has the form ity)(omega(L )(2)-omega(2))/(omega(T)(2)-omega(2)), where epsilon(infinity) is the optical frequency dielectric constant, while omega(L) and omega(T) are the frequencies of the longitudinal optical and transverse optical-vi bration modes of infinite wavelength, respectively. For electromagneti c waves of both polarizations the problem of obtaining the photonic ba nd structure is reduced to the solution of a generalized eigenvalue pr oblem. In comparison with the dispersion curves of electromagnetic wav es in vacuum, the photonic band structures are the most significantly affected by the particular form of the dielectric function we have ass umed for frequencies in the vicinity of the polariton gap omega(T)<ome ga<omega(L). For small filling fractions of the GaAs cylinders the pho tonic band structure for each polarization, except within the frequenc y range of the polariton gap, is a slightly perturbed version of the d ispersion curves of electromagnetic waves in vacuum. For higher values of the filling fraction the dispersion curves deviate substantially f rom the dispersion curves of electromagnetic waves in vacuum within a broader frequency range, and in the case of E polarization, the photon ic band structures reveal the existence of absolute band gaps. As the most striking feature, the calculated photonic band structures yield a dditional, nearly dispersionless bands that for waves of both polariza tions occur at and below omega(T) and in the case of H polarization oc cur also within the frequency range omega(T)<omega<omega(L) where epsi lon(omega) is negative. The results for H polarization and small filli ng fractions of the GaAs cylinders are reproduced by an approach in wh ich the zeros of a determinant are sought. A possible origin of the fl at bands obtained in this polarization by both approaches is discussed .