We call a photonic crystal tunable if its spectrum can be altered by an external electric or magnetic field. One of the two constitutive components of the proposed periodic composite structure has either electric permittivity or magnetic permeability dependent on the external electric or magnetic field. Consequently, the electromagnetic spectrum of the photonic crystal can be altered over a wide range by the external quasistationary uniform field. The tunable photonic crystal exhibits some useful features reminiscent of those accompanying the well-known electronic topological phase transitions in metals. Thorough theoretical analysis of a two-dimensional tetragonal periodical structure is undertaken. This specific periodic structure exhibits the most important features of a tunable photonic crystal. ͓S0163-1829͑98͒06305-X͔

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex-valued tensor can exhibit non-monotonic behavior as functions of volume fraction of cylinders, and can be either greater or less than that of the constituents.Comment: 13 pages, 14 figure

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We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity tensor as well as its expansion in terms of volume fraction of the cylinders. Results are illustrated by examples.Comment: 21 pages, 5 figure

The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix, we investigate the dependence of the Lyapunov exponent on the frequency and magnitude of the disorder . It is shown that in the bulk of the bands $ 2 , while near the band edges it has order $ 2/3 . This dependence is illustrated by numerical simulations.