We study band dispersion relations omega(k-->) of a photonic crystal with at least one of the constitutive components being a magnetically ordered material. It is shown that by proper spatial arrangement of magnetic and dielectric components one can construct a magnetic photonic crystal with strong spectral asymmetry (nonreciprocity) omega(k-->) not equal omega(-k-->). The spectral asymmetry, in turn, results in a number of interesting phenomena, in particular, one-way transparency when the magnetic photonic crystal, being perfectly transparent for a Bloch wave of frequency omega, "freezes" the radiation of the same frequency omega propagating in the opposite direction. The frozen radiation corresponds to a Bloch wave with zero group velocity partial differential omega(k)/ partial differential k=0 and, in addition, with partial differential(2)omega(k)/ partial differential k(2)=0.

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

Public reporting burden for this collection of information is estimated PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)University of California, Irvine Department of Mathematics 420 rowland Hall Irvine, CA 92697-3875 Our initial theoretical work with Dr. Yu. Godin on asymptotic models for 3D thin-film photonic crystals Is out. The results establish a possibility of spectral gaps and provide new computational tools for studies of 3D photonic crystals. A. Eigotin and Yu. Godin, "Spectral Properties of Thin-film Photonio Crystals", SIAN J. Appl. Math., 61, No. 6, pp. 2008-2035(2001. We finished our work on nonlinear photonic crystals with quadratic nonlinearity including the role the group velocity matching for nonlinear interactions in periodic media. We can see looking at publications a growing interest to nonlinear periodic dielectric structures, especially with quadratic nonlinearity. We believe that the work we have conducted is an achievement in that area. We learned from the editor that our paper was "one of the most accessed orticles for the Journal las: SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)AFOSR