We call a photonic crystal tunable if its spectrum can be altered by a
n external electric or magnetic held. One of the two constitutive comp
onents of the proposed periodic composite structure has either electri
c permittivity or magnetic permeability dependent on the external elec
tric 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 s
ome useful features reminiscent of those accompanying the well-known e
lectronic topological phase transitions in metals. Thorough theoretica
l analysis of a two-dimensional tetragonal periodical structure is und
ertaken. This specific periodic structure exhibits the most important
features of a tunable photonic crystal.