  Photonic crystals are periodic structure of dielectric materials that can
control light propagations in the media because of their photonic-dispersion
led by the well-ordered lattice-points arrangements. We here study the behavior
of light propagation in distorted-photonic crystals (D-PCs), which possess the
gradual spatial distortion of lattice-points positions, as the effective field
theory in terms of the differential geometry. In order to investigate the
trajectory of light ray in the D-PC, we derive the geodesics equation that is
given from the principle of least action, with defining the metric tensor in
terms of the lattice-positions distortion. The geodesics equation indicates
that the trajectory can be bent by just introducing lattice-positions
distortion. We show some exact solutions of the trajectory in the case of
simple distortion and that those results well agree with the results of the
Finite Difference Time Domain (FDTD) simulations.
