  We present analytical and numerical study of photonic lattice with short- and
long-range harmonic modulations of the refractive index. Such structures can be
prepared experimentally with holographic photolithography. In the spectral
region of photonic bandgap of the underlying single-periodic crystal, we
observe a series of bands with anomalously small dispersion. The related
slow-light effect is attributed to the long-range modulation in the photonic
lattice, that leads to formation of an array of evanescently-coupled high-$Q$
cavities. The band structure of the lattice is studied with several techniques:
(i) transfer matrix approach; (ii) analysis of resonant coupling in process of
band folding; (iii) effective medium approach based on coupled-mode theory; and
(iv) Bogolyubov-Mitropolsky approach. The latter method, commonly used in the
studies of nonlinear oscillators, was employed to investigate the behavior of
the eigen-function envelopes and the band structure of our dual-periodic
photonic lattice. We show that reliable results can be obtained even in the
case of large refractive index modulation.
