We present analytical and numerical studies of a 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 the 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 of 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) an analysis of resonant coupling in the process of band folding; (iii) effective-medium approach based on coupled-mode theory; and (iv) the Bogolyubov–Mitropolsky approach. The latter method, commonly used in the studies of nonlinear oscillators, was employed to investigate the behavior of eigenfunction envelopes and the band structure of the dual-periodic photonic lattice. We show that reliable results can be obtained even in the case of large refractive index modulation.
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