Slow-light effect in dual-periodic photonic lattice

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.