Weak disorder in photonic crystals

Finite one-dimensional photonic crystals with geometric and compositional disorder are studied via a perturbative approach in the weak effective disorder limit. Our model gives expressions that, when used to compute disorderaveraged reflectivity spectra around the photonic band gap, yield accurate results and significantly more efficiently than through a direct numerical average over disorder realization. The method is specially suited to deal with atomic photonic crystals with low levels of disorder and a substantial number of periods.