Defect modes in helical photonic crystals: An analytic approach

Considering helically periodic structures with a twist defect, we define the defect mode in unbounded media and the scattering properties of bounded samples. The mode frequency, the lifetime of the defect mode, and the spectral width of the transmittance and reflectance peaks are expressed by fully analytic and very simple equations, the simplest ones appearing in the literature of photonic band gap materials. Our approach provides a clear explanation of the interesting optical properties of lossless samples with a twist defect and shows that the absorption greatly changes such properties, giving rise to unexpected effects. In particular, the total absorption within thick samples can decrease drastically when the absorption coefficient is increased beyond a well defined value.