The limits for complete photonic bandgaps in low-contrast media

The minimal refractive index contrast to obtain a complete photonic bandgap (CPBG) in structured media was not identified so far. We address this problem by considering distributed quasicrystals in with arbitrary number and positions of Bragg peaks in reciprocal space. For these structures an analytical estimation is derived which predicts that there is an optimal number of Bragg peaks for any refractive index contrast and finite CPBGs for an arbitrarily small refractive index contrast in 2D and 3D. Results of numerical simulations of dipole emission in 2D structures support our estimation. In 3D an emission suppression of almost 10 dB was demonstrated with a refractive index contrast of 1.6. The reason for residual leakage in 3D structures has to be further investigated.