  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.
