Reciprocal space engineering allows tailoring the scattering response of media with a low refractive-index contrast. Here it is shown that a quasiperiodic leveled-wave structure with well-defined reciprocal space and random real space distribution can be engineered to open a complete photonic bandgap (CPBG) for any refractive-index contrast. For these structures, an analytical estimation is derived, which predicts that there is an optimal number of Bragg peaks for any refractive-index contrast. A finite 2D or 3D CPBG is expected at this optimal number even for an arbitrarily small refractive-index contrast. Results of numerical simulations of dipole emission in 2D and 3D structures support the estimations. In 3D simulations, an emission suppression of almost 10 dB is demonstrated with a refractive index down to 1.38. The 3D structures are realized by additive manufacturing on millimeter scale for a material with a refractive index of n ≈ 1.59. Measurements confirm a strong suppression of microwave transmission in the expected frequency range.
