Photonic bandgap via nonlinear modulation assisted by spontaneously generated coherence

•Photonic bandgap is formed in standing-wave driven atomic system assisted by spontaneously generated coherence.•Quantum interference from the spontaneous emission significantly reduces the absorption and enhances the refractivity of the medium.•The photonic bandgap is originated from the Kerr nonlinear modulation between the probe and trigger fields.•This scheme is different from the other schemes based on linear modulation.

A four-level double-ladder atomic system with two upper states coupled to the excited state by a standing-wave trigger field is explored to generate photonic bandgap (PBG) structure. With the assistance of spontaneously generated coherence (SGC) from the two decay pathways, we can obtain single or double fully developed PBG when the trigger field is far away from resonance or resonant. While in the absence of SGC, the atomic medium becomes strong absorptive to the probe field, and therefore the resulting PBGs are severely malformed or even cannot be opened up. Numerical results show that the PBG structure is originated from the third-order cross Kerr nonlinear modulation between the probe and trigger fields. This mechanism differs from the recent schemes based on linear modulation.