Optical processes in different types of photonic band gap structures

• We reveal four wave mixing band gap signal based on the multi-wave mixing technology.
• The dressing detuning is scanned so that the quantum effect can be stood out.
• Positions of PBG structure are different with different scanning fields.
• The four wave mixing band gap signal can be modulated by multi-parameters.

For the first time, we investigate the photonic band gap (PBG) structure in the static and moving electromagnetically induced grating (EIG) through scanning the frequency detunings of the probe field, dressing field and coupling field. Especially, the suppression and enhancement of the four wave mixing band gap signal (FWM BGS) and the probe transmission signal (PTS) can be observed when we scan the dressing field frequency detuning in the FWM BGS system. It is worth noting that the PBG structure and FWM BGS appear at the right of the electromagnetically induced transparency (EIT) position in the case of scanning the frequency detuning of the coupling field in the FWM BGS system, while the PBG structure and FWM BGS appears at the left of the EIT position on the condition of scanning the probe field frequency detuning. Moreover, in the moving PBG structure, we can obtain the nonreciprocity of FWM BGS. Furthermore, we can modulate the intensity, width, location of the FWM BGS and PTS through changing the frequency detunings and intensities of the probe field, dressing field and coupling field, sample length and the frequency difference of coupling fields in EIG. Such scheme could have potential applications in optical diodes, amplifiers and quantum information processing.