Modulated photonic band gaps generated by high-order wave mixing

For the first time, to the best of our knowledge, we investigate the photonic band gap (PBG) structure through scanning the frequency detunings of the probe field, the dressing field, and the coupling field in the static and moving electromagnetically induced grating (EIG) field. When we scan the frequency detuning of the coupling field, the PBG structure and six-wave-mixing band gap signal (SWM BGS) appear at the right of the electromagnetically induced transparency (EIT) position. But the PBG structure and SWM BGS appear at the left of the EIT position in the case of scanning the probe field frequency detuning. Also, on the condition of scanning the probe field frequency detuning, the SWM BGS appears in two frequency ranges. Moreover, in the moving PBG structure, nonreciprocity of the SWM BGS can be obtained. Furthermore, the intensity, width, and location of the SWM BGS can be modulated through changing the frequency detunings and intensities of the probe field, the dressing field, and the coupling field; the sample length; and the frequency difference of coupling fields in EIG. Such a scheme could have potential applications in optical diodes, amplifiers, and quantum information processing.