Modulation instability in positive refractive metamaterials with higher-order dispersion and saturable nonlinearity

After taking the higher-order dispersion and three kinds of saturable nonlinearities into account,we investigate the characteristics of modulation instability(MI)in real units in the positive refractive region of metamaterials(MMs).The results show that the gain spectra of MI consist of two spectral regions,one of which is close to and the other is far from the zero point.In particular,the spectral region far from the zero point also has high cut-off frequency but narrow spectral width just as those revealed in the negative refractive region.Moreover,the gain spectra can change with the normalized angular frequency,the normalized optical power and the form of the saturable nonlinearity.Concretely,the spectral width increases with increase of the normalized angular frequency.But both of the spectral width and the peak gain increase and then decrease with increase of the normalized optical power.In other words,the MI characteristics and MI related applications can be controlled by adjusting the structure of the MMs,the form of the saturable nonlinearity and the normalized optical power.