We present an analytical study of modulation instability (MI) in metamaterial (MM) with first-order and second-order nonlinear dispersion for three types of saturable nonlinearity. Apart from the conventional MI gain spectrum, we find two additional MI gain spectra that arise from the second-order nonlinear dispersion in the MM (provided that the group-velocity dispersion does not vanish): one showing a low cutoff frequency but no high cutoff frequency and the other showing no cutoff frequency. Under certain conditions, a threshold power may be required for MI to occur. These MI gain spectra rarely exist in conventional materials and suggest the possibility of observing MI at arbitrarily high perturbation frequencies, which could be explored for the generation of high-repetition-rate ultrashort electromagnetic pulse trains.
© 2014 Optical Society of America
Original Manuscript: January 2, 2014
Revised Manuscript: April 9, 2014
Manuscript Accepted: May 5, 2014
Published: June 5, 2014
Xianqiong Zhong, Ke Cheng, and Kin Seng Chiang, "Modulation instability with arbitrarily high perturbation frequencies in metamaterials with nonlinear dispersion and saturable nonlinearity," J. Opt. Soc. Am. B 31, 1484-1493 (2014)