Modulation instability in a triangular three-core coupler with a negative-index material channel

Abstract

A theoretical investigation of the modulation instability (MI) in the three core triangular oppositely directed coupler with negative index material channel is presented. This class of couplers have an effective feedback mechanism due to the opposite directionality of the phase velocities in the negative and positive index channels. It is found that the MI in the nonlinear three core triangular oppositely directed coupler is significantly influenced by the ratio of the forward- to backward-propagating wave power and nonlinearity. Also, in the case of the normal dispersion regime a threshold-like behavior is observed, whereas this behavior is not identified in the anomalous dispersion regime. For the asymmetric case ( ), two pairs of instability bands are observed for both the nonlinear NIM and PIM channels, while a single pair of instability bands is noted for the symmetric case (h = 1). In the normal dispersion regime, the defocusing nonlinearity is found to suppress the MI by reducing both the gain and width of the instability band, whereas the MI is enhanced in the anomalous dispersion regime due to the defocusing nonlinearity. Thus we report new ways to generate and manipulate the MI and solitons in three-core triangular oppositely directed couplers with a particular emphasis on a negative-index material (NIM) channel.

Saturable higher nonlinearity effects on the modulational instabilities in three-core triangular configuration couplers

“…Figure 4 shows the effect of the frequency of light Ω propagating in the coupler on the instability for different input powers P. When we increase the peak power, the MI gain also increases. This feature was also observed previously in the absence of saturable nonlinearity [10,37].…”

“…The difference is that, in the case of the latter, we have to consider the sign of l also. MI in the normal dispersion regime occurs when f and l are positive [36][37][38]. In principle, the normal dispersion regime does not exhibit MI due to the lack of phase matching between the linear and nonlinear components.…”

“…MI in the presence of higher-order dispersion effects [40], the existence of MI due to the cross-phase modulation [41,42], MI in the non-instantaneous nonlinear system, and instability bands in the case of directional couplers are some examples of MI in this regime. In the anomalous dispersion regime, MI occurs when f and l are negative [36][37][38]. The anomalous dispersion regime is suitable to achieve MI and solitons because of the good balance between the nonlinearity and the negative group dispersion coefficient.…”

“…As far as three-core coupler optical couplers are concerned, there are only a few investigations reported, and the topic is of interest because of its tunable nonlinear properties and quick power switching [30][31][32][33][34][35]. Recent theoretical investigations can be found in [36][37][38]. Recently, there have been experimental findings [39][40][41][42] of MI in optical fibers that agree with theoretical and numerical computations, which creates further interest in theoretical investigations.…”

Effects of saturable function in three-core PIM-NIM-PIM coupler through modulation instability

“…Such couplers improved transmission characteristics that why they attracted much attention. Sharper power switching curves are well offer by three core couplers than conventional two-core coupler and for that raison three core couplers are really significant [24][25][26]. Many physical systems present nonlinear saturation that may influence them.…”