Modulation instabilities in equilateral three-core optical fibers

Modulation instabilities (MIs) of the continuous-wave (CW) states in equilateral three-core fibers are analyzed in detail. For the equilateral-triangle symmetric CW state where the fields in the three cores are identical, conventional MI characteristics similar to those of two-core fibers are obtained. For the antisymmetric CW state where the fields in two of the three cores have equal amplitudes of opposite signs and in the third core it is zero, new MI characteristics are found. In the normal dispersion regime, there are in general two MI bands, one of which is generated above a critical total power and quickly becomes the dominant band as the total power increases. This critical power is insensitive to the group-velocity dispersion, increases (decreases) with the coupling coefficient (the nonlinear coefficient) almost linearly, and decreases rapidly to almost zero as the coupling-coefficient dispersion (CCD) increases. In the anomalous dispersion regime, there are two significant MI bands, which are governed by two separate dispersion relations. The lower-frequency band, which is similar to the MI band of a single-core fiber, is not affected by the coupling coefficient and the CCD, while the higher-frequency band is sensitive to these two parameters. The lower-frequency band always has a higher gain than the higher-frequency band, which converges to the lower-frequency band as the coupling coefficient and the CCD approach zero. For the isosceles-triangle symmetric CW state where the fields in two of the three cores are equal, the MI characteristics are qualitatively similar to those of the asymmetric state of two-core fibers. Simulation results based on solving the nonlinear coupled-wave equations agree well with the MI analysis.