Modulation instability in collinear three-core optical fibers

Abstract

Modulation instability (MI) in a collinear three-core optical fiber, namely, an optical fiber that consists of three identical cores aligned symmetrically along a straight line, is analyzed in detail for the symmetric and antisymmetric continuous-wave (CW) states in the normal and anomalous dispersion regimes. The symmetric CW state, where the fields in the two side cores are identical, exists only with certain combinations of powers in the side cores and the center core within a limited range of total power, and these characteristics are governed by the linear coupling and the nonlinear coefficient of the fiber. The symmetric CW state generates MI characteristics not observed previously. In the anomalous dispersion regime, as the total power increases from a threshold value, three MI bands are generated and then merge rapidly into a single band, and the MI gain is insensitive to the linear coupling coefficient and the coupling-coefficient dispersion (CCD) of the fiber. In the normal dispersion regime, the generation of MI depends critically on the CCD. Two MI bands are generated from the CCD at a total power smaller than a critical value that depends on the linear coupling, the dispersion, and the nonlinear coefficient of the fiber. No MI can be generated without CCD. The antisymmetric CW state, where the fields in the two side cores have equal amplitudes of opposite signs and the field in the center core is zero, exists at any power. For this state, the MI characteristics are qualitatively similar to those of an equilateral three-core fiber. The study also includes direct numerical verification of the MI analysis with wave propagation simulation.