Modulation instabilities in equilateral three-core optical fibers for isosceles-triangle symmetric continuous waves

Abstract

Modulation instability (MI) of the isosceles-triangle symmetric continuous wave in equilateral three-core fibers (ETCFs) is studied in detail. The so-called isosceles-triangle symmetric continuous wave state is the planar wave where the fields in its two cores are identical but different from the field in the third core, and the premise of its existence is that the total power (P) exceeds a minimum value (Pmin) that depends on the linear coupling coefficient and nonlinear coefficient of ETCFs. For a given total power P (P ≥ qslant Pmin), set the power in one core to be P1, and the powers in the other two cores to be P2 (P=P1 + 2P2), then two kinds of filed distributions will be found. The first kind is for P1 > P2 with P1 becoming more and more large as total power P increases. By the linear stability analysis method, the main characteristics of MI in ETCFs are found which are quite similar to those of the asymmetric continuous wave states in two core optical fibers (TCFs). The other kind is that P1 becomes more and more small and P2 becomes more and more large as total power P increases. Through the same method, the main characteristics of MI in ETCFs are found which are distinctively different from those of the asymmetric continuous wave states in TCFs. On the one hand, MI can be generated in both normal and anomalous dispersion regimes without perturbations. In addition, the zero-perturbation frequency corresponds to the largest gain of MI in the normal dispersion regime. On the other hand, the coupling coefficient dispersion, which can dramatically modify the spectra of MI in TCFs, plays a minor role in both normal and anomalous dispersion regimes in ETCFs. In practical application, the findings in this paper are of guiding significance for studying the nonlinear effects of mode-division multiplexing system based on the multimode or multicore optical fibers.