A non-orthogonal coupled mode theory for super-modes inside multi-core fibers.

In this paper, a non-orthogonal coupled mode theory is proposed to analyze the super-modes of multi-core fibers (MCFs). The theory is valid in the strong coupling regime and can provide accurate analytical formulas for the super-modes inside MCFs. MCFs with circularly distributed cores are analyzed as an example. Analytical formulas are derived both for the refractive indexes and the eigen vectors of the super-modes. It is rigorously revealed that the eigen vectors for the super-modes of such MCFs are the row vectors of the inverse discrete Fourier transform (IDFT) matrix. Therefore, by pre-coding the signal channels via IDFT, one is able to generate the super-modes for the MCFs with circularly distributed cores.