Supermodes of a double-ring fibre array with symmetric coupling

Abstract

We study the structure of supermodes of a double-ring array of identical evanescently coupled single-mode fibres with the same coupling constant, which describes interaction between the fibres. We obtain the expressions for normal modes of such an array and the spectrum of their propagation constants. We show that these supermodes are represented by symmetric and antisymmetric combinations of supermodes of a single-ring circular array.

Analytical Formulation of Supermodes in Multicore Fibers With Hexagonally Distributed Cores

“…[7]- [9], [20], [21]. This kind of core distribution is different from that in previous papers [24], [25], and the corresponding super-modes have not been analyzed.…”

“…3. The fiber parameters are set as: core diameter 5 um, gap size 1 um, cladding index 1.45, and relative index difference 1.2%, which are the same as previous papers [4], [21], [24]. In Fig.…”

“…They can be used to analyze behaviors of the super-modes fast and completely [4], [5]. Currently, quite a few analytical results for the super-modes of MCFs have been derived, including MCFs with linear aligned cores [22], circularly aligned cores within one ring [11], [23], two rings [24], and multi rings [25]. In [24] and [25], the adjacent rings are assumed to have the same number of cores, and each core in one ring is only coupled with one special core in the adjacent ring.…”

“…Currently, quite a few analytical results for the super-modes of MCFs have been derived, including MCFs with linear aligned cores [22], circularly aligned cores within one ring [11], [23], two rings [24], and multi rings [25]. In [24] and [25], the adjacent rings are assumed to have the same number of cores, and each core in one ring is only coupled with one special core in the adjacent ring. However, in practice, the cores of MCFs are generally distributed in a hexagonal pattern, since it is the densest two-dimensional distribution and suitable for dense MCF design, e.g., 7 cores, 19 cores, 37 cores, etc.…”

Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

“…(14), which at I → J tend to 1/ √ 2. The resulting modes are given by symmetric and antisymmetric combinations of single-ring modes [28], which propagate with phase velocities that differ by K/β. In this way the energy oscillates between the rings almost without spreading over them, which is clearly seen in Fig.…”