Analytical Formulation of Supermodes in Multicore Fibers With Hexagonally Distributed Cores

Abstract

The supermodes in 19-core multicore fibers (MCFs) with identical hexagonally distributed cores are analyzed in detail by using the coupled mode theory and matrix operation. The analytical formulations for both the propagation constants and modal distribution vectors of the supermodes are derived. Simulation results show that the analytical results agree well with the numerical results. In addition, the features of the effective indices and modal distributions of the supermodes are discussed by using the analytical expressions combined with the applications. The analytical expressions provide a fast and accurate method to reveal the properties and characteristics of the supermodes for MCFs and are helpful for the design and applications of MCFs.

Coupled two-core integrated waveguides modal analysis

“…where ℱ denotes Fourier transform, 𝑖 = √−1, 𝜆 is the input light wavelength, 𝑓 is the L3 lens focal distance and the coordinates at the focal plane (𝑢, 𝑣) are related to the Fourier transform frequency space coordinates 𝑓 𝑥 and 𝑓 𝑦 by means of 𝑢 = 𝜆𝑓𝑓 𝑥 , 𝑣 = 𝜆𝑓𝑓 𝑦 . When the isolated cores of the multicore structure are single mode, the multicore waveguide has the same number of supermodes than cores [24]. Thus, the transverse optical field at the two-core waveguide output end can be expressed as 𝑈(𝜂, 𝜉) = 𝑐 𝑠 𝜑 𝑠 (𝜂, 𝜉) + 𝑐 𝑎 𝜑 𝑎 (𝜂, 𝜉), (2) being (𝜂, 𝜉) the spatial coordinates at the waveguide output end, 𝜑 𝑚 the symmetric (m=s) and antisymmetric (m=a) supermodes, and 𝑐 𝑚 = 𝜌 𝑚 𝑒 𝑖𝜃 𝑚 their complex expansion coefficients with amplitude 𝜌 𝑚 and phase 𝜃 𝑚 .…”

Mode-division and spatial-division optical fiber sensors

“…In a certain region of such a coupler, two single-mode cores can be close to each other and share the same cladding. In fact, the analysis of fused-fiber couplers was done in terms of supermode beating [127][128][129]. MCFs with strongly coupled cores embedded in a common cladding were demonstrated experimentally in 2014 for high-temperature sensing [130].…”

Optimized active multicore fiber bending sensor

“…In waveguiding structures with multiple cores, the eigenmodes of the structure, so called supermodes, can be perceived combination of the individual modes of the single core waveguides. Supermodes are useful in order to understand the MCF properties [4], and have been directly utilized in optical communication systems [5]. The supermodes of the structures can be computed either through analytical methods or by numerical simulations [6].…”