Analysis of modal coupling due to birefringence and ellipticity in strongly guiding ring-core OAM fibers

Abstract

After briefly recalling the issue of OAM mode purity in strongly-guiding ring-core fibers, this paper provides a methodology to calculate the coupling strength between OAM mode groups due to fiber perturbations. The cases of stress birefringence and core ellipticity are theoretically and numerically investigated. It is found that both perturbations produce the same coupling pattern among mode groups, although with different intensities. The consequence is that birefringence causes the highest modal crosstalk because it strongly couples groups with a lower propagation-constant mismatch. The power coupling to parasitic TE and TM modes is also quantified for both perturbations and is found to be non-negligible. Approximate modal crosstalk formulas valid for weakly-guiding multi-core fibers, but whose parameters are adapted to the present case of strongly guiding OAM fibers, are found to provide a reasonable fit to numerical results. Finally, the effect that modal coupling has on OAM transmission is assessed in terms of SNR penalty.

Analytic Expressions for Orbital Angular Momentum Modal Crosstalk in a Slightly Elliptical Fiber

“…Inserting Eq. 2 and integrating over the azimuthal part, we immediately see that the δ H matrix elements are symmetric (δ H (l,m)(n,k) = δ H (n,k)(l,m) ), and nonzero only when |n − l| = 2, a selection rule also pointed out in [7]. Invoking this selection rule, we obtain simplified forms…”

“…An analytic treatment of the effect of ellipticity on OAM modes was earlier provided [2], but it was limited to a low topological charge l, primarily l = 1 or 2 (l is the OAM carried by a single photon in units of the reduced Planck's constant (h/(2π)); besides, the methodology as presented could not incorporate mode mixing with the neighboring OAM modes differing in topological charges by a unit or more. More recently, several authors have carried out numerical studies of the impact of ellipticity on OAM modes in a variety of fibers: ring fiber [3,5,7], multi-ring fiber with trench [4], and a graded-index fiber [6] but the studies are based on computationally-intensive finite-element approximation methods, where it is not always easy to ascertain the inherent behavior of the impact of a perturbation like ellipticity in any detailed manner due to the associated high demands of accuracy.…”

Quantifying the Coupling and Degeneracy of OAM Modes in High-Index-Contrast Ring Core Fiber

“…In our notation (+) 4AA indicates OAM with topological charge of +4 and left circular polarization, or OAM − +4,1 . For fibers with high index contrast, the solution of the waveguide characteristic equation will result in impure eigenmodes [11], [16]. The transverse components of the fiber OAM modes, with respect to cylindrical coordinates (r, ϕ), can be written as…”

“…A gap currently exists between the predictions made from OAM numerical propagation models and observations made both experimentally and analytically. Current numerical propagation models fail to predict and quantify the coupling varying from low to high order [11]. The models also assume complete coupling within degenerate A(AA) mode pairs, whereas this coupling was overcome in the MIMO-free experimental reception of these mode pairs [8].…”

“…This birefringence was recognized in [14], [15] to decrease gradually with mode order, but the effect on coupling was not examined. In [11] the coupling coefficients were calculated, but assuming zero birefringence between the even and odd fiber eigenmodes.…”