Guided modes of circular multi-step index optical fibers
An online solver for the guided modes supported by circular dielectric optical fibers with radially piecewise constant refractive index profiles. Following the fiber definition in terms of (outer) core radius, refractive indices, and thicknesses of intermediate layers, if applicable, and the specification of a vacuum wavelength, the script calculates the effective mode indices and propagation constants of the vectorial, hybrid modes supported by the fiber. Facilities for detailed inspection of the mode profiles, and for exporting data and figures, are provided.
For a circular fiber with N intermediate layers, the input mask receives the vacuum wavelength λ, the radius R of the outer rim of the radial layer system, refractive index values ni (interior core region), n1, ... , nN (intermediate layers 1 to N), ne (exterior cladding region), and thicknesses t1, ... , tN of the intermediate layers. Select N=0 to specify a uniform circular dielectric core. All dimensions are meant in micrometers. The figure illustrates the relevant geometry:
Polar coordinates r, θ span the Cartesian x-y-plane; the center of the fiber cross section is located at the origin of both coordinate systems. The refractive index profile is independent of θ and piecewise constant in the radial direction r. All electromagnetic fields and the refractive index distribution are assumed to be constant along the z-axis (perpendicular to the x-y- and r-θ-plane, not shown).
The vectorial modal eigenproblem is independent of the azimuthal angle θ. In the formulation employed here, all modes are thus characterized by an integer angular mode order l, which corresponds to a θ-dependence ∼exp(-i l θ) of all electromagnetic field components. In certain contexts, this number l is called the topological charge of the vortex field associated with the orbital-angular-momentum (OAM) -modes. The solver accepts a range [lmin, lmax] of integer angular mode orders. Supply an interval [l, l] to calculate modes of specific order l only.