The geometry of the two-dimensional model of SMF-28e single-mode fiber section with scatterers is shown in Figure 1. The geometrical dimensions of the fiber were specified in the model according to the specification of the fiber under study: the fiber core (#1 in Fig. 1) has diameter dcore = 8.2 μm, while the fiber sheath (#2 in Fig. 1) has diameter dcladding = 125 μm. The length of the fiber section L = 200 µm is chosen for subsequent analysis of radiation propagation along the fiber before and after microcavities (#3 in Fig. 1).

The geometry of the microcavities is shown in Figure 2. The characteristic dimensions of the microcavities were set according to the real dimensions of the microcavities measured in the prototype scatterer [6]. Each of the microcavities is shaped like an elongated formation, given in the model by means of two parts: the tip and the body of the microcavity. The characteristic diameter of the microcavity "tip" is dm = 2.576 µm, the characteristic length of the microcavity "body" lm = 6.589 µm and the repetition period of this structure ld = 12.756 µm.

## Materials.

The refractive index dispersions for the model are taken from the reference book, for fiber cladding modelling data for fused silica is used "SiO2 (Silicon dioxide, Silica, Quartz) (Malitson 1965: Fused silica; n 0.21-6.7 µm)" [8], for microcavity modelling - data for "oxygen O2 (Oxygen, Zhang et al. 2008: n 0.4-1.8 µm)" is used [9]. The fiber core material is modelled as a material with a refractive index dispersion higher by 0.36% than for fused quartz (from SMF-28e fiber specification).

## System of equations.

To simulate the problem of scattering in a single-mode fiber, we used the problem formulation in terms of wave optics, Electromagnetic Waves, Frequency Domain unit in COMSOL Multiphysics. To solve the problem, a system of harmonic equations describing the propagation of a plane electromagnetic wave in matter was constructed. It has the following form:

" where ∇ is the Nabl operator, μr – is the relative magnetic permeability of the medium, k0 – is the wave number, εr – is the relative permittivity of the medium, j – is the imaginary unit, σ – is the conductivity of the medium, ω – is the frequency, ε0 – is the electric constant, E is the electric field strength, α – is the complex spreading constant, β - is the spreading constant, λ = jω + δ is the natural frequency of solution, δ is the damping factor. The vector of electric displacement is set in terms of refractive index, thus εr = (n – jk)2, σ = 0, μr = 1, where n - refractive index of medium, k - extinction coefficient of medium". [10].

## Boundary conditions.

At the vertical boundaries of the computational domain Port-type conditions were put. The left boundary is declared to be the input port with radiation power of 1 W, the right one - the output port. The port type is numerical, so the electric field distribution at the model boundary is given on the basis of propagation constant β, which value is a numerical solution of the system of equations

for each port for the case of the fundamental mode of radiation propagating along the investigated fiber (here n is the normal vector).

Additional absorption layers (Perfect Matching Layer - PML) of thickness tPML = 1.5 µm have been added on all outer geometric boundaries of the model to avoid re-reflections inside the model.

Thus, the model is considered as a section of an infinitely long optical fiber with micro-cavities filled with oxygen inside the core.

## Mesh.

In order to obtain realistic results in the calculation of the wave equations, a model mesh of at least 5 elements per wavelength λ0_min = 1.54 μm in vacuum in the medium of the fiber core was constructed. Thus, the maximum linear size of one element was emin = λ0_min/ncore(λ0_min)/5 ≈ 0.2 µm.

Inside the microcavities and in the boundary layer around them, the linear size of one element was set to emin = 0.1 μm for better resolution. The selected area of the model mesh around the microcavity is shown in figure 4.

The total number of grid elements was approximately 2∙106.

## Parametrization of the solution.

In the investigated wavelength range λ0 = 1540-1560 nm, with a step Δλ = 0.5 nm, for each value of λ0, the boundary problem of determining the fundamental mode propagation constant for the investigated waveguide (Boundary Mode Analysis) for each port was solved. The solution was found in the region of the effective refractive index value neff, which was taken as a linear approximation of the refractive index value for the value λ0 between the values n(λ0_min) и n(λ0_max). Using the obtained value of the propagation constant, the electric field strength at each node of the model was calculated. These operations were repeated for all wavelengths between λ0 = 1540-1560 nm