FDTD analysis of modal dispersive properties of nonlinear photonic crystal fibers

Abstract

This paper presents a full-wave electromagnetic analysis of soft-glass photonic crystal fibers developed for the generation of supercontinuum based on third-order nonlinearity. It is shown that a two-dimensional finite-difference time-domain method for guided problems provides results very similar to the measurement data of real fiber structures, enabling the reduction of costly hardware prototyping, thus, opening the way for the application of FDTD to the modeling of nonlinear optical processes.

Computationally-efficient FDTD modeling of supercontinuum generation in photonic crystal fibers

“…The real part of the refractive index of glass contained in the PCFs is usually represented with a Sellmeier equation, which has to be transformed into a Lorentz model with its representation in the FDTD method (Karpisz et al 2014) given as:…”

“…If the transverse field distribution (mode) does not have its analytical representation, unlike homogeneously filled rectangular or circular metallic waveguides (Collin 1990), it has to be computed with the aid of a rigorous (full-wave) numerical technique, such as a finite element method (FEM) or FDTD. Consequently, the analysis reduced to the crosssection of a waveguide's structure allows evaluating properties of the considered mode such as effective refractive index, group velocity dispersion, effective mode area, or confinement loss (Karpisz et al 2014).…”

Electromagnetic Modeling of Third-Order Nonlinearities in Photonic Crystal Fibers Using a Vector Two-Dimensional FDTD Algorithm

“…Assume now that the material is dispersive and described with a Lorentz model [10]. As a result, the Ampere's law, applied to derive (4), takes the following form:…”

“…The solitons are excited in phase, out of phase, and in quadrature to observe well-known phase-induced differences in their mutual interaction. Material properties are as follows [10]: ε ∞ = 1.0, ε s1 = 1.6962, A 1 = 1.0, A 2 = 0.586, A 3 = 1.2891, ω a1 = 2π × 4.3827 × 10 15 rad/s, ω a2 = 2π × 2.5791 × 10 15 rad/s, ω a3 = 2π × 30.294 × 10 12 rad/s, Δω a1 = 2π × 10 11 s −1 , Δω a2 = 2π × 10 11 s −1 , Δω a3 = 2π × 10 9 s −1 , χ The size of the 2D model is 50 μm × 20 μm and is discretized with a 10 nm cell size. In each case, the whole simulation undertaken on Intel Core i7 CPU 950 takes about 3.4 h with the speed of 1.2 FDTD iterations per second.…”

“…Measured dispersive and nonlinear properties of those materials are available in [29]. Both glasses are represented in FDTD with a triple-pole Lorentz model [10], supplemented with the third-order nonlinearity discussed in Section II (see Table II). Lorentz parameters are derived from measured Sellmeier coefficients [10], which account for the real part of the refractive index only.…”