A dedicated 3D numerical model based on coupled mode theory and solving the rate equations has been developed to analyse, design and optimize an optical amplifier obtained by using a tapered fiber and a Er³⁺-doped chalcogenide microsphere. The simulation model takes into account the main transitions among the erbium energy levels, the amplified spontaneous emission and the most important secondary transitions pertaining to the ion-ion interactions. The taper angle of the optical fiber and the fiber-microsphere gap have been designed to efficiently inject into the microsphere both the pump and the signal beams and to improve their spatial overlapping with the rare earth doped region. In order to reduce the computational time, a detailed investigation of the amplifier performance has been carried out by changing the number of sectors in which the doped area is partitioned. The simulation results highlight that this scheme could be useful to develop high efficiency and compact mid-infrared amplifiers.

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A novel finite-difference time-domain algorithm for modeling ultra-wideband electromagnetic pulse propagation in arbitrary multi-relaxed dispersive media is presented. The proposed scheme is based on a general, yet computationally efficient, series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material. Dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time-marching scheme. Moreover, a total field/scattered field formulation is adopted in order to analyze the material response under plane-wave excitation. Compared to alternative numerical methodologies available in the scientific literature, the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher-order dispersive dielectrics, such as the ones typically encountered in geoscience and bio-engineering applications.