Nonlinear refractive index in erbium-doped optical amplifiers

Nonlinear effects in erbium-doped fibre amplifiers are analysed by a numerical approach based on the combined use of the finite element method and the Runge-Kutta algorithm. In particular, the variation of the refractive index due to the perturbation in the gain coefficient is evaluated through the nonlinear Kramers-Kronig relations. For the first time the nonlinear coefficients of the polynomial expansion of the refractive index variation have been calculated. Several kinds of perturbation, produced by signal and pump intensity, by amplifier length and by dopant concentration have been considered to investigate the refractive index change behaviour. The use of the finite element method allows the local evaluation of the pump and signal intensities without introducing any simplifying hypothesis on the electromagnetic field distribution.     

Complex FEM modal solver of optical waveguides with PML boundary conditions

A full-wave modal analysis of two-dimensional, lossy and anisotropic optical waveguides using the finite element method (FEM) is presented. In order to describe the behavior of radiating fields, anisotropic perfectly matched layer boundary conditions are applied for the first time in modal solvers. The approach has been implemented using high order edge elements. The resulting sparse eigenvalue algebraic problem is solved through the Arnoldi method. Application to an antiresonant reflecting optical waveguide is reported.     

Impact of the cell geometry on the spectral properties of photonic crystal structures

Photonic-crystal-based devices are expected to perform many of the functionalities of standard integrated optics devices used in optical communication systems. Their reliability and the reliability of fabrication technologies in achieving acceptable geometrical tolerance are still to be demonstrated. In this work an analysis of the effects of the cell geometry is presented, showing how small variations can cause hundreds of GHz shifts in the spectral response. A wide-band, finite-element time-domain approach and a frequency-domain formulation have been used for this kind of analysis. The ability of the finite-element method in coping with any kind of geometry has been successfully exploited to investigate the effect of the cell shape. Received: 16 May 2001 / Revised version: 8 August 2001 / Published online: 30 October 2001     

Active nonlinear integrated optical devices: a numerical analysis

A finite element beam propagation method to analyze nonlinear active optical waveguides is presented. The model takes into account the mutual coupling among the equations describing the electromagnetic field propagation and the ones governing the signal amplification due to a doped medium. The approach is able to distinguish the different behavior of E^x (quasi-TE) and E^y (quasi-TM) polarizations. The performances of nonlinear and doped couplers are analyzed in detail by varying the input power, the field polarization and the pumping scheme.     

Overview on finite-element time-domain approaches for optical propagation analysis

Several finite-element based time-domain approaches for the analysis of photonic devices are discussed in details. Narrowband and different kinds of wideband formulations are derived highlighting strengths and weaknesses related to the initial analytical equation and to the numerical implementation through the finite element method. A formulation which directly implements the unknown field without separating the envelope and the fast varying carrier is also presented. Performances and limits of the various algorithms are discussed by analyzing the simple and clear case of time and space evolution of gaussian beams propagating in a homogeneous medium. Comparison of the modules and arguments of the spectral response is also provided.