M. Zoboli

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.

Leakage properties of photonic crystal fibers

An analysis of the con.nement losses in photonic crystal fibers due to the finite numbers of air holes is performed by means of the finite element method. The high flexibility of the numerical method allows us to consider fibers with regular lattices, like the triangular and the honeycomb ones, and circular holes, but also fibers with more complicated cross sections like the cobweb fiber. Numerical results show that by increasing the number of air hole rings the attenuation constant decreases. This dependence is very strong for triangular and cobweb fibers, whereas it is very weak for the honeycomb one.

Amplification properties of Er/sup 3+/-doped photonic crystal fibers

The amplification properties of different photonic crystal fibers have been studied by means of a full vector finite-element modal formulation combined with a population and propagation rate equation solver. A honeycomb as well as a cobweb photonic crystal fiber have been considered. The consequences of the defect dimension and the dopant radius on the field intensity distribution as well as the overlap integrals have been analyzed. Results demonstrate that a proper photonic crystal fiber design can be usefully exploited in order to obtain active fibers with superior characteristics compared to standard step index ones. In particular, photonic crystal fibers open up the possibility of a gain medium with highly flexible geometric, dispersion, and amplifying characteristics.

Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method

Perturbations to the ideal cross section of photonic crystal fibers (PCFs) are introduced in order to investigate their performance as a function of the structural fluctuations which may occur during fabrication. The effects of the cross-section geometry perturbations on dispersion characteristics like dispersion parameter and differential group delay are presented and discussed. The analysis has been performed through the finite element method which assures high flexibility and high solution accuracy.

Finite-element full-vectorial propagation analysis for three-dimensional z-varying optical waveguides

A finite-element-based full-vectorial beam propagation method (BPM) for the analysis of the electromagnetic field evolution in three-dimensional (3-D) dielectric waveguides is presented. The approach has been derived in order to be suitable for the numerical discretization through finite elements and to fully account for the vectorial nature of the electromagnetic field. To this aim the problem related to the permittivity derivative at dielectric interface has been addressed and overcome. The advantages and the potentialities of the finite elements usage are discussed. The precision and the correctness of the proposed approach is demonstrated through numerical examples. Typical integrated optics structures, as a tapered waveguide and a Y-junction, are analyzed to assess the applicability of the method.

Performance comparison of finite-element approaches for electromagnetic waveguides

The accuracy of finite-element-method techniques used for waveguide modal analysis has usually been assessed by testing the precision of the propagation constant. As a consequence, no useful criteria have been proposed for checking the spatial distribution of the evaluated unknown field. To overcome this lack, two error figures have been introduced and applied to different finite-element-method formulations. In particular, the following approaches have been compared: the one based on the transverse magnetic field, those based on the so-called edge elements, and a new one presented by the authors. The new approach, obtained by simply operating on the matrices of the original node-based formulation, directly solves for the propagation constant at a given frequency, preserves the matrix sparsity, and directly evaluates all of the unknown magnetic field components. Results demonstrate the applicability of the proposed approach and the usefulness of the introduced figures for a deep waveguide analysis.

Full-vector finite-element beam propagation method for anisotropic optical device analysis

A finite-element full-vectorial beam-propagation method is presented, for the first time, for the analysis of 3-D anisotropic optical waveguides. Full 3/spl times/3 permittivity and permeability tensors are considered. The formulation takes into account the polarization dependence and the component coupling due to the waveguide geometry and the medium anisotropy without any analytical approximations. The perfectly matched anisotropic absorber is introduced to eliminate the influence of the computational border on the numerical solutions. The correctness of the proposed approach is verified by analyzing several kinds of anisotropies. For the first time, a full vectorial finite-element propagation analysis is presented for diffuse waveguides and magnetooptic devices.

Numerical and experimental analysis of erbium-doped fiber linear cavity lasers

A numerical and experimental analysis of an erbium-doped linear cavity laser is presented. In particular a numerical model for the laser continuous wave and multiwavelength operation has been developed. In the proposed approach, according to the spectral model, the propagation rate equations have been used to predict the evolution of forward and backward signals and amplified spontaneous emission in the doped waveguide and properly boundary conditions have been imposed to describe the resonant etalon. The performances of the erbium-doped linear cavity laser are investigated in detail and the best parameters to optimize the laser design as, for example, the mirror or grating reflectivities, the cavity length and the pump power are investigated. Comparisons with experimental data confirm the validity of the approach. Numerical results point out the model usefulness for device design.

Three-dimensional finite-element beam propagation method: assessments and developments

In recent years the finite-element method (FEM) has been widely applied to three-dimensional beam propagation analysis, and several FEM propagators have been presented. Up to now, as far as we know, an exhaustive, deep, and comparative analysis of these formulations and of the related algorithms has never been presented. We critically analyze and numerically compare, to our knowledge for the first time, different vectorial, semivectorial, and scalar formulations in order to check their performances, point out weaknesses, and suggest future developments. The results obtained highlight once more the inadequacy of scalar approaches in dealing with actual photonics devices and suggest vector formulations worthy of further development and future research.

Modeling of erbium doped fiber ring laser

Abstract A numerical model for the analysis of the continuous wave operation of an erbium doped fiber ring laser is presented. The model has been obtained by developing the so called spectral one already presented for the analysis of erbium doped fiber amplifiers (EDFA). In particular the approach has been modified to account for the cyclical propagation of the field in the ring laser. The effects of multi-wavelength signals propagating within the laser cavity have been analyzed both in linear and in saturated gain regime. Numerical simulations provide interesting information on the spectral behavior as well as important parameters for device analysis and design as, for example, the lasing wavelength and the output power. Comparisons with experimental data confirm the validity of the approach and the correctness of the numerical solutions.