Publications

2002

• L'identification à divulgation nulle de connaissance
  
  • Loidreau Pierre
  MISC - Le journal de la sécurité informatique, Lavoisier, 2002, 1.
• Derivation of semiconductor laser mean-field and Swift-Hohenberg equations
  
  • Mercier Jean-François
  • Moloney Jerome
  Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], American Physical Society, 2002, 66, pp.036221. Bulk and quantum well semiconductor lasers by nature display fundamentally different physical characteristics relative to multilevel gas and solid state lasers. In particular, the refractive index is nonzero at peak gain and the peak gain can shift strongly with varying carrier density or temperature. Moreover, a quantum well laser gain may be strongly asymmetric if more than the lowest subband is populated. Rigorously computed and experimentally validated, gain and refractive index spectra are now available for a variety of quantum well structures emitting from the infrared to the visible. Active devices can be designed and grown such that the gain spectrum remains approximately parabolic for carrier density variations typically encountered in above threshold pumped broad area edge-emitting semiconductor lasers. Under this assumption, we derive a robust optical propagation model that tracks the important peak gain shifts and broadening as long as the gain remains approximately parabolic over the relevant energy range in a running laser. We next derive a multimode model where the longitudinal modes are projected out of the total field. The next stage is to derive a mean-field single longitudinal mode model for a wide aperture semiconductor laser. The mean-field model allows for significant cavity losses and widely different facet reflectivities such as occurs with antireflection- and high-reflectivity-coated facets. The single mode mean-field model is further reduced using an asymptotic expansion of the relevant physical fields with respect to a small parameter. The end result is a complex semiconductor Swift-Hohenberg description of a single longitudinal mode wide aperture laser. The latter should provide a useful model for studying scientifically and technologically important lasers such as vertical cavity surface emitting semiconductor lasers. (10.1103/PhysRevE.66.036221)
  DOI : 10.1103/PhysRevE.66.036221
• A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems
  
  • Henry Jacques
  • Ramos Angel M.
  , 2002. In this report we come back to the method of factorization of a second order elliptic boundary value problem presented in . In this paper, it was shown that, in the case of a cylinder, the boundary value problem can be factorized in two uncoupled first order initial value problems. This factorization utilizes the Dirichlet to Neumann operator which satisfies a Riccati equation. Here we consider Hilbert-Schmidt operators, a framework already used by R. Temam which provides tools for a direct study of this Riccati equation.
• A singular field method for Maxwell's equations: numerical aspects for 2D magnetostatics
  
  • Hazard Christophe
  • Lohrengel Stéphanie
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2002, 40 (3), pp.1021--1040. The present paper deals with the solution of Maxwell-type problems by means of nodal H1-conforming finite elements. In a nonconvex piecewise regular domain surrounded by a perfect conductor, such a discretization cannot in general approximate the singular behavior of the electromagnetic field near "reentrant" corners or edges. The singular field method consists of adding to the finite element discretization space some particular fields which take into account the singular behavior. The latter are deduced from the singular functions associated with the scalar Laplace operator.The theoretical justification of this approach as well as the analysis of the convergence of the approximation are presented for a very simple model problem arising from magnetostatics in a translation invariant setting, but the study can be easily extended to numerous Maxwell-type problems. The numerical implementation of both variants is studied for a domain containing a single reentrant corner. (10.1137/S0036142900375761)
  DOI : 10.1137/S0036142900375761
• Measures of Sub-Riemannian Paths
  
  • Jean Frédéric
  • Falbel Elisha
  , 2002.