Publications

2002

• 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
• L'identification à divulgation nulle de connaissance
  
  • Loidreau Pierre
  MISC - Le journal de la sécurité informatique, Lavoisier, 2002, 1.
• Le partage de secret
  
  • Loidreau Pierre
  MISC - Le journal de la sécurité informatique, Lavoisier, 2002, 3.
• Theoretical tools to solve the axisymmetric Maxwell equations
  
  • Assous Franck
  • Ciarlet Patrick
  • Labrunie Simon
  Mathematical Methods in the Applied Sciences, Wiley, 2002, 25 (1), pp.49-78. In this paper, the mathematical tools, which are required to solve the axisymmetric Maxwell equations, are presented. An in-depth study of the problems posed in the meridian half-plane, numerical algorithms, as well as numerical experiments, based on the implementation of the theory described hereafter, shall be presented in forthcoming papers. In the present paper, the attention is focused on the (orthogonal) splitting of the electromagnetic field in a regular part and a singular part, the former being in the Sobolev space H-1 component-wise. It is proven that the singular fields are related to singularities of Laplace-like operators, and, as a consequence, that the space of singular fields is finite dimensional. Copyright (C) 2002 John Wiley Sons, Ltd. (10.1002/mma.279)
  DOI : 10.1002/mma.279
• 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.