Publications

1994

• Guided Waves by Electromagnetic Gratings and Non-Uniqueness Examples for the Diffraction Problem
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Starling Felipe
  Mathematical Methods in the Applied Sciences, Wiley, 1994, 17 (5), pp.305-338. We consider the two-dimensional scalar problem of the diffraction of a plane wave by an infinite grating of conducting bodies immersed in a periodical dielectric medium. A Fredholm-type formulation is derived and studied. The existence of a solution is proved and some uniqueness results are established. A detailed description of the guided modes of the grating is carried out. Finally, various non-uniqueness examples for the diffraction problem are exhibited. (10.1002/mma.1670170502)
  DOI : 10.1002/mma.1670170502
• High frequency asymptotics of guided modes in optical fibres
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Djellouli Rabia
  IMA Journal of Applied Mathematics, Oxford University Press (OUP), 1994, 52 (3), pp.271-287. The high-frequency asymptotics of guided modes of dielectric waveguides is studied, firstly under the weak guidance assumptions which lead to a scalar problem, and then for Maxwell's system. The authors prove that the field tends to vanish everywhere the refractive index is not maximum. Moreover, for the vector model, it is proved that the field tends to become transverse. If the core of the guide is homogeneous, then the limit problem, which is an eigenvalue problem set inside the core, is derived. Various asymptotic estimates on the dispersion curves are established. (10.1093/imamat/52.3.271)
  DOI : 10.1093/imamat/52.3.271