Vorlesung MATHEMATICAL FOUNDATIONS OF NONLINEAR OPTICS
Mo 10-12, Do 14-16 ab 15. Mai 1998
Seminarraum I des Mathematischen Instituts
Übungen nach Vereinbarung
Seminar nach Vereinbarung
These lectures will deal with various aspects of the propagation of guided waves through a nonlinear dielectric. Most attention will be devoted to the case of a cylindrical optical fiber.
To motivate the subsequent discussion and give it an intuitive basis, the guidance problem will first be discussed from the point of view of geometrical optics using the eikonal equation for a medium with refractive index which varies with position.
The equations for guided waves in the electromagnetic theory will be derived from Maxwell's equations together with the constitutive assumption which is usually adopted, allowing for both inhomogeneity and anisotropy of the dielectric medium. The equations for TE and TM modes will be derived.
The mathematical analysis of the equations for guided TE and TM modes will be based on a variational approach in an appropriate function space. Constrained minimization and minimax methods will be used. Stability of the fundamental modes will be discussed.
References
T. Okoski : Optical Fibers, Academic Press, 1982
R.V. Akhmanov, R.V. Khokhlov and A.P. Sukhorukov : Self-focusing, self-defocusing and self-modulation of laser beams, in Laser Handbook, North-Holland 1972
C.A. Stuart : Magnetic field wave equations for TM-modes in nonlinear optical waveguides, in Reaction Diffusion Systems, Marcel Dekker, 1997
C.A. Stuart : Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rational Mech. Anal., 113 (1991), 65-96
Anmerkung:
Die Vorlesung steht im Zusammenhang mit Forschungsprojekten am Lehrstuhl Küpper zum Bereich „Nichtlineare Optik“ und ist geeignet zur Vorbereitung auf eine Mitarbeit dort in Form von Diplomarbeiten oder Dissertationen. Prof. Stuart wird am Dienstag, dem 10.2.98, um 15.30 Uhr im Hörsaal des Math. Instituts eine Einführung in diese Vorlesung geben.