 
Summary: Seminar Mathematical Physics,
3 lectures on Optics
E van Groesen
Autumn 2000
Abstract
Lecture 1: Aspects of NLS, 28 Sept.
Lecture 2: Photonic Band Gaps
Lecture 3: Tunneling through Localised States
Lecture 1: 28 September
1 Lecture 1: Aspects of NLS
1.1 Appearance of NLS (Nonlinear Schrödinger equation)
in 1 space and time variable:
· in weaklynonlinear, dispersive, conservative wave equation for physical quantity (x, t); disper
sion given by D(k, ) = 0, with solution = (k), or k = K() for modes ei[kxt]
, and K
real and odd functions
· looking for slow, small deviations caused by nonlinearity of one monochromatic wave solution
(`mode'), described by complex amplitude A
A(x, t)ei[k0x0t]
, k0 = K(0)
