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Seminar Mathematical Physics, 3 lectures on Optics

Summary: Seminar Mathematical Physics,
3 lectures on Optics
E van Groesen
Autumn 2000
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 weakly-nonlinear, 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[kx-t]
, 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[k0x-0t]
, k0 = K(0)


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering