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Electromagnetic Gaussian beams using Riemannian geometry
M. Dahl
Progress In Electromagnetics Research,
Vol. 60, pp. 265-291, 2006
[
.pdf,
bibtex]
Additional material
Below are various notes and some Mathematica toolbooks related to this paper.
- Existence and uniqueness theorem for complex Riccati equation (Proposition 3.2):
[ .pdf , .ps ,
.tex ]
- .. by a topological argument .. (p. 280):
[ .pdf , .ps ,
.tex ]
- All sign configurations can be achieved (Property (iv) in Lemma 4.2):
[ .nb ,
.ps ] Expressions for D (equations 24-27):
[ .nb ,
.ps ]
- Algebraic computations for Lemma 4.5:
An inequality for the square root :
[ .nb ,
.ps ]
Acknowledgements
This paper is based on my licentiate thesis, Propagation of Gaussian beams
using Riemann-Finsler geometry, 2006, instructed by doctor Kirsi Peltonen
and supervised by professor Erkki Somersalo.
The above notes are extracted from
this thesis.
This work has been funded by the
Graduate School Of Applied Electromagnetism
and the
Institute of Mathematics
at the
Helsinki University of Technology.
Contact
If you have questions or comments, please contact me
at matias.dahl
.
Last modified 27.3.2006 -- Matias Dahl
