phy617 - Fourier Methods (Complete module description)

Physics with ultrashort pulses:

Students will get competences on the special aspects on ultrashort laser pulses which do not play a role in standard optics or laser physics. Starting from basics, the module yields advanced knowledge of the physics of femtosecond light pulses and their interaction with matter, as well as the physics of femtosecond lasers. The students will obtain skills to work with such lasers, in particular, on generation, handling, measurement, application of femtosecond pulses.

Fourier methods:

The course consists of two parts, both strongly related to Fourier physics:

1) Physics with ultrashort pulses:

Linear and non-linear optics of ultrashort pulses such as: amplitude, phase and spectral phase of the electric field, chirp, phase and group velocity, dispersion, group velocity dispersion, pulse compression, self focusing, self phase modulation, frequency conversion, multi photon effects; femtosecond laser pulse generation and amplification with various schemes, measurement of ultrashort pulses; applications

2) Fourier methods:

Motivation: Application of Fourier transformation within physics. Examples of Fourier pairs; properties of Fourier transformation; symmetries; important theorems; displacement, differentiation, convolution, uncertainty relation; examples to convolution theorem, frequency comb, Hilbert transformation, auto correlation function methods of time/frequency analysis, Wigner distribution; Fourier transformation in higher dimensions: tomography; discrete Fourier transformation, sampling theorem; applications

Physics with ultrashort pulses:

C. Rullière: Femtosecond Laser Pulses. Springer, Berlin,2004

J.-C. Diels, W. Rudolph: Ultrashort Laser Pulse Phenomena. Academic Press, Amsterdam, 2006

K. Jesse: Femtosekundenlaser. Springer, Berlin, 2005

A.M. Weiner: Ultrafast Optics, Wiley

Fouriertechniken in der Physik:

R. Bracewell: ”The Fourier Transform and its Applications“, McGraw-Hill, 3. Auflage (1999)

T. Butz: ”Fouriertransformation für Fußgänger“,Vieweg+Teubner, 7. Auflage (2011)

D. W. Kammler: ”A First Course in Fourier Analysis”,Cambridge University Press (2008)

M. Wollenhaupt, A. Assion and T. Baumert: “SpringerHandbook of Lasers and Optics”, Springer, Chapter 12, 2.Auflage (2012)

L. Cohen: ”Time Frequency Analysis“, Prentice Hall(1995)