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25.05.2022 13:08:17
phy617 - Fourier Methods (Complete module description)
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Module label Fourier Methods
Module code phy617
Credit points 6.0 KP
Workload 180 h
Attendance: 56hrs, Self Study: 124 hrs
Institute directory Institute of Physics
Applicability of the module
  • Master's Programme Engineering Physics (Master) > Advanced Physics
Responsible persons
Teubner, Ulrich (Module responsibility)
Teubner, Ulrich (Authorized examiners)
Skills to be acquired in this module

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 students acquire deeper knowledge on Fourier mathematics and ist applications within physics. They will learn related definitions, properties, theorems. Many examples will be presented. The students should be able to apply Fourier technology for physical and technical problems, in particular with relation of spatial and temporal domain to (spatial) frequency domain. They will get deepened insight on physical procedures by analysis within frequency domain.
Module contents

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

Reader's advisory

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)

Weitere spezielle Literatur wird in der Vorlesung bekannt gegeben.
Language of instruction English
Duration (semesters) 1 Semester
Module frequency jährlich
Module capacity unlimited
Modullevel / module level MM (Mastermodul / Master module)
Modulart / typ of module Wahlpflicht / Elective
Lehr-/Lernform / Teaching/Learning method lecture: 4 SWS
Vorkenntnisse / Previous knowledge Basics of Optics and Laser Physics
Examination Time of examination Type of examination
Final exam of module
2 * 3 hours written or 2 * 30 minutes oral exams
Course type Lecture
Frequency SuSe or WiSe
Workload attendance 28 h