phy617 - Fourier Methods (Complete module description)

# phy617 - Fourier Methods (Complete module description)

 Module label Fourier Methods Modulkürzel phy617 Credit points 6.0 KP Workload 180 h (Attendance: 56hrs, Self Study: 124 hrs) Institute directory Institute of Physics Verwendbarkeit des Moduls Master's Programme Engineering Physics (Master) > Advanced Physics Zuständige Personen Teubner, Ulrich (module responsibility) Teubner, Ulrich (Prüfungsberechtigt) Silies, Martin (Prüfungsberechtigt) Prerequisites 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 Literaturempfehlungen 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. Links Language of instruction English Duration (semesters) 1 Semester Module frequency jährlich Module capacity unlimited Type of module Wahlpflicht / Elective Module level MM (Mastermodul / Master module) Teaching/Learning method lecture: 4 SWS Previous knowledge Basics of Optics and Laser Physics
Examination Prüfungszeiten Type of examination
Final exam of module
2 * 3 hours written or 2 * 30 minutes oral exams
 Form of instruction Lecture SWS 2 Frequency SoSe oder WiSe Workload Präsenzzeit 28 h