טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAlon Ofir
SubjectSelection Rules for the High Harmonic Generation Spectra
by Dynamical Symmetry Analysis
DepartmentDepartment of Chemistry
Supervisor Professor Emeritus Nimrod Moiseyev


Abstract

A unified theory for obtaining the selection rules for the high-order harmonic generation spectra in various experimental setups is formulated by identifying the dynamical symmetries of the molecular and atomic targets inside laser fields. By doing so, we place dynamical symmetry analysis of harmonic generation processes on a foundation equally as firm as that possessed by symmetry analysis in spectroscopy.

For three-dimensional many-electron time-periodic Hamiltonians (T=2p/w) which are invariant under an N-th order dynamical symmetry we prove that only the (kN±R)-th  (k=1,2,3,…;0<R<N) high-order harmonics are generated. In fact, dynamically symmetric systems can be used not only as “filters” of the high-order harmonics, but also as their “amplifires”.

We show that the selection rules for the high-order harmonic generation spectra obtained under specific experimental conditions may break down when the dipole approximation is not applicable. This finding is important in view of the increasing effort in using the high-order harmonic generation from atoms as a source for coherent X-rays and sub-femtosecond pulses.

Using the theory of dynamical symmetry we find the selection rules for the harmonic generation sepctra by single-walled carbon nanotubes interacting with monochromatic circularly-polarized laser fields. Our results show that carbon nanotubes can be excellent candidates for a selective generation of soft X-ray radiation.

By analyzing the point-groups of the non-symmorphic rod-groups of single-walled carbon nanotubes we show for the first time that all single-walled achiral carbon nanotubes possess only 8 Raman-active and 3 infrared-active phonon modes. This is in contrast to previously predicted 15-16 and 6-7 active modes, respectively. On the same ground we show that all single-walled chiral carbon nanotubes possess 14 (instead of 15) Raman-active and 6 (instead of 9) infrared-active phonon modes.