Floquet group theory and its application to selection rules in harmonic generation

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Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.

Original languageEnglish
Article number405
JournalNature Communications
Issue number1
StatePublished - 24 Jan 2019

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Biochemistry,Genetics and Molecular Biology
  • General Physics and Astronomy


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