Selection rules and dynamical symmetry breaking spectroscopy in (high) harmonic generation


In the early days of nonlinear optics (NLO), symmetries were used to derive a set of rules for nonlinear photonic processes according to the medium’s symmetries that are reflected in the NLO coefficient tensor [1]. While this approach was believed to be complete and closed, the field of symmetries and selection rules in NLO has recently reignited as multi-color ultrashort laser pulses with tailored polarization and spatiotemporal structures become standard drivers of NLO processes.  We develop a more complete theory which incorporates all possible dynamical degrees of freedom of light: spin and orbital angular momentum, spatial structure, time-dependent polarization, temporal envelope, etc., in addition to the symmetries of the medium [2,3]. This formalism already resulted with many new selection rules in nonlinear optics [2-5], schemes for very efficient chiral discrimination based on only electric dipole interaction [6-8], definition of a new symmetry-based measure for light’s chirality (analogous to the molecular definition) [9,10], and all-optical method for diagnostics of ultrafast ring currents, e.g. in gas of atoms and molecules [11].

We also discovered that a symmetry breaking imposes selection rules on the symmetry-broken system, which manifest as scaling laws of selection rule deviations. We term these rules ‘selection rules for breaking selection rules’ [12] and showed that they can be derived from symmetries in real and synthetic dimensions of the symmetry-broken system [13].

  1. Nonlinear optics, Boyd, Elsevier; 2003
  2. O. Neufeld, D. Podolsky and O. CohenFloquet group theory and its application to selection rules in harmonic generationNat. Commun., 10, 405 (2019)
  3. G. Lerner, O. Neufeld, L. Hareli, G. Shoulga, E. Bordo, A. Fleischer, D. Podolsky, A. Bahabad and O. Cohen, Multi-scale dynamical symmetries and selection rules in nonlinear optics, Science Advances, 9, eade0953 (2023)
  4. O. NeufeldE.BordoA. Fleischer and O. CohenHigh harmonic generation with fully tunable polarization by train of linearly-polarized pulsesNew Journal of Physics, 19, 023051 (2017)
  5. O. NeufeldE. BordoA. Fleischer and O. CohenHigh Harmonics with Controllable Polarization by a Burst of Linearly-Polarized Driver PulsesPhotonics, 4, 31 (2017)
  6. D. Ayuso*O. Neufeld*, A. Ordonez, P. Decleva, G. Lerner, O. Cohen, M. Ivanov and O. Smirnova, Synthetic chiral light for efficient control of chiral light matter interactionNature Photonics, 13 866 (2019)
  7. O. Neufeld*, D. Ayuso*, P. Decleva, M. Ivanov, O. Smirnova and O. Cohenultrasensitive chiral spectroscopy by dynamical symmetry breaking in high harmonic generationPhys. Rev. X 9, 031002 (2019)
  8. O. NeufeldO. WengrowiczO. Peleg, Angel Rubio and O.  Cohen, Detecting multiple chirality centers in chiral molecules with high harmonic generation, Opt. Express, 30, 3729 (2022)
  9.  O. Neufeld, M. Even-Tzur and O. Cohen, Degree of chirality (DOC) of Electromagnetic fields and maximally chiral light Phys. Rev. A101, 053831 (2020)
  10. O. Neufeld and Oren Cohen, Unambiguous definition of handedness for locally chiral light, Phys. Rev. A, 105, 023514 (2022)
  11. O. Neufeld and O. Cohen, Background-Free Measurement of Ring Currents by Symmetry Breaking High Harmonic SpectroscopyPhys. Rev. Lett 123, 103202 (2019). Highlighted as Editors’ suggestion
  12. M. Even-Tzur, O. Neufeld, A. Fleischer and O. Cohen, Selection rules for breaking selection rules, New J. Phys., 23, 103039 (2021)
  13. M. Even-Tzur, O. Neufeld, E. Bordo, A. Fleischer, and O. Cohen, Selection rules in symmetry broken systems by symmetries in synthetic dimensions, Nature Communications, 13, 1312 (2022)