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


In the current general theory of nonlinear optics, the symmetries of the medium are analyzed to derive the minimally represented nonlinear tensors that describe the selection rules (e.g. allowed/forbidden harmonics and their polarization states) of various processes [1]. However, the theory does not describe cases in which the driving lasers exhibit non-trivial dynamical symmetries. We formulate a general group-based theory to derive the selection rules of harmonic generation (both in the perturbative and in the non-perturbative regimes) from the dynamical symmetries of the system (light and medium) [2,3]. This formalism leads to many new selection rules. For example, we discovered the elliptic dynamical symmetry [2] that yields ‘conservation of ellipticity’ in high harmonic generation (HHG) – the ellipticity of ALL the harmonics is the same as the ellipticity of the pump, which can vary all the way from linear to circular [4,5].

Utilizing the selection rules formalism, we develop and explore, theoretically and experimentally, ultrafast spectroscopic methods that are based on dynamical symmetry breaking. For example, we identify chiral-sensitive HHG geometries in which the chiral signal is background-free and relies on the electric dipole interaction only (and not on the magnetic interaction which was previously assumed mandatory for chiral-sensitive HHG), hence leading to huge chiral signals [6]. The method is implemented through non-collinear HHG, where the beams’ properties are chosen through symmetry considerations that lead to forbidden harmonic selection rules from achiral media that are broken in chiral media. As a result, ‘forbidden’ harmonics are emitted only if the medium is chiral; their intensity is correlated to the enantiomeric excess; and their polarization handedness is associated with the medium’s handedness. Furthermore, we use a similar approach to define a new symmetry-based measure for light’s chirality within the dipole approximation (analogous to the molecular definition) [7,8]. Similarly, we develop an all-optical method for diagnostics of ultrafast ring currents, e.g. in gas of atoms and molecules [9].

  1. Nonlinear optics, Boyd, Elsevier; 2003
  2. O. Neufeld, D. Podolsky and O. Cohen, Floquet group theory and its application to selection rules in harmonic generation, Nat. Commun., 10, 405 (2019)
  3. O. Neufeld, E.BordoA. Fleischer and O. Cohen, High harmonic generation with fully tunable polarization by train of linearly-polarized pulses, New Journal of Physics, 19, 023051 (2017)
  4. O. Neufeld, E. Bordo, A. Fleischer and O. Cohen, High Harmonics with Controllable Polarization by a Burst of Linearly-Polarized Driver PulsesPhotonics, 4, 31 (2017)
  5. O. Neufeld*, D. Ayuso*, P. Decleva, M. Ivanov, O. Smirnova and O. Cohen, ultrasensitive chiral spectroscopy by dynamical symmetry breaking in high harmonic generation, Phys. Rev. X 9, 031002 (2019)
  6. D. Ayuso*O. Neufeld*, A. Ordonez, P. Decleva, G. LernerO Cohen, M. Ivanov and O. Smirnova, Synthetic chiral light for efficient control of chiral light matter interactionNature Photonics, 13 866 (2019)
  7.  O. Neufeld, M. Even-Tzur and O. Cohen, Degree of chirality (DOC) of Electromagnetic fields and maximally chiral light, Phys. Rev. A101, 053831 (2020)
  8. 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
  9. M. Even-Tzur, O. Neufeld, A. Fleischer and O. Cohen, Selection rules for breaking selection rules, New J. Phys., 23, 103039 (2021)
  10. M. Even-Tzur, O. Neufeld, A. Fleischer and O. Cohen, Selection rules in symmetry-broken systems by symmetries in synthetic dimensions, arXiv:2106.04301
  11. 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, arXiv:2109.01941
  12. O. Neufeld, O. Wengrowicz, O. Peleg, A. Rubio, O. Cohen, Detecting multiple chirality centers in chiral molecules with high harmonic generation, arXiv:2110.05307