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].

- Nonlinear optics, Boyd, Elsevier; 2003
- O. Neufeld, D. Podolsky and O. Cohen, Floquet group theory and its application to selection rules in harmonic generation,
*Nat. Commun*., 10, 405 (2019) __O. Neufeld__, E.Bordo,__A. Fleischer__and__O. Cohen,__High harmonic generation with fully tunable polarization by train of linearly-polarized pulses,*New Journal of Physics*, 19, 023051 (2017)- O. Neufeld, E. Bordo, A. Fleischer and O. Cohen, High Harmonics with Controllable Polarization by a Burst of Linearly-Polarized Driver Pulses,
*Photonics*, 4, 31 (2017) __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)- 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 interaction,*Nature Photonics*, 13 866 (2019) -
__O. Neufeld,____M. Even-Tzur__and__O. Cohen,__Degree of chirality (DOC) of Electromagnetic fields and*Phys. Rev. A*101, 053831 (2020) __O. Neufeld__and__O. Cohen,__*Phys. Rev. Lett*123, 103202 (2019). Highlighted as Editors’ suggestion- M. Even-Tzur, O. Neufeld, A. Fleischer and O. Cohen, Selection rules for breaking selection rules,
*New J. Phys.*, 23, 103039 (2021) - M. Even-Tzur, O. Neufeld, A. Fleischer and O. Cohen, Selection rules in symmetry-broken systems by symmetries in synthetic dimensions, arXiv:2106.04301
- 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
- O. Neufeld, O. Wengrowicz, O. Peleg, A. Rubio, O. Cohen, Detecting multiple chirality centers in chiral molecules with high harmonic generation, arXiv:2110.05307