Multiscale dynamical symmetries and selection rules in nonlinear optics

Abstract

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields’ time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet–x-ray beams, attosecond pulses, or the interacting medium itself.

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

“…While ample evidence suggests nonlinearity's impact on synchronization behavior, existing studies mostly assume synchronization regions to be symmetric to the self-oscillation frequency [28][29][30]. Yet, due to the amplitude-frequency effect [24] induced by nonlinearity, synchronization regions can exhibit asymmetry [31]. Such results have been shown in the experimental measured synchronization region in [26,27]; however, the asymmetry of synchronization has been largely unexplored regarding the intrinsic mechanism of nonlinearity's influence.…”

Floquet systems with continuous dynamical symmetries: characterization, time-dependent noether charge, and solvability

“…In summary, a CDS with A determines H(t) in the form of equation ( 12) using an H 0 . In addition, the periodicity imposes the Aʼs properties equations ( 14) and (15). This is a complete characterization of H(t) having a CDS.…”

“…Since the generator A is a traceless Hermitian matrix, it can be written as a linear combination of N − 1 diagonal (Cartan) generators of SU(N) group. And thus, the quantization condition corresponding to (B2) can also be found to satisfy equation (15). Additionally the time-evolution of Hamiltonian with CDS can be written by using structure constant of the SU(N) algebra.…”

“…In this paper, we refer to this case as continuous dynamic symmetry (CDS). While there have been discussions on harmonic generation based on CDS [10,14,15], a systematic understanding of it has not been achieved.…”

High-harmonic spin-orbit angular momentum generation in crystalline solids preserving multiscale dynamical symmetry

“…The applicability of DS has been extended to multiscale spatial light structures, and, thereby, it allows for comprehensive predictions to be made on a wide range of nonperturbative optical phenomena induced by spatially nonuniform driving fields ( 18 , 19 ). Micro- and macroscale light structures are respectively characterized by spin angular momentum, corresponding to the helicity of the polarization, and orbital angular momentum (OAM), which corresponds to the twist in the wavefront of light ( 20 ).…”