Orbital Angular Momentum Generation, Detection, and Angular Momentum Conservation with Second Harmonic Generation

Electromagnetic (EM) waves can carry angular momenta that are decomposed into a spin and angular momenta. While circularly polarized waves take nonzero spin angular momentum (SAM), structured waves with helical wavefronts carry orbital angular momentum (OAM). Manipulation of OAM especially for the interaction between SAM and OAM obeys the angular momentum (AM) conservation law. In this chapter, we will mainly focus on the following two aspects. First, the generation and the detection of OAM at radio frequencies are demonstrated. Several types of metasurfaces are proposed to generate EM waves with OAM. Moreover, dielectric photonic crystals that convert guided modes to radiated OAM modes are proposed. Additionally, a mode analysis approach based on dynamic mode decomposition is developed to extract the OAM modes information of the receiving EM waves. An alternative approach to detect the OAM modes by using metasurfaces is also introduced. Second, spin–orbit interaction in plasmonic and dielectric nanostructures upon the second‐harmonic (SH) generation process is studied by boundary element method. The phase singularities and vorticities in the longitudinal components of the fundamental and SH fields have been discussed and their relations with the rotational symmetry of the scatterer have been analyzed. A general angular momenta conservation law, including the quasi‐angular‐momentum of chiral nanostructures, has been formulated to describe how the rotational symmetry properties affect the transfer of optical AM from incident beams to the scattered fundamental and SH fields.