Fig. 1: Nonlinear total angular momentum z-projection addition.
From: Light structuring via nonlinear total angular momentum addition with flat optics
a Illustration of the nonlinear total angular momentum (TAM) \(z\)-projection (\(m\)) addition process. When a circularly polarized (CP) pump beam (\({m}_{\omega }=1\)) is incident on a thin isotropic layer with \({\chi }^{\left(3\right)}\) nonlinearity, the generated signal at third-harmonic (TH) frequency has tripled \({\rm{TAM}}\) (\({m}_{3\omega }=3\)). b Schematic of the optical setup for observation of the nonlinear TAM projection addition in a thin film of a-Si. Bottom panel shows numerical simulations of the intensity, \({\left|{\bf{E}}\cdot {{\bf{e}}}_{{{R}}}^{* }\right|}^{2}\), and phase, \(\arg \left({\bf{E}}\cdot {{\bf{e}}}_{{{R}}}^{* }\right)\), distributions of the dominant polarization components in the right CP pump and in the generated TH signal on the thin film surface
