Electronic multipoles in second harmonic generation and neutron scattering

Nonlinear optics, and particularly second harmonic generation (SHG), is increasingly used in many modern disciplines from material characterization in physical sciences to bioimaging in medicine and optical signal processing in information technology. We present a theoretical analysis yielding a strong estimate of the energyintegrated SHG response. Compact spherical multipoles are provided for the corresponding natural and magnetic circular dichroic signals. Like symmetry requirements in time and space are traced in the amplitude for magnetic neutron scattering, which includes all axial and polar (Dirac) contributions. Our method of working in terms of, now standard, electronic multipoles and Racah algebra, with full implementation of discrete symmetries, could be of use in a variety of other probes of matter.

Automated summary

Nonlinear optics, particularly second harmonic generation (SHG), is widely used in modern disciplines for material characterization and bioimaging. A theoretical analysis provides a strong estimate of the energy-integrated SHG response, along with compact spherical multipoles for natural and magnetic circular dichroic signals. Applying symmetry requirements in magnetic neutron scattering and working with electronic multipoles and Racah algebra may have potential utility in various other probes of matter.