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 bio-imaging in medicine and optical signal processing in information technology. We present a theoretical analysis providing a strong estimate for the energy-integrated SHG response. Requirements of symmetry in time and space are fully respected in the calculation, and estimates of natural and magnetic circular dichroic signals are superior to previous ones. Like symmetry requirements are traced in the amplitude for magnetic neutron scattering, which includes all axial and polar (Dirac) contributions. Our method of working, in terms of spherical multipoles and implementation of symmetry, could be of use in a variety of other probes of electronic properties.