Circular dichroism of second harmonic generation response

Abstract

Polarization-dependent photon spectroscopy (dichroism) of the second-harmonic generation response is shown to reveal chiral and magnetic properties of a sample. Two dichroic signals are allowed with electric-dipole and electric-quadrupole scattering events, and both require circular polarization in the primary beam. Explicit expressions for the signals are derived using theoretical techniques from atomic physics.

Electronic multipoles in second harmonic generation and neutron scattering

“…Simply put, the multipole {R ⊗ C 2 } 2 for the material under illumination is allowed to be different from zero when NCD is detected. As in our previous calculation, the operator equivalent is a dyadic [46]. The index p = 2 for the MCD signal and another lengthy mathematical exercise yields…”

“…Two dichroic signals are allowed with electric-dipole (E1) and electric-quadrupole (E2) scattering events, and both require circular polarization in the primary beam. NCD is derived from an (E1 -E1-E1) event, and a parity-even event (E1 -E2-E1) yields MCD [46].…”

“…Again, products of matrix elements factor, as depicted in Fig. 3, although the analog of the photon tensor X K is more complicated [46]. Our goal is to produce operator equivalents for multipoles in NCD and magnetic circular dichroism (MCD), i.e., F(NCD) and F(MCD), defined by corresponding response RMEs that we derive in accord with Eq.…”

“…, where q 0 ≡ q z represents the primary wave vector [46]. For a crystalline material, permitted motifs of {R ⊗ C 2 } 2 and {C 2 ⊗ L} K are delineated by time and space in the unit cell, and prescribed by the relevant space group, likewise for symmetry in reduced dimensions and molecular systems.…”

“…But, our innovation for SHG starts by finding a representation for the response in terms of a spherical tensor operator. We have already accomplished this task with extensive use of Racah algebra, and we refer the reader to a previous publication for additional details [46]. Beyond are superior results for NCD and MCD, reported in Sec.…”