Abstract
Polarization-dependent photon spectroscopy (dichroism) of the second-harmonic generation (SHG) response is shown to reveal chiral and magnetic properties of a sample. Two dichroic signals are allowed with electric-dipole (E1) and electric-quadrupole (E2) scattering events, and both require circular polarization in the primary beam. Explicit expressions for electronic multipoles, which benefit from equivalent electronic operators, in NCD and MCD of the SHG response are derived using theoretical techniques from atomic physics.
Highlights
Second-harmonic generation (SHG) was first demonstrated from a quartz crystal soon after the invention of the ruby laser [1]
Results in Eqs. (15) and (16) completely define the multipole U2(1) for the natural circular dichroism (NCD) signal derived from the SHG response using E1 -E1-E1
We presented a theory for circular dichroism in the second-harmonic generation (SHG) response
Summary
Second-harmonic generation (SHG) was first demonstrated from a quartz crystal soon after the invention of the ruby laser [1]. When a pure transition (parity-even) is time-odd the material tensor needs to be time-odd (magnetic polarization), which allows for the Faraday effect and MCD in any spatial symmetry group. In a mixed transition (parity-odd) the NCD reverses the rotation angle (handedness) of both the matter and the light, leaving the total system invariant. In this case, the multipole can be described by pseudotensors UK of even rank K. We extend the established concepts for ordinary dichroic signals to tertiary events of the generic form shown in Fig. 1 and Eq (A4) On this basis, a theory of dichroism in the SHG response clearly needs a different approach than used for ordinary NCD. Appendix A contains technical details and auxiliary information about our method of working [16]
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