A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams

Abstract

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance. A dichroic signal exploiting the Borrmann effect with a linearly polarized beam presents charge-like multipoles that include a hexadecapole. A difference between dichroic signals obtained with a twisted beam carrying spin polarization (circular polarization) and opposite winding numbers presents charge-like atomic multipoles, whereas a twisted beam carrying linear polarization alone presents magnetic (time-odd) multipoles. Charge-like multipoles include a quadrupole, and magnetic multipoles include a dipole and an octupole. We discuss the practicalities and relative merits of spectroscopy exploiting the two remarkably closely-related processes. Signals using beams with topological charges l ≥ 2 present additional atomic multipoles.

Superchiral photons unveil magnetic circular dichroism

“…Atomic multipoles for MCD are gathered in Appendix A. Use of an effective wavevector is central to our method of working [9].…”

“…Likewise, electronic positions in the E2-E2 absorption event may be represented by a sum of tenors with rank K = 0, ... , 4. The formulation we describe for the Borrmann effect has been applied also to dichroic signals obtained with twisted photon beams [9], and it is exploited in this communication for signals obtained with a superchiral beam.…”

“…The effective vector κ κ κ κ = (0, 0, 1) with spherical components κ±1 = 0, κ0 = 1 (R+1 = − (x + iy) /√2, R−1 = (x − iy) /√2, R0 = z for a vector (x, y, z) = R). Circular polarization represented by a polarization vector ε ε ε ε = (1, i, 0)/√2 is right-handed and corresponds to a Stokes parameter P2 = + 1 (definitions of Stokes parameters follows references [9,11]).…”

“…Specifically, the Borrmann effect and twisted photon beams enhance and isolate electric quadrupole absorption (E2-E2). Building on a previous investigation that unified dichroic signals retrieved with the Borrmann effect and twisted photon beams [9] we are able to adopt superchiral beams in a family of photon-electron spectroscopies. A judiciously chosen effective wavevector in an established quantum-mechanical formulation of dichroic signals provides the familial linkage.…”

Electronic multipoles in second harmonic generation and neutron scattering

“…Our use of them here to formulate response functions for SHG and neutron scattering has previously proved useful in several other photon scattering processes. Examples include x-ray magneto-optical sum rules [40][41][42], a unified formulation of dichroic signals using the Borrmann effect and twisted photon beams [43], resonant x-ray diffraction from chiral electric-polarization structures [44], and a demonstration that superchiral photons reveal magnetic circular dichroism [45]. But, our innovation for SHG starts by finding a representation for the response in terms of a spherical tensor operator.…”