Soft x-ray polarizer for optical productions of any orthogonal state of the linear and circular polarization modes

Abstract

An efficient soft x-ray polarizer that is able to optically convert a linear polarization state to any orthogonal state of not only linear but also circular polarization modes is found by means of numerical calculations of the intensities of individual orthogonal polarization components in reflected waves. Calculation results, using the known linear-polarization-mode based Kerr matrix as well as a newly derived circular-polarization-mode based Kerr matrix, indicate that a +45° or −45° linearly polarized incident wave can be readily converted to any orthogonal states of both circular and linear polarization modes, i.e., left- and right-handed circular and s- and p-linear polarizations through reflection, at certain grazing angles of incidence near the critical angle from a simple ferromagnetic thin film of Co(9.0nm)∕Si substrate. The intensities of almost pure circularly or linearly polarized reflected waves are about 10% or less in a certain spectral soft x-ray range just below the absorption edges of constituent magnetic elements. The counterpart orthogonal states of the linear as well as circular modes can be rapidly switched simply by reversing oppositely the orientation of longitudinal magnetizations. These results suggest that the orthogonal polarization states of the circular- and linear-polarization modes converted from such a polarizing optical element through reflection can be practically used in probing the vector quantities of element specific magnetizations in multicomponent magnetic materials.

Giant asymmetry of soft x-ray magnetic scattering between opposite circular polarizations near the Brewster angle

“…This work is studied not only by the theoretical derivation of the XRMS amplitudes and phases of individual scattering sources using the circular-polarizationmode basis newly developed from this work, but also by the numerical calculations of the individual intensities of the RCP and LCP components using the circular-mode-based magneto-optical Kerr matrices. 9 Also, continuously variable polarization state, from the RCP, through the linear s polarization, to the LCP ͑or vice versa͒ is observed in a wideangle region around B n . First, we derive XRMS amplitudes with respect to the circular-mode basis by considering a total coherent elasticscattering amplitude in the pure electric dipole ͑E1͒ transition for the case of 3d transition-metal ferromagnetic materials.…”

“…In the calculations, we used the circularmode-based magneto-optical Kerr matrix 10 and the optical parameters of a Co thin film obtained from soft x-ray circular dichroism spectra. 9 Figure 3͑a͒ shows the angular variations of the individual reflectivities of individual polarization components for a demagnetized state of the Co film. In the reflectivity profiles, there exists only the B n due to no net magnetization.…”