Determination of the element-specific complex permittivity using a soft x-ray phase modulator

We report on directly determining the complex permittivity tensor using a method combining a developed light source from a segmented cross undulator of synchrotron radiation and the magneto-optical Kerr effect. The empirical permittivity, which carries the electronic and magnetic information of a material, has element specificity and has perfect confirmation using the quantum-mechanical calculation for itinerant electrons systems. These results help in understanding the interaction of light and matter, and they provide an interesting approach to seek the best materials as optical elements, for example, in extended-ultraviolet lithographic technologies or in state-of-the-art laser technologies.

Figure 1

(a) Image of the polarization-modulated light with the L-MOKE setup. (b) Time dependence of the retardation $\delta =\left(\pi /2\right)sin2\pi pt$. The polarization of light with retardation $\delta$ varies skew linearly ($\mathrm{SL})\to$ right-handed circular$\to \mathrm{SL}\to$ left-handed circular$\to \mathrm{SL}$. (c) and (d) Schematic for why the $p$ and $2p$ components represent MCD and the Kerr rotation, respectively. Projections onto the $x$ axis of the electric field reflected from samples (c) with MCD and (d) with the Kerr rotation [17].

Figure 2

Geometries and results of L-MOKE measurements for an Fe nanofilm at the $L$-edge using the polarization-modulated light for (a) the $s$ wave and (b) the $p$ wave. Red solid circles and blue open circles represent the spectra of ${\theta }_{\mathrm{K}}$ (left axis) and ${\varepsilon }_{\mathrm{K}}$ (right axis), respectively.

Figure 3

(a) ${\epsilon }_{xz}$ spectra of the Fe nanofilm at the $L$ edge obtained from L-MOKE measurements with polarization-modulated light. Red solid circles and blue open circles represent its real and imaginary parts, respectively. (b) ${\epsilon }_{xz}$ spectra of bulk Fe (bcc) at the $L$ edge obtained using the first-principles calculation within the KKR formalism. Red and blue lines represent its real and imaginary parts, respectively. (c) Density of states of bulk Fe (bcc) calculated using the first-principles calculation. Red and green lines represent the density of states of all states and the $d$ state, respectively. The inset illustrates the crystal structure of bulk Fe (bcc).

Figure 4

Relation between the unit vectors $\mathit{i}$, $\mathit{j}$, ${\mathit{s}}_{\mathrm{A}}$, and ${\mathit{p}}_{\mathrm{A}}$ and the rotation angle $\chi$.