Modeling and empirical characterization of the polarization response of off-plane reflection gratings

Abstract

Off-plane reflection gratings were previously predicted to have different efficiencies when the incident light is polarized in the transverse-magnetic (TM) versus transverse-electric (TE) orientations with respect to the grating grooves. However, more recent theoretical calculations which rigorously account for finitely conducting, rather than perfectly conducting, grating materials no longer predict significant polarization sensitivity. We present the first empirical results for radially ruled, laminar groove profile gratings in the off-plane mount, which demonstrate no difference in TM versus TE efficiency across our entire 300-1500 eV bandpass. These measurements together with the recent theoretical results confirm that grazing incidence off-plane reflection gratings using real, not perfectly conducting, materials are not polarization sensitive.

Extreme Ultraviolet and Soft X-Ray Diffraction Efficiency of a Blazed Reflection Grating Fabricated by Thermally Activated Selective Topography Equilibration

“…This was handled using the software package PCGrate-SX version 6.1, 10 which solves the Helmholtz equation through the integral method for a custom grating boundary and incidence angles input by the user (Goray & Schmidt 2010). Based on the findings of Marlowe et al (2016), which verify a lack of polarization sensitivity for SXR gratings used in extreme off-plane mounts, PCGrate-SX calculations were carried out assuming a perfectly conducting grating boundary with perfectly smooth groove facets and an incident wavefront with transverse electric polarization. While perfect conductivity combined with the absence of surface roughness implies a lossless response from the grating grooves, PCGrate-SX modulates the predicted diffraction efficiency by the reflectivity of a user-input, stratified medium defined by optical constants and custom layer thicknesses.…”

On obtaining high spectral resolution in extreme ultraviolet/soft X-ray monochromators operating off-plane diffraction in a divergent incident beam

“…In the first case the electric field vector will be rotated with respect to the incident beam, while in the second case the electric field vector will start to rotate, giving rise to the progression of elliptically and eventually circularly polarized light. According to Marlowe et al (2016), a polarization effect has not been found for gratings operated in the offplane configuration in the soft X-ray range considered here. Kortright & Underwood (1990) showed that significantly different reflection coefficients and phase shifts different from will not be found at rather small grazing angles, but in the vicinity of the Brewster angle, which in this case for soft X-rays occurs at a larger angle of grazing incidence of about 45 .…”

X-ray verification of sol-gel resist shrinkage in substrate-conformal imprint lithography for a replicated blazed reflection grating

“…Previous test campaigns have demonstrated that reflection gratings operated in an extreme off-plane mount can be measured for soft x-ray diffraction efficiency using a beamline facility suitable for short-wavelength reflectometry [2,6,24,25]. The experiments described here took place at beamline 6.3.2 of the ALS, which provides a highly-coherent beam of radiation tunable over extreme UV and soft x-ray wavelengths that strikes a stage-mounted optic [19][20][21].…”

“…Absolute diffraction efficiency in the th propagating order is measured through E ≡ I /I inc , where I and I inc are noise-subtracted intensity measurements of the th diffracted beam and the incident beam, respectively, which can be gathered for each order using a vertical, 0.5-mm-wide slit to mask the detector [2,6]. Although this beam is s-polarized to a high degree, x-ray reflection gratings have been demonstrated experimentally to have a polarization-insensitive efficiency response for extreme off-plane geometries [25]. With the SCIL imprint described in section 2 emulating the UV-NIL replica tested by Miles, et al [2], diffraction-efficiency testing was carried out in a nearly identical geometry where the half-cone opening angle is ≈ 1.7 • while the azimuthal incidence angle, , is close to the nominal blaze angle of = 29.5 • in a near-Littrow configuration.…”