Science-driven design and performance evaluation of a Silicon Laue Component lens for hard X-ray polarimetry
Focusing hard X-rays above 80 keV is challenging for grazing-incidence optics. Laue lenses offer an alternative based on crystal diffraction. We assess a lens based on Silicon Laue Components (SiLCs), consisting of stacked silicon plates, for polarimetry of accreting stellar-mass black holes and strongly magnetized neutron stars in the 80-200 keV band. We derive effective-area requirements from the minimum detectable polarization at 99% confidence (MDP99) for an XL-Calibur-inspired polarimeter observing a 100-mCrab source for 100 ks. We evaluate an 18-m-focal-length lens combining Si(220) and Si(111) reflections, with a 63 arcsec diffraction bandpass and a 90% optical filling factor, using on-axis ray tracing of a perfectly aligned lens with uniform crystal curvatures. An MDP99 of 5% requires mean effective areas of approximately 260, 400, and 740 cm^2 in the 80-100, 100-130, and 130-200 keV bands, respectively. The lens spans radii of 356-1453 mm and continuously covers 80-200 keV. Its effective area reaches approximately 375 cm^2 near the low-energy boundary and falls to approximately 200 cm^2 at 180 keV. The focal-plane diameters enclosing 50% and 90% of the focused signal are 5.4 mm (62 arcsec) and 9.8 mm (112 arcsec). Mean effective areas of approximately 320, 250, and 220 cm^2 give reference MDP99 values of approximately 4.5%, 6.4%, and 9.5% in the three bands. The design reaches few-percent polarimetric sensitivity below 100 keV but does not maintain a 5% MDP99 across 80-200 keV under the adopted detector assumptions. It remains relevant for more strongly polarized hard components and provides a reference for end-to-end optimization of the optics, detector response, and background.