Weak-value-amplification enhancement of the magneto-optical Kerr effect in nanoscale layered structures

The achievement of a larger magneto-optical Kerr effect (MOKE) in nanoscale layered structures is extremely important for both theoretical understandings and practical applications. However, nanoscale layered structures may not always exhibit enhanced MOKE under certain geometries. In this paper, we present a scheme based on weak-value amplification (WVA) for simultaneously detecting and enhancing the Kerr signals in nanoscale layered structures. The Kerr signals can be effectively amplified as the parameters of the preselection in WVA. We numerically investigate the dependence of the thickness $d$ of Co in the sample ${\text{HfO}}_{2}(10\phantom{\rule{0.16em}{0ex}}\text{nm})/\text{Co}(d\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/{\mathrm{HfO}}_{2}(30\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Al}(40\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Si}$ and the sample $\text{Co}(d\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Si}$ in the range of 5 nm $<\phantom{\rule{4pt}{0ex}}d\phantom{\rule{4pt}{0ex}}<$ 50 nm. Our results indicate that the combination of the cavity and WVA can simultaneously amplify the MOKE signals when compared to the application of WVA on the sample $\text{Co}(d\phantom{\rule{0.16em}{0ex}}\mathrm{nm})/\mathrm{Si}$ and the application of traditional MOKE setup (TMOKES) on the two samples. Importantly, our results highlight that WVA maintains its ability to amplify MOKE signals even in cases where the cavity in the TMOKES scheme fails to enhance the Kerr signals. This signifies the exceptional advantage of WVA in amplifying Kerr signals over TMOKES, regardless of the sample structures and specific MOKE geometries employed.