Control of beam shifts via tunable epsilon-near-zero point with atomic-scale isotope in black phosphorus-hBN metamaterials

Abstract This paper explores the influence of isotopic effects on spatial shifts within a metamaterial structure that incorporates black phosphorus (BP) and hexagonal boron nitride (hBN) with varying hBN isotopes, namely 98.7% ¹⁰B hBN, natural hBN, and 99.2% ¹¹B hBN. Our findings reveal that hBN isotopes significantly modulate the optical phonon frequencies of hBN, leading to redshift or blueshift of the epsilon-near-zero (ENZ) point, which subsequently influences the magnitude and distribution of spatial shifts. The incorporation of BP layers not only induces the emergence of novel reststrahlen frequency bands (RBs) but also significantly enhances the beam shift performance by precisely tuning the doping concentration, layer number and twist angles. The simulation outcomes present that 98.7% ¹⁰B hBN and 99.2% ¹¹B hBN display a pronounced enhancement in both Goos-Hänchen shifts (GHS) and Imbert-Fedorov shifts (IFS) at specific conditions, whereas 99.2% ¹¹B hBN maintains larger shifts over a wide twist angle. The findings provide a theoretical foundation for developing isotope-tailored 2D photonic platforms, enabling multi-dimensional optical control.