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As a unique optical phenomenon, the Goos–Hänchen (GH) shift has attracted considerable interest due to its broad potential in high-sensitivity sensing, optical switching, and nanoscale photonic devices. In this work, a multilayer heterostructure constructed by alternating layers of black phosphorene (BP) and silicon (Si) is designed, and its GH shifts are systematically investigated, aiming to achieve large-amplitude, electrically tunable GH shifts in the near-infrared region. Furthermore, we elaborate on the underlying phase-modulation mechanisms and the sensing performance of the proposed structure. Based on the transfer matrix method and the optical conductivity of BP calculated via the Kubo formalism, we comprehensively examine the cooperative effects of polarized modes, structural periodicity, incident optical energy, and external voltage on the evolution of the reflection phase and the consequent GH displacement. The results indicate that the incorporation of BP, through the introduction of complex surface conductivity, substantially modifies the phase response of transverse magnetic (TM) waves near the conventional Brewster angle, converting the original π-phase jump into a continuous and differentiable phase transition. This effect enables a GH shift as large as 40λ even in a single-period structure. Although transverse electric (TE) waves do not exhibit Brewster-angle behavior, several-wavelength-scale GH shifts can still be achieved under near-grazing incidence due to Fabry–Pérot interference. Further analysis reveals that increasing the number of (BP–Si) periods steepens the slope of the reflection phase, thereby enhancing the GH shift of the TM wave from 40λ to 128λ in a fourperiod structure at the incident optical energy of 1.52 eV. In addition, the application of an external voltage modulates the energy bandgap and optical conductivity of BP, providing dual control over the magnitude and angular position of the GH shift. For example, under an external voltage of 0.5 eV, the maximum GH shift of the TM wave in a single-period structure at an incident optical energy of 1.4 eV increases from 184λ to 586λ. The structure also exhibits an ultrahigh refractive index sensitivity exceeding 105λ/RIU toward variations in the refractive index of the terminal medium, with further enhancement under electrical bias. These findings reveal the mechanism through which two-dimensional materials induce phase continuity and enhanced GH shifts, while demonstrating the strong potential of BP–Si multilayers for the development of tunable near-infrared photonic components and high-sensitivity optical sensing platforms.
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Keywords:
- Black phosphorene /
- Goos-Hänchen shift /
- Transfer matrix /
- Optical sensing
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