Wide-range breakdown of effective medium theory via photonic spin Hall effect in graphene- <i>h</i> -BN heterostructure

Abstract The effective medium theory (EMT) simplifies the analysis of electromagnetic responses by homogenizing heterogeneous structures. Research on the photonic spin Hall effect (PSHE) indicates that in low-dimensional materials, EMT breakdown may occur at non-critical angles. However, this breakdown occurs only within a narrow incident angle range △ θ ＜1°, with weak differences in the PSHE between real and effective structures. In the paper, we reveal the EMT breakdown at a wide-range of incident angles by comparing the significant PSHE differences between the real and effective graphene- h -BN heterostructure. The study shows that the in-plane angular shift difference between the real and effective structures can reach 2.5mm, while within the range of incident angles 1°~25°, the shift difference is usually at the micrometer level. The transverse angular shift difference can reach 230.6μm, and the shift difference remains in the micrometer range within the incident angle range of 1°~11°. In addition, the breakdown of EMT can also be significantly observed by the spatial shift difference. Further analysis reveals that the EMT breakdown is due to its inability to capture the phase accumulation effect at the interface, whereas PSHE possesses phase-sensitive characteristics. These discoveries not only deepen our understanding of the limitations of EMT, but also provide new ideas for designing precision optical sensors and quantum photonic devices.