Golden-Ratio Exceptional Contours in a Non-Hermitian RH/LH Quadrilayer Metamaterial

A non-Hermitian LC quadrilayer metamaterial formed by alternating right-handed (RH) and left-handed (LH) circuit layers is investigated. The layers are connected through identical nearest-neighbor imaginary couplings, providing a minimal multilayer extension of the RH/LH bilayer. The quadrilayer connectivity generates two non-Hermitian spectral scales related by the golden ratio, giving rise to two exceptional families and up to four exceptional contours in the two-dimensional reciprocal space. The RH/LH circuit duality organizes the exceptional solutions into reciprocal pairs, while the golden-ratio structure determines the relative scale of the critical couplings. Increasing the coupling consequently changes the number of physically accessible exceptional contours from four to three and finally two. In the four-contour regime, the nested exceptional structure separates reciprocal-space regions containing zero, two, and four complex eigenfrequencies. These results show that the connectivity of an LC multilayer can generate multiple exceptional boundaries and golden-ratio spectral scaling using a single microscopic non-Hermitian coupling.