Fig. 4: Circuit model representation and numerical analysis of the ISRR/YIG sample.
a A circuit model based on the transmission line theory for coupled ISRR/YIG hybrid, illustrating the theoretical framework for the subsequent analyses. b Numerical calculations for S21 (top) and S12 (bottom) spectra, along with the derived real part of the refractive index n’ for coupling constants Mc = 0.0093–0.0028i and M*c = 0.0093 + 0.0028i. Dashed lines indicate the split hybrid modes (ω±/2π) derived from Eq. 1. c Circuit model analysis of varying imaginary parts of the coupling constant (Im[Mc]) on |Sij| and n’, for specific values, while maintaining the real part constant (Mc = 0.0093), displaying the dependence of spectral and refractive properties on the imaginary coupling constant, where (top) Im[Mc] = −0.0024, −0.002, 0, and (bottom) Im[Mc] = 0.0024, 0.002, 0. d Numerical calculation of the peak value of n’ (red) and the field region ΔHAD indicating anti-damping (blue) as a function of κ/κc (solid lines) and κ*/κ*c (dotted lines), comparing with experimental measurements (solid square and circles, respectively), to validate the model against observed NRI phenomena.
