Fig. 1: Scattering parameter measurement and NRI estimation in an ISRR/YIG hybrid sample.
a Setup schematic for measuring Sij scattering parameters versus AC current frequency (fAC = ω/2π) and varying magnetic field strengths (μ0H), applied at a 33° angle to the x axis. b Photo images of the ISRR/YIG sample, showcasing both front and backside views. c Experimental data presentation: Magnitude (dB scale, top row) and phase (radian, second row) for S21 (left) and S12 (right) transmission as functions of fAC and μ0H. Refractive index (third row) estimated from the scattering parameters, is highlighted in blue. The calculation of \({\varepsilon }_{{eff}}^{{\prime} }\cdot {\mu }_{{eff}}^{{\prime} {\prime} }+{\varepsilon }_{{eff}}^{{\prime} {\prime} }\cdot {\mu }_{{eff}}^{{\prime} }\) (last row) should be negative to indicate the occurrence of NRI. Solid lines trace the uncoupled photon and magnon modes (ωISRR/2π and ωr/2π), with dashed lines indicating the split hybrid modes from photon-magnon interactions, as described by Eq. 1.
