1：Experimental Design and Method Selection:

Numerical calculations are carried out with finite difference time domain technique in commercial software FDTD Solutions, Lumerical Inc. The simulation is implemented for a 3D system with periodic boundary conditions on both X- and Y-axis, while along Z-axis perfectly matched layers are placed. Spectra are calculated for normal incidence of a plane electromagnetic wave along the Z-axis. The polarization direction is parallel to the X-axis. An external magnetic field is oriented along the Y-axis for Voigt geometry.

2：Sample Selection and Data Sources:

A two-dimensional square array of asymmetric nanodisks made of a magnetic dielectric, bismuth-substituted yttrium iron garnet (Bi:YIG, n =

3：09, g = –001), is simulated. The disks height h = 227 nm, and radius R = 248 nm. The disks are placed on a quartz substrate SiO2 (n = 45). Every garnet nanodisk has a hole with the radius r = 62 nm. This hole is displaced from the disk center in the positive direction of the Y-axis. The asymmetry factor is defined as the ratio of this translocation y0 to disk’s radius R:

α = y0/R. Period d in both directions is 679 nm.

4：List of Experimental Equipment and Materials:

Commercial software FDTD Solutions, Lumerical Inc.

5：Experimental Procedures and Operational Workflow:

Simulations begin from a symmetric structure (α = 0), when the hole is located at the garnet disk center. The small symmetry disturbance by the hole displacement results in a transformation of BIC resonance to quasi-BIC mode with the following appearance of the dip in the transmittance spectrum.

6：Data Analysis Methods:

A relative variance of transmittance is calculated according to the equation: δ = (T(H) – T(0))/T(0), where T(H) and T(0) are transmittance spectra in case of the external dc-magnetic field and without it, respectively. The angle of the rotation is evaluated as the ratio of Ey/Ex in a far-field diffraction zone.