Analytical description of the mode hybridization in a restricted two-dimensional model for an electromagnetic cavity containing a thin magnetized slab

Analytical solutions to the problem of mode splitting caused by a thin plain magnetized slab placed in a rectangular electromagnetic cavity are found in two special cases: an infinite slab between two ideal infinite plain mirrors (1D model) and a 2D model of a cavity confined in the direction of permanent magnetization. Under the resonance conditions, the time-dependent magnetization vectors inside the slab are strongly enhanced, with opposite directions in the split modes. For realistic parameters, the frequency splitting does not depend on the dielectric constant of the slab and the Landau-Lifshitz-Gilbert damping coefficient, whereas the loaded cavity quality factor is not sensitive to the slab position.

Figure 1

Geometry of the problem.

Figure 2

The dimensionless frequency shift $f\equiv \delta \omega /{\omega }_n$ versus the dimensionless magnetic field $h\equiv {\omega }_H/{\omega }_M=H/M_0$ in the case of ${\omega }_n={\omega }_M$ and $R={10}^{-4}$.

Figure 3

The dimensionless Rabi frequency $S\equiv \mathrm{\Delta }/{\omega }_n$ versus the ratio $m\equiv {\omega }_M/{\omega }_n$ for $R={10}^{-4}$.

Figure 4

The imaginary parts of dimensionless frequency shifts $f\equiv \delta {\omega }_{\pm }/{\omega }_n$ versus the dimensionless magnetic field $h\equiv H/M_0$ for $\alpha ={10}^{-3},{\omega }_n={\omega }_M$, and $R={10}^{-4}$.