Polarization switching and nonreciprocity in symmetric and asymmetric magnetophotonic multilayers with nonlinear defect

A one-dimensional magnetophotonic crystal with a nonlinear defect placed either symmetrically or asymmetrically inside the structure is considered. Simultaneous effects of time-reversal nonreciprocity and nonlinear spatial asymmetry in the structure are studied. Bistable response is demonstrated in a such system, accompanied by abrupt polarization switching between two circular or elliptical polarizations for transmitted and reflected waves. The effect is explained in terms of field localization at defect-mode spectral resonances and can be used in the design of thin-film optical isolators and polarization transformation devices.

Figure 1

Magnetophotonic structure with nonlinear defect.

Figure 2

Frequency dependencies ($\ae =D/\lambda$) of the transmission coefficient ($T$) of the LCP ($-$) and RCP ($+$) waves in the (a) linear (b) nonlinear case for $m=n=5$, ${\varepsilon }_1=10$, ${\mu }_1^T={\mu }_1^L=1$, $\alpha =0.05$, ${\varepsilon }_2={\mu }_2={\mu }_{\mathrm{d}}=1$, ${\varepsilon }_{\mathrm{d}}^{\mathrm{l}}=4$. For the nonlinear case, ${\tilde{\varepsilon }}_{\mathrm{d}}^{\mathrm{nl}}={\varepsilon }_{\mathrm{d}}^{\mathrm{nl}}{I}_0=1.5\times {10}^{-4}$, which corresponds to the incident light intensity $I_0=15\mathrm{kW}/{\mathrm{cm}}^2$ for ${\varepsilon }_{\mathrm{d}}^{\mathrm{nl}}\simeq 1.0\times {10}^{-5}{\mathrm{cm}}^2/\mathrm{kW}$.

Figure 3

Same as Fig. 2 but for the reflection coefficient ($R$).

Figure 4

Frequency dependencies ($\ae =D/\lambda$) of the magnitudes of the copolarized (co) and cross-polarized (cr) components of the transmission (a) and reflection (b) coefficients of linearly polarized waves. The input intensity $I_0$ in the nonlinear regime is taken to be 5, 10, and 15 $\mathrm{kW}/{\mathrm{cm}}^2$. Other parameters are as in Fig. 2.

Figure 5

Frequency dependencies ($\ae =D/\lambda$) of (a) the elipticity angle $\eta$ and (b) the polarization azimuth $\theta$ of the transmitted and reflected fields. The incident light is linearly polarized, and structure parameters are as in Fig. 2. The vertical line marks the bistable polarization switching at ${\ae }_0$.

Figure 6

Frequency dependencies ($\ae =D/\lambda$) of the transmission ($T$) and reflection ($R$) coefficients of the LCP ($-$) and RCP ($+$) waves of the MPC with asymmetrically placed ($m\ne n$) nonlinear defect. Here, ${\tilde{\varepsilon }}_{\mathrm{d}}^{\mathrm{nl}}={\varepsilon }_{\mathrm{d}}^{\mathrm{nl}}{I}_0=1.0\times {10}^{-4}$ (i.e., $I_0=10\mathrm{kW}/{\mathrm{cm}}^2$ for ${\varepsilon }_{\mathrm{d}}^{\mathrm{nl}}\simeq 1.0\times {10}^{-5}{\mathrm{cm}}^2/\mathrm{kW}$). Other parameters are as in Fig. 2. Solid and dashed lines correspond to configurations ($m=5$, $n=6$) and ($m=6$, $n=5$), respectively.

Figure 7

Frequency dependencies ($\ae =D/\lambda$) of the elipticity angle (a) and the polarization azimuth (b) of the transmitted and reflected fields of the MPC with asymmetrically placed ($m\ne n$) nonlinear defect. Parameters are as in Fig. 6. The vertical line marks the bistable polarization switching at ${\ae }_0$.

Figure 8

Frequency dependencies ($\ae =D/\lambda$) of the magnitudes of the copolarized (co) and cross-polarized (cr) components of the transmission (a) and reflection (b) coefficients of the linearly polarized waves of the MPC with asymmetrically placed ($m\ne n$) nonlinear defect. Parameters are as in Fig. 6.