Controlled opacity in a class of nonlinear dielectric media

Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.

Figure 1

Plots of $\epsilon \mu {\left(v^{\pm }\right)}^2$ as function of $\theta$ for the model given by $f={(E_{{}_{\omega }}/E)}^2$. It was set $E=100E_{\omega }$.

Figure 2

Plots of $\epsilon \mu {\left(v^{\pm }\right)}^2$ as function of $\theta$ for the power-law model described by Eq. (33) with $x=-1.05$. The solutions were set with $E=\xi E_{\omega }$ for a few illustrative values of $\xi$. Here $\left[{\widehat{k}}_i\right]=(sin\theta ,0,cos\theta )$ and $\left[{\widehat{E}}_i\right]=(1/2)(1,\sqrt{3},0)$.

Figure 3

Plots of $\epsilon \mu {\left(v^{\pm }\right)}^2$ as function of $\theta$ in the case of an exponential model with $\alpha =0.1$. The solutions were set with $E=\xi E_{\omega }$ for a few illustrative values of $\xi$. Here $\left[{\widehat{E}}_i\right]=(1/\sqrt{2})(1,1,0)$.

Figure 4

Plots of $\epsilon \mu {\left(v^{\pm }\right)}^2$ as function of $\theta$ for the model given by $m={(B_{\omega }/B)}^2$. Here $B=100B_{\omega }$.

Figure 5

Plots of $\mu \epsilon v^2$ as a function of $\theta$ from Eq. (40) with $\gamma =15$, for $\phi$ slightly larger than $8\pi /25$. For $\phi <12\pi /25$ there exists a window of opacity near $\theta =\pi /8$, as depicted in the inset frame for $n=1000,1500,1588$.