Optical band gap in a cholesteric elastomer doped by metallic nanospheres

We analyzed the optical band gaps for axially propagating electromagnetic waves throughout a metallic doped cholesteric elastomer. The composed medium is made of metallic nanospheres (silver) randomly dispersed in a cholesteric elastomer liquid crystal whose dielectric properties can be represented by a resonant effective uniaxial tensor. We found that the band gap properties of the periodic system greatly depend on the volume fraction of nanoparticles in the cholesteric elastomer. In particular, we observed a displacement of the reflection band for quite small fraction volumes whereas for larger values of this fraction there appears a secondary band in the higher frequency region. We also have calculated the transmittance and reflectance spectra for our system. These calculations verify the mentioned band structure and provide additional information about the polarization features of the radiation.

Figure 1

Schematic of the system.

Figure 2

Resonance wavelength of the relative permittivities (a) ${\epsilon }_d$ and (b) ${\epsilon }_{\perp }^e$ versus filling factor parametrized for various values of the deformation parameter.

Figure 3

Averaged refraction index $n_{av}=(n_1+2n_2)/3$ for an elastomer without deformation versus wavelength parametrized by the volume fraction $f$. (a) Real part and (b) imaginary part. In both panels, insets are shown.

Figure 4

The same as Fig. 3 but parametrized by the deformation parameter $\eta$ for the volume fraction $f=0.001$. (a) Real part and (b) imaginary part. In both panels, insets are shown.

Figure 5

The same as Fig. 4 but parametrized by the deformation parameter $\eta$ for the volume fraction $f=0.01$. (a) Real part and (b) imaginary part. In both panels, insets are shown.

Figure 6

Refraction indexes $n_1$ and $n_2$ for the elastomer without contamination ($f=0$) against wavelength parametrized by $\eta$. (a) Real part of $n_1$, (b) imaginary part of $n_1$, and (c) real part of $n_2$.

Figure 7

Refraction indexes for a doped elastomer without deformation ($\eta =1$) parametrized by $f$. (a) Real part of $n_1$, (b) imaginary part of $n_1$, (c) real part of $n_2$, and (d) imaginary part of $n_2$.

Figure 8

Refraction indexes for a doped stretch elastomer ($\eta =1.054$) parametrized by $f$. (a) Real part of $n_1$, (b) imaginary part of $n_1$, (c) real part of $n_2$, and (d) imaginary part of $n_2$.

Figure 9

Refraction indexes for a doped stretch elastomer ($\eta =1.104$) parametrized by $f$. (a) Real part of $n_1$, (b) imaginary part of $n_1$, (c) real part of $n_2$, and (d) imaginary part of $n_2$.

Figure 10

Refraction indexes for a doped stretch elastomer ($f=0.01$) parametrized by the deformation parameter $\eta$. (a) Real part of $n_1$, (b) imaginary part of $n_1$, (c) real part of $n_2$ and (d) imaginary part of $n_2$.

Figure 11

Reflectance ($R_{RR},R_{LR}$, and $R_{LL}$) and transmittance ($T_{RR}$, $T_{LR}$, and $T_{LL}$) versus vacuum wavelength for $f=0.01$, in (a) and (b) $\eta =1$ and in (c) and (d) $\eta =1.05$. The right panels display the interval (350 nm, 500 nm) whereas the left panels show the interval (550 nm, 700 nm).