Photonic defect modes in a cholesteric liquid crystal with a resonant nanocomposite layer and a twist defect

We have studied spectral properties of a cholesteric liquid crystal with a combined defect consisting of a nanocomposite layer and a twist. The nanocomposite layer is made of metallic nanoballs dispersed in a transparent matrix and featuring effective resonant permittivity. A solution has been found for the transmission spectrum of circularly polarized waves in the structure. We have analyzed spectral splitting of the defect mode in the band gap of the cholesteric when its frequency coincides with the nanocomposite resonant frequency. Defect modes have characteristics strongly dependent on the magnitude and the sign of the phase difference of the cholesteric helix on both sides of the defect layer. It has been found that the band gap width and the position and localization degree of defect modes can be effectively controlled by external fields applied to the cholesteric.

Figure 1

Schematic of the CLC with a combination of defects.

Figure 2

Imaginary ${\varepsilon }_{\mathrm{mix}}^{\prime \prime }$ (dashed curve) and real ${\varepsilon }_{\mathrm{mix}}^{\prime }$ (solid curve) parts of the effective permittivity ${\varepsilon }_{\mathrm{mix}}$ versus wavelength. The filling factors (a) $f = 0.02$ and (b) $f = 0.1$.

Figure 3

Transmission spectrum for right- (solid curve) and left-handed (dashed curve) polarizations for α = 0: (a) $f = 0$ and (b) $f = 0.02$.

Figure 4

Transmission spectra of the structure for various α's: (a) α > 0 and (b) α < 0. The bold curves refer to the right-handed circular polarizations, and the thin curves refer to the left-handed circular polarizations of light, $f = 0.02$.

Figure 5

Distribution of the squared electric field modulus in defect modes with λ = 388 nm [option $\alpha ={30}^{\circ }$ corresponds to option 2 in Fig. 4]. (a) Wave with right-handed circular polarization and (b) wave with left-handed circular polarization, $f = 0.02$.

Figure 6

Transmission spectrum for various helix pitches. (a) $p = 305$ nm and (b) $p = 320$ nm. The solid and dashed curves refer to the right-handed and left-handed circular polarizations of light, respectively, $f = 0.02$ and α = −30°.

Figure 7

(a) Transmission coefficient for a system of two cholesterics with a defect (solid curve) and for each of the cholesterics (dashed curve) with the pitch on the left of the defect $p_1=275\mathrm{nm}$ (dotted curve) and $p_2=290\mathrm{nm}$ (dotted curve). (b) Maximum squared modulus of the electric field of the defect mode as a function of the pitch $p_2$. The remaining parameters are the same as in Fig. 3.

Figure 8

(a) Transmission spectra for various $p_2$'s, dashed-and-dotted curve: $p_2=275\mathrm{nm}$; dashed curve: $p_2=290\mathrm{nm}$; solid curve: $p_2=305\mathrm{nm}$; and $\alpha =-{30}^{\circ }$. (b) Maximum of the squared electric field modulus of the long-wavelength defect mode as a function of the pitch $p_2$, $\alpha =-{30}^{\circ }$. The bold curves refer to the right-handed circular polarizations, and the thin curves refer to the left-handed circular polarizations of light, $f=0.02$.