Eigenmodes in a photonic structure with a torsion-deformed nematic liquid crystal exposed to a magnetic field

The polarized components of transmission spectrum of a multilayered photonic structure containing a nematic liquid crystal under the magnetic-field-induced torsion deformation have been investigated. Since the planarly twisted director structure of the nematic is unrelated to a decrease in its optical anisotropy, the control of the polarization and spectral characteristics of the eigenmodes is based on the occurrence of a geometric phase, whose contribution gradually increases upon nematic deformation. Along with the previously observed blue shift of the cavity $o$ modes, the anomalous shift of the cavity $e$ modes to the long-wavelength region (red shift) of the transmission spectrum has been detected. It has been shown that the countershift of the modes narrows the intermode interval. Remarkably, the extremal approaching of $e$ and $o$ modes in magnetic field $H_{ex}$ occurs below the avoided crossing phenomenon observed in the stronger equalization field $H_{eq}$ ($H_{ex}<H_{eq})$. The experimental results have been interpreted by the numerical simulation of the transmission spectra of the chiral photonic structure using the transfer matrix method.

Figure 1

Magnetooptical setup for studying the polarization and spectral characteristics of a multilayered photonic structure with a nematic LC in the torsion effect regime. Nematic molecules (shown by dashes) are initially aligned in the $x$-axis direction of the laboratory coordinate system, magnetic field $H$ is directed along the $y$-axis, $K$ are the collimators, and $P$ is the polarizer.

Figure 2

Spectra of polarization components (a) $T_{\left|\right|}\left(\lambda \right)$ and (b) $T_{\perp }\left(\lambda \right)$ without field (dashed lines) and in a field of $H=10.1\mathrm{kOe}$ (solid lines). Vertical arrows show the spectral points corresponding to the Gerber-Schadt extrema. Horizontal arrows show the cavity mode shift direction.

Figure 3

$T_{e,o}\left(\lambda \right)$ spectra (solid lines) of the eigenmodes with (a) ${\lambda }_e=472.4\mathrm{nm}$ and (b) ${\lambda }_o=474.0\mathrm{nm}$ of the PSLC cell against the background of the corresponding polarization components $T_{\left|\right|,\perp }\left(\lambda \right)$ (dashed lines). All the spectra were obtained in a field of $H_{eq}=10.1\mathrm{kOe}$.

Figure 4

Field-effect dependences of the angles of deviation of the linear polarization $\theta \left(H\right)$ from the director n on the PSLC cell output mirror for the modes with ${\lambda }_e=472.4\mathrm{nm}$ (red circles) and ${\lambda }_o=474.0\mathrm{nm}$ (blue circles) experiencing the avoided crossing ($\theta =\pm {45}^{\circ }$) in a field of $H_{eq}=10.1\mathrm{kOe}$. The threshold Fréedericksz transition field is $H_c=6.5\mathrm{kOe}$. Dashed lines correspond to the interpolation.

Figure 5

Grayscale patterns of the (a) experimental and (b) calculated unpolarized transmission spectra of the PSLC cell given as functions of wavelength and applied magnetic field. The bars on the right indicate the transmittance value.

Figure 6

Against the background of experimental transmittance (grayscale pattern), analytical trajectories (1) of spectral positions of the maxima of the eigenmodes with ${\lambda }_e=479.3\mathrm{nm}$ and ${\lambda }_o=481.7\mathrm{nm}$ for the increasing (red curves) and constant (series of green curves) mode coupling coefficient are plotted as functions of applied magnetic field.