Voltage-induced defect mode coupling in a one-dimensional photonic crystal with a twisted-nematic defect layer

Defect modes are investigated in a band gap of an electrically tunable one-dimensional photonic crystal infiltrated with a twisted-nematic liquid crystal. Their frequency shift and interference under applied voltage are studied both experimentally and theoretically. We deal with the case where the defect layer thickness is much larger than the wavelength (i.e., the Mauguin condition). It is shown theoretically that the defect modes could have a complex structure with elliptic polarization. Two series of polarized modes are coupled with each other and exhibit an avoided crossing phenomenon in the case of opposite parity.

Figure 1

Schematic of LC reorientation in a TNC under applied voltage. (a) Constant rotation at voltages below the Fréedericksz threshold. (b) Homeotropic lubrication. (c) High voltage reduces boundary planar layers.

Figure 2

Experimental layout for the measurement of transmission spectra of a PCTN cell. The light source and spectrometer blocks are built-in components of the Shimadzu UV-3600 spectrophotometer. “P” is a polarizer.

Figure 3

Experimental (solid line) and numerical (dashed line) transmission spectra of the PCTN for transverse polarizer orientation. (a) Spectral data within the PBG. (b) An extended scale showing four typical defect transmission peaks.

Figure 4

(a) Experimental and (b) simulated data of voltage-induced spectral shift of the four transmission peaks as shown in Fig. 3b. The darker color corresponds to the higher transmittance. The numbers labeled on the top and the bottom in (b) stand for the mode numbers.

Figure 5

Voltage-induced spectral shift of transmission peaks for longitudinal polarizer orientation mode. Darker color represents higher transmittance. (a) Experiment; (b) simulation.

Figure 6

Calculated transmission spectrum of unpolarized light versus voltage. Darker color corresponds to higher transmittance. The regions of intersection of T-mode No. 68 with L-modes No. 74 (a), 72 (c), 70 (e) are shown by dashed circles (same mode parity). The regions of coupling of T-mode No. 68 with L-modes No. 73 (b), 71 (d), 69 (f) are shown by solid circles (opposite mode parity). Dashed lines separate four voltage ranges exhibiting different types of mode behavior: below the threshold (I), L-mode shift (II), strong mode coupling (III), and doublets (IV).

Figure 7

The regions of mode intersection as zoomed in from encircled zones in Fig. 6. (a) Same-parity modes cross each other (see Fig. 6, zone a). (b) Opposite-parity modes avoid crossing (see FIG. 6, zone b).

Figure 8

Spatial distribution of local intensity inside the PCTN for L-mode at 558.1 nm. Oscillation suppression embarrasses calculation of the mode number. The parameters are the same as used to produce Fig. 3, except for the LC layer of 2.2 μm thickness, which is five times reduced to show the frequent oscillations in detail. The ordinary refractive index is shown by dashed line and the extraordinary refractive index in the NLC layer is indicated by a dash-dot line.