# Light Propagation in Confined Nematic Liquid Crystals and Device Applications
## 4 Device Applications
### Nematic LC Electrically Tunable Bragg Reflectors  
Tunable Bragg reflector structures based on an LC waveguide between two glass plates have been demonstrated, where the peak reflection wavelength tuning is driven electro-optically by modifying the LC refractive index [64; 65]. Hereinafter, relying on the  
Figure 16: LC:PDMS zero\(-\)gap directional coupler switch with bimodal central waveguide and coplanar electrodes: (**a**) device top view; (**b**) cross-section of the bimodal LC waveguide. Figure 15: LC guided\(-\)wave electro\(-\)optic router light propagation in the (y; z) plane: (**a**) \(V=V_{l}=0.98\) V; (**b**) \(V=V_{h}=1.19\) V; (**c**) corresponding output intensity distributions. same physical model, two possible arrangements of electrodes are reported: a top-bottom electrode disposition and a coplanar electrode configuration. The working principle is based on a refractive index modulation to obtain a Bragg grating along the propagation direction, which allows a wavelength-selective propagation of an optical signal inside the LC layer. Estimation of the reorientation of the LC molecular director has been evaluated as described in Section 2 by considering only an elastic term and an electrostatic term in the expression of \(F\). Coupled mode theory was used for both configurations to evaluate both resonant Bragg wavelength and back-reflected power for TM or TE polarized input light at a specific grating length. A wide wavelength tuning range and a high wavelength selectivity can be achieved in both structures through application of low voltages. The configuration of the Bragg reflector device based on top-bottom electrodes to obtain an electro-optic distributed feedback waveguide (DFBW) with full adjustability of confinement and Bragg resonance wavelength is shown in Figure 17[66]. It consists of a planar glass cell with a nematic LC layer and a top-bottom configuration of transparent electrodes allowing an external voltage application. LC molecules are arranged with a planar alignment with the director **n** parallel to the propagation direction. Two-dimensional optical confinement of propagating transverse-magnetic TM light polarization is ensured through a graded-index channel by a suitable voltage applied between the comb-shaped top electrode periodic along the propagation direction and the ground plane at the opposite boundary. A Bragg grating can be induced through LC refractive index modulation over a finite propagation distance and for a given operation wavelength to allow a one-dimensional photonic lattice entailing Bragg reflection via distributed feedback. The structure can be optimized in terms of electrode dimensions, periodicity and duty-cycle along the propagation direction and the LC layer thickness to meet the required operation mode as wavelength-selective reflector and tunable drop-multiplexer. Modulation of the refractive index 100 nm below the top electrode experienced by the TM\({}_{00}\) mode versus propagation distance or applied voltages from 2 to 3 V (in 0.2 V steps) is reported in Figure 18a. As reported in Figure 18b, a wavelength tuning of 14 nm (1536-1550 nm) is achievable with applied voltages ranging from 2.5 V to 3 V (further details on technology parameters can be found in ref [66]). Figure 17: Tunable Bragg reflector with top–bottom electrode configuration with planarly anchored nematic LC. Another structure of LC tuneable Bragg reflector with a coplanar electrode configuration has been investigated and demonstrated allowing a wavelength tuning range of more than 100 nm in the near infrared with about 10 V applied [67]. Figure 19a is a schematic three-dimensional view of the device. The arrangement is made with a nematic LC planar waveguide restrained between two parallel glass slides. A pair of coplanar comb-shaped 100 nm thick ITO transparent electrodes are deposited and patterned on the inner face of the bottom substrate periodically positioned along the propagation direction.