# Light Propagation in Confined Nematic Liquid Crystals and Device Applications
## 4 Device Applications
### Electro-Optic Router  
An integrated LC guided-wave electro-optic router based on a zero-gap directional coupler structure sketched in Figure 13 has been successfully designed [61] and experimentally demonstrated [62]. The device is made from a thin layer of nematic LC sandwiched between two glass plates to operate as a planar waveguide.  
Figure 11: Operation of a SiO2/Si groove LCW, with an electric field applied between n-Si substrate and an ITO layer: (**a**) case of no external voltage applied; (**b**) case of voltage above threshold to tilt LC molecules which allows light propagation. Reprinted with permission from Ref. [4]. Copyright 2010 IEEE.  
Figure 12: Plot of the extinction ratio (\(ER\)) as a function of the applied voltage for a SiO2/Si LCW.  
The working principle is based on an optical addressing, exploiting the relative wave-vector difference between two copropagating TM-polarized modes. The device works as an adjustable Y junction in a nematic LC, with an input bimodal stem from which two identical single-mode channels depart at a small angle, thus providing two output ports, as illustrated in Figure 14. When it is properly biased, this structure can route an optical signal towards any of the two output ports, switching between them by means of a small voltage modulation over a short propagation distance. In absence of bias, instead, the device does not provide transverse light confinement.  
A near infrared switching and signal routing at the wavelength of 1064 nm with a positive uniaxial nematic LC 5 CB has been experimentally demonstrated, with modulations of 210 mV for a device length of 160 \(\upmu\)m. The balanced superposition of TM\({}_{00}\) and TM\({}_{01}\) modes has been excited with a 0.4 mW power beam focused on the waveguide facet. The tilt and offset with respect to the channel axis was carefully adjusted using a 10\(\times\) microscope. The propagating modes gain a relative phase \(\Delta\Phi=2\pi\) after 160 \(\upmu\)m, and the output intensity peaks on the same side of the excitation when a bias of \(V_{l}=0.98\) V is set, as reported in Figure 15a,b, which shows a clear switching for \(V=V_{h}=1.19\) V. Finally, the transverse intensity profiles acquired in \(z=L\) for the two previous cases, reported in Figure 15c, highlight the substantial lateral shift achieved, with a modulation \(\Delta V=210\) mV in 0.16 mm.  
Figure 14: Image of the field distribution due to two superimposed TM guided modes in a 1 \(\times\) 2 optical switch encompassing an output Y-junction.  
Figure 13: Electro-optic router: (**a**) three-dimensional view; (**b**) side view; (**c**) top view.  
An optical switch based on the same principle as the previous device has been designed by using a zero-gap directional coupler based on LC:PDMS technology [63]. The coupling condition depends on LC refractive index controlled by in-plane voltage applied to coplanar electrodes. Figure 16a shows the top view of the device, in which two-input single mode optical waveguides are brought together at zero distance between them to form a two-mode region. The 3 \(\upmu\)m \(\times\) 3 \(\upmu\)m square cross-section of the bimodal region is reported in Figure 16b, in which coupling occurs because of the interference between the two modes propagating controlled by a voltage applied to coplanar electrodes. Light can be switched to either of the two output waveguides with an extinction ratio higher than 16 dB over a coupling length of 0.5 mm; an applied voltage of just 1.62 V is required to route light to the right-hand output waveguide (Pout 2), while 1.76 V are needed to route light to the left-hand output waveguide (Pout 1). The coupler can also be designed to behave as a demultiplexer for wavelengths 980 nm and 1550 nm by separating them into the two different output ports with a contrast better than 10 dB. Coplanar gold electrodes are used and consist of gold thin films deposited by electroplating, which can switch LC in a PDMS channel by applying only 2.85 V.