# Addressable Refraction and Curved Soliton Waveguides Using Electric Interfaces
## 2 Materials and Methods
At 20 kV/cm, a clean waveguide is indeed formed, whose propagating modes still beat in a breathing propagation. Figure 1: Self-focusing, self-confinement and solitonic regimes as function of the static applied bias. Without bias, beam diffraction occurs. At 5 kV/cm, self-focusing is present. Between 10 and 20 kV/cm, the beam is self-confined, with a very strong pulsing. Above this bias, pulsing is reduced and the beam gets a homogeneous shape. The pure soliton regime is reached at 27 kV/cm for which the input and output beam profiles coincide. Above this formation threshold, the beam maintains a solitonic profile. At 27 kV/cm, the solitonic regime of the writing beam is reached and the propagating signal gets a homogeneous transverse profile along the entire length. The electric reflector for the self-written waveguides was investigated by dividing the whole integration volume in two regions with different applied biases. The first zone before the interface, called volume 1, received \(E_{bias}=E_{1}\) while the second zone just after the interface, called volume 2, received \(E_{bias}=E_{2}\). In Figure 3 we have reported the results of the writing beam propagation through the electric interface for different biases. Here, we injected the \(A_{W}\) at 0.6\({}^{\circ}\) with respect to the interface line direction, i.e., its complementary angle is the incidence one, and measures 89.4\({}^{\circ}\). Since the electro-optic effect decreases the refractive index, the condition \(E_{2}<E_{1}\) corresponds to a refraction angle smaller than the incidence one, as shown for the 25/20 and 25/22.5 interfaces. If \(E_{2}=E_{1}\), no interface occurs, and the soliton beam propagates straight without any modification. For \(E_{2}>E_{1}\), the refractive index of volume 2 becomes lower than the refractive index of volume 1 and consequently the transmission angle is larger than the incidence one, as for the 25/28 interface and higher. At about 25/29.38 kV/cm, the soliton receives a \(\pi\)/2 refraction, which means that the incidence angle corresponds to the critical one. Under such conditions, the beam travels along the interface; this is somehow unstable, in the sense that any slight variation of the interface electric gradient would cause a reflection or a refraction of the beam. In fact, for slightly higher interface gradients (see for example the 25/29.45 interface), after some propagation parallel to the interface, the beam will be reflected back towards volume 1. Consequently, above the critical voltage, very large lateral displacements (Giant Goos-Hanchen shift) might be experienced by the reflected beam just before being rejected back towards volume 1. Such displacement is very large close to the critical condition, decreasing as the electric contrast increases. Please note that the total reflection regime requires the beam to penetrate into volume 2 before being reflected back, as a shock against an elastic wall. Even at the critical condition, the \(\pi\)/2 refracted beam travels below the interface, not on it. The radius of curvature of the total reflection curve becomes smaller and smaller as the electric gradient increases. Figure 2: Linear propagation of the signal beam within the nonlinear waveguides as a function of the applied bias. Only at about 27 kV/cm is the signal propagation clean and without pulsing, which we call soliton waveguiding or propagation inside a waveguiding soliton.