# Tailorable Brillouin Light Scattering in a Lithium Niobate Waveguide
## 3 Results  
Based on the formulas derived above, in this article, we designed a lithium niobate-suspended waveguide to measure the SBS gain that could be achieved when LN crystal is used as the medium, using COMSOL to study the inter-mode SBS effect, as shown in Figure 2c. The schematic diagram of the suspended waveguide system structure is shown in Figure 2a. Since we chose silicon dioxide as the substrate, and we exposed most of the lithium niobate to the outer air surface, few parts were in contact with the silicon dioxide substrate. The refractive index between the two materials is relatively large. The light field enhancement is located in the LN. Due to the high acoustic contrast of the lithium niobate-air interface, phonon vibration is restricted to the solid material. The general process of SBS is shown in Figure 2c (2): SBS is the interaction of light and phonons in the waveguide and is divided into FSBS and BSBS. In the process of the forward SBS effect, the strong restraint on light waves and elastic waves also increases the disturbing effects of the PE effect and the moving boundary (MB) effect [12]. This disturbance mainly comes from the Stokes (or anti-Stokes) signal scattered by the incident pump light. Therefore, when the pump light becomes larger, the electrostrictive force generated becomes larger and larger, and so has a considerable influence on Brillouin gain. This is determined by the electrostrictive force [16]. The selected waveguide width was \(w=1.5\)\(\upmu\)m, \(t=230\) nm and ring radius \(R=762.5\) nm. Under this condition, the gain of the forward SBS is shown in Figure 3.  
Figure 3: Contribution of different effects to the FSBS gain coefficient in the stimulated Brillouin scattering process, including the MB effect (orange short line), radiation pressure effect (red short line) and the entire Brillouin contribution of gain (short green line, when the waveguide width \(w=1500\) nm. Figure 2: **(a)** Schematic diagram of the suspended waveguide system; (b) Design drawing of suspended waveguide; \(t=230\) nm, \(w=1.5\)\(\upmu\)m, SiO\({}_{2}\) radius corresponds to \(R=762.5\) nm; (c) Schematic diagram of the optical dispersion diagram. Optical resonance is represented by discrete points (red and blue) along the overall dispersion curve (solid line). In the figure, \(k_{s}\) and \(k_{p}\) represent the wave vectors of stoke light and pump light, respectively. \(\omega_{s}\), \(\omega_{p}\) and \(\Omega\) represent Stokes light, pump light and generated phonon frequencies, respectively. (2) Schematic diagram of the conversion of pump light to Stokes light and phonons. Similar to the process of forward SBS, a hybrid waveguide model is also designed, and the waveguide width is selected as \(w=2.818\)\(\upmu\)m, \(t=230\) nm and ring radius \(R=1417\) nm. Since the characteristic frequency \(\Omega\) generated by phonons is very small and can be ignored compared with the frequency \(\omega\) of pump light, pump and Stokes light can be regarded as the same waveguide mode [15]. Under this condition, the BSBS gain diagram obtained is shown in Figure 4.  
By comparing the gain data of FSBS and BSBS above, it can be concluded that the Brillouin gain in BSBS can reach 0.249 W\({}^{-1}\)m\({}^{-1}\), and the FSBS gain can reach 0.31 W\({}^{-1}\)m\({}^{-1}\). FSBS achieved a higher gain, so it can be concluded that the effect of forward SBS is better than that of backward SBS, which also provides a direction for future experiments. The following is a detailed discussion on the forward SBS. When pump light and Stokes light enter the waveguide, the interaction between the two produces greater electrostrictive force and radiation pressure. Under the action of these two forces, the sound field mode will be excited in order to produce phonons. Additionally, phonons can also propagate in the waveguide, and this process is the photon-phonon coupling process. When pump light, Stokes light and phonons satisfy the conservation of energy and momentum, strong acoustic-optic coupling and FSBS effects will occur.