# Timing Photonic Topological Insulator for Laser Applications
## 3 Results  
Figure 2 schematically demonstrates the stability of the beam trajectory; resonator #3, as denoted in Figure 1b, was removed in order to experimentally create the lattice defect of the TPhTI. Here, the green color indicates the trajectory of the beam. _In_ and _Out_ denote the entry and exit points of the beam, respectively. The input and output can be swapped; this does not affect the beam trajectory in any way. In the considered case, when removing nine resonators (#8-#9, #12-#16 and #19-#20), we observe an ordinary waveguide. However, while preserving the structure, we can observe robust beam trajectory relative to the removal of resonator #3 from the TPhTI. In this case, resonators #8, #9, and #13-15 are used to compensate for the absence of resonator #3. Obviously, all nine internal resonators have the same purpose with respect to other restructurings. For example, the removal of resonator #22 is compensated for by resonators #12, #13, and #19. This is the main topological insulator feature; an ordinary waveguide lacks this feature and behaves unstably with respect to the mentioned restructurings.  
The topological properties of the prism array yield a robustness to restructuring. Similar photonic topological insulators are theoretically described in [17; 18; 19; 24], and practically implemented [18; 24] on several platforms. Due to the angle of incidence of the beam trajectory, the prism array is a practical implementation of [PERSON]'s toy [17], which provides a simple example of a topological insulator. As a class of restructuring, we chose the addition and removal of resonators from the array. Deeper explanations behind the topology are included in the Supplementary Materials.  
Figure 3 shows that the laser beam bypasses the defect and exits the triangular coupler. The beam trajectory passes along the surface of the TPhTI structure due to the effect of total internal reflection on the faces of the prism resonators and exits back, as evidenced by the bright spot in the upper left corner of Figure 3b. The propagating state persists against removing (Figure 3b,d) or attaching new prism resonators (Figure 3e).  
Figure 2: (**a**) The beam trajectory inside a smooth TPhTI model. (**b**) The corrected trajectory inside the TPhTI without prism resonator #3, as denoted in (**b**). The model shows that the light beam successfully bends around the defect of TPhTI.  
Figure 4 shows that the presence of a topological state does not depend on prism resonator size. To demonstrate this scalability, the rectangular prism resonators were made in two versions. The first set was manufactured from quartz glass with a refractive index of 1.43, with linear dimensions 12 \(\times\) 12 \(\times\) 8 mm\({}^{3}\) (Figure 4a). Their linear dimensions were ensured by the Maksutov method [23] with 10 um accuracy. The second set was manufactured from Chinese crown glass K9 with a refractive index of 1.517 and linear dimensions 30 \(\times\) 30 \(\times\) 30 mm\({}^{3}\), with 30 um accuracy (Figure 4b).  
Figure 3: Beam trajectory photographs. The trajectory for smooth TPhTI **(a,c)** is robust against a defect obtained by removing prism resonator #3 (**b,d**) or attaching a new prism resonator below resonator #28 **(e)**. Light beams for both a violet laser of 405 nm wavelength **(a,b)** and green laser of 532 nm (**c–e**) act in the same manner, proving the wavelength independence of the TPhTI principle.  
In Figure 5, the scalability of the TPhTI principle is stressed. First, it works for every wavelength in the visible range, as long as the refractive index is sufficiently high. Second, the resonator size was fixed at the centimeter scale; nonetheless, the principle is valid for arbitrary sizes larger than the wavelength and the beam cross-section. Please see additional trajectories for different wavelengths, resonator sizes, and tiling configurations in the Supplementary Materials.