In this study, we propose a splitter in a silicon photonics platform which separates optical vortex signals into two branches with the desired wave intensity. The splitting operation is installed in a very small area keeping the global structure of the topological and trivial regions intact. Explicitly, the topological waveguide is formed by interfacing two topologically distinct honeycomb-type photonic crystals (PhCs) [9], where the topological optic modes propagate in a way mimicking the spin-momentum locking in the prominent quantum spin-Hall insulators with the role of optic spin played by vorticity associated with the whirling Poynting vector in hexagonal unit cells. As shown schematically in Fig. 1a, b, the splitter device is composed of five semiconductor photonic crystals, two topological insulators, and two trivial insulators surrounding a rhombic patch X. Patch X varies from trivial to topological via a semi-metallic state with a linear Dirac dispersion similar to graphene. Upon engineering the sign and size of the photonic band gap of the central X patch, an effective potential is formed for the input topological interface wave, which controls the tunnelling route and relative mode intensity [Fig. 1c, d, and e]. It is confirmed experimentally that in Si-photonics platform the power ratio between two output ports of the splitter can be continuously tuned in the range of 10.2 to -9.2 dB with the optic vortex modes intact. With a miniaturization capability of approximately 10 µm, surpassing traditional silicon-based Y-splitters, the proposed topological photonic splitter is useful for topological photonics applications. Moreover, it is expected to significantly improve the information processing speed and transportation density in T-bit class optical networks.
The photonic topology in a honeycomb-type PhC emerges from its trivial counterpart via a band inversion between the \(p\) and \(d\) eigenmodes hosted in the hexagonal unit cell [9]. The \({k}\bullet {p}\) Hamiltonian around the Γ point of the Brillouin zone takes the Dirac form
$${H}_{+}=\left[\begin{array}{cc}M& -i\left|A\right|{k}_{+}\\ i\left|A\right|{k}_{-}& -M\end{array}\right]$$
with basis \(\left(|{p}_{+}⟩ |{d}_{+}⟩\right),\)effective mass \(M\) (\(-M\)) of mode \(|{p}_{+}⟩\) (\(|{d}_{+}⟩\)) referring to the frequency measured from the bandgap centre, and \({k}_{\pm }={k}_{x}\pm i{k}_{y}\), where \(|{p}_{+}⟩\) (\(|{d}_{+}⟩\)) carries optical vorticity + 1 (+ 2). Adapting to the input channel along \(y=0\) as shown in Fig. 1a, we recast the above Dirac Hamiltonian as
$${H}_{+}=\left[\begin{array}{cc}M& \left|A\right|\left({-k}_{x}-{\partial }_{y}\right)\\ \left|A\right|\left({-k}_{x}+{\partial }_{y}\right)& -M\end{array}\right]$$
where the basis is transformed to \({\left(|{p}_{+}⟩ {e}^{-i\pi /2}|{d}_{+}⟩\right)}^{T}\), \(M>0\) for \(y<0\) and \(M<0\) for \(y>0\) with the size of the bandgap common to topological and trivial PhCs upon design. A zero-energy soliton can be derived as
$$\psi =\left[\begin{array}{c}1\\ 1\end{array}\right]{e}^{\left(M/\left|A\right|\right)y}$$
for \({k}_{x}=0\), similar to the Jackiw-Rebbi soliton for the spin-1/2 fermion, in which the soliton wavefunction decays exponentially from the interface on both sides [39].
In the device shown in Fig. 1a, an EM flow \(\left|0\right.⟩\to\)\(\left|1\right.⟩\) (\(\left|0\right.⟩\to\)\(\left|2\right.⟩\)) occurs when X is the extension of the topological (trivial) PhC, as shown in Fig. 2a (Fig. 2e) obtained by numerical simulations. Now we consider the case where the central rhombic patch X is fabricated as a topological PhC with a smaller mass \(0<m<M.\) Primarily, the topological interface channel is along the course \(\left|0\right.⟩\to \left|1\right.⟩\). Nevertheless, the wavefunction with amplitude \(\text{exp}\left[y/\left(\left|A\right|/m\right)\right]\) penetrates into patch X and reaches the course \(\left|0\right.⟩\to \left|2\right.⟩\) provided that the width of patch X is small compared with the decay length \(\left|A\right|/m\). The intensity of the tunnelled wavefunction increases when the bandgap of patch X is reduced, as shown in Fig. 2b. When the band gap is closely associated with a perfect honeycomb structure, output porters \(\left|1\right.⟩\) and \(\left|2\right.⟩\)have the same intensities (Fig. 2c). A similar process occurs when patch X is fabricated as a trivial PhC with a smaller photonic bandgap (Fig. 2d). This achieves the functionality of a splitter for present topological photonic waveguides.
We now proceed to experimentally realise the above idea. First, photonic structures were placed in each domain, as shown in Fig. 1a, where triangular nanoholes were arranged in a honeycomb-type lattice with C6v symmetry on a silicon-on-insulator (SOI) wafer (see Fig. 1b). In this structure, a Si core layer with a film thickness of 220 nm, which is normally used in silicon photonics circuits, was sandwiched between a ~ 3 µm thick SiO2 cladding and an air cladding. In the simulation, the period of the honeycomb-type lattice was fixed at 800 nm, and the distance from the centre of the hexagonal unit cell to the centre of the nanoholes (R) and the length of one side of the nanoholes (L) were used as parameters for analysis.
Using the designed photonic structure, the transmission characteristics of the optical vortex splitter were analysed based on the operating principles in Figs. 1c-e. Figure 2 shows the propagation characteristics of the device calculated using the finite-difference time-domain (FDTD) method, where patch X comprises 4×6 = 24 unit cells. Figures 2a, c, and e show the magnetic field distributions of the propagating optical vortices (Hz) when placing a topological photonic structure (R = 284 nm, L = 270 nm), a gapless photonic structure (R = 267 nm, L = 270 nm), and a trivial photonic structure (R = 244 nm, L = 270 nm) in patch X, respectively. When a topological or trivial photonic structure was arranged in patch X, the input was directly connected to each output through a topological edge-state waveguide, and the optical vortex signal was output only to \(\left|1\right.⟩\) or \(\left|2\right.⟩\). In contrast, when the gapless photonic structure, wherein the \(|{p}_{+}⟩\) and \(|{d}_{+}⟩\) modes degenerate in frequency at the centre of the Brillouin zone, was arranged in patch X, the intensity ratio of the optical vortex signal emitted from outputs \(\left|1\right.⟩\) and \(\left|2\right.⟩\) approached 1:1 (see Supplementary Information S1 for time-dependent propagation characteristics).
Based on the design shown in Fig. 2, various PhCs with different parameters were prepared and their optical properties were evaluated before fabricating the actual devices. Figure 3a shows the scanning electron microscopy (SEM) images of PhCs varying from topological to trivial in a graphene-like structure. The dimensions of each structure were (R, L) = (284 nm, 270 nm), (276 nm, 270 nm), (267 nm, 270 nm), (252 nm, 270 nm), and (244 nm, 270 nm). To suppress the rounded corners of the triangular nanoholes due to the proximity effect in electron beam lithography, mask shape correction based on big data processing was introduced. Consequently, the corner radius of the triangular nanoholes “r” was less than 30 nm (see supplementary information S2 for details on device fabrication), which was considered in the analysis in Fig. 2. Figure 3a also shows photonic band diagrams of each structure measured in the energy range from 0.73 eV (λ = 1700 nm) to 0.92 eV (λ = 1350 nm) using infrared hyperspectral Fourier image spectroscopy [40, 41] (see methods section and supplementary information S3 for more information on measurement). The band structures were found to be almost the same as those in Figs. 2a-e, and the topology of the PhCs changed around (R, L) = (267 nm, 270 nm) because the band intensity of the structure with a graphene-like band diagram was weakened in this measurement. Moreover, as shown in Fig. 3a, the intensities of the high-energy and low-energy bands switched near the Γ point in the band diagrams of the topologically distinct PhCs, indicating that the electromagnetic modes of the \(p\)-wave and \(d\)-wave underwent band inversion. These results correspond well with the simulation results shown in Fig. 2.
An optical vortex splitter was fabricated based on the design (see the Methods section and Supplementary Information S4 for more information on the device fabrication and layout). Figure 3b shows the optical microscopy and SEM images of the device. In this device, a topological converter was inserted to realise high-efficiency coupling between the silicon wire and topological waveguides [35]. The values of R and L for the trivial/topological photonic structures were set to 244/270 and 284/270 nm, respectively. As described above, R of the photonic structure arranged in patch X was varied from 244 to 284 nm so that the centre frequency of the bandgap would always be nearly equivalent to the wavelength of the input light of 1540 nm (see Methods section and Supplementary Information S5 for more information on the measurement setup). Figure 3c shows the output ratio (\(\left|2\right.⟩\)/\(\left|1\right.⟩\)) of the device as a function of the dimensions of the photonic structure placed in patch X (simulation results considering the rounded corners of the triangular nanohole (r = 30 nm) are also plotted). In this experiment, we prepared several types of devices in which various photonic structures with different parameters were arranged in patch X. Based on the design shown in Fig. 2, R was changed such that the band diagram of the photonic structure gradually shifted from a topological structure to a trivial one. As R of the photonic structure arranged in patch X increased, the output intensity of \(\left|2\right.⟩\) was suppressed and the output intensity of \(\left|1\right.⟩\) gradually increased. Consequently, the output intensity ratio changed from 10.2 to -9.2 dB (see supplementary information S6 for propagation characteristics of the topological splitter when switching input ports). This demonstration of the controlled splitting of topological photonic waveguides is crucial for the development of TPICs. The phenomenon unveiled in this work sheds new light on the engineering of topological propagation in various platforms towards innovative functionality.