The valley topological edge states (VTESs) and resonance loops are both important in optical communication systems, but they are usually two separate structures. In this paper, multi-layer nested valley photonic topological structures are designed. The energy transfer between loops is realized through the coupling of the evanescent field. By choosing its resonance frequency or changing the position of the light source, each loop has its own resonance frequency, and single loop or multiple-layer loops can be solely excited in the nested layered structure. Compared with similar studies, the loops do not design defects to form a resonant cavity and thus retain the integrity of the valley photonic crystal structures. This design has both the functionalities of resonance and waveguide transmission and increases the density of transmission channels. The results have application value in the reconfigurable photonic circuits.

Quantum valley Hall effects (QVHEs) are realized by introducing angular rotation of the electron wave function at points K and K' in the first Brillouin zone (BZ), which provides an intrinsic magnetic moment, analogous to that provided by the electron spin. Similarly, vortex chirality (i.e., pseudospin) of photonic energy flow provides a new degree of freedom for optical waves via the orbital angular momentum, which can be realized by reducing the lattice rotation symmetry. By constructing different types of domain walls via these structures, valley edge states can be achieved. Firstly, it is necessary to construct a two-dimensional photonic crystal unit cell. The design of the unit cell structure in this article takes into account that Bragg-scattering not only exists between lattices but also occurs between the various medium columns within the lattice. In order to obtain a wider bandgap, the method of rotating the medium columns is used to break the spatial symmetry of the photonic crystal so that the degeneracy at the high-symmetry point K in the first BZ of the reciprocal lattice is separated, thereby showing a complete bandgap in the energy band diagram. Subsequently, by analyzing the phase difference between the two lattices at point K after rotating the medium columns (i.e., the topological invariant), it is proved that the structure has opposite topological phases at the K point, thereby indicating that the edge mode is the topological boundary mode. Secondly, by periodically arranging the two lattices, a supercell can be formed. After the frequency domain simulation, the supercell in this article has two edge states, and the spin-locked properties of the VTESs can be studied. Based on the above studies, we construct a nested loop model to achieve energy exchange between photonic crystals in the form of loop coupling. The principle of this coupling is evanescent field coupling. Compared with most current coupling methods that use waveguides and cavities, evanescent field coupling does not require the construction of waveguides or other defects or cavities. The topological edge mode of the valley photonic crystal designed in this article has great local properties and does not require additional defects. Last but not least, based on the advantages of topological properties, the design can also achieve efficient transmission while maintaining the original structure.

We propose a new reconfigurable topological photonic structure model, which is a multi-layer nested photonic topological ring similar to Russian dolls. Based on the one-way transmission property of topological boundary states and the theory of coupling of electromagnetic waves, a three-layer nested loop (Fig. 7) is designed. The source position is at the center of any loop, and when the frequency is the same, different source positions will excite different transmission channels of the circuit. Furthermore, keeping the source position unchanged and changing the frequency of the source can excite multiple transmission channels. According to statistics (Fig. 8 and Fig. 9), the transmission channels in the structure will exhibit diverse forms such as single external loop, single inner loop, single middle loop, as well as double loops and triple loops. Compared with other similar schemes, the model design in this paper is intuitive, and there are no transmission channels connecting the loops. Energy transmission is entirely carried out by the coupling of the evanescent field to achieve reconfigurability. Its reconfigurability does not require any external conditions, which greatly reduces the complexity and difficulty of the design.

The VTES has become a new research hotspot in topological photonics because of its flexibility and diversity. In this paper, reconfigurable topological channels in the form of multiple-layer nested loops have been designed. By combining the topological edge states of the valley photonic crystal with the resonance loops, a variety of different channels can be excited. Although the reconfigurable topological waveguides have been widely studied, the unique value of our design is that the reconfigurable method does not rely on external conditions; instead, single or multilayer circuits can be selectively excited by setting the location and frequency of the source. This model can be used as a multi-channel frequency selector or optical resonator. Different from the general selector and resonator, the channel in the structure is a topological loop, which combines the common characteristics of topological protection and resonance, so as to reduce the loss as far as possible. It provides a new idea for the application of VTESs in optical devices.