The photonic artificial intelligence (AI) acceleration chip has emerged as a breakthrough in high-performance intelligent computing due to the advantages of photonic high-speed, parallelism, low crosstalk, low energy consumption, and high interconnection bandwidth [1]. This advancement is further facilitated by the rapid development of integrated optoelectronics technology. Optical synaptic arrays are the core hardware components of AI acceleration chips. By leveraging large-scale optical synaptic array integration, it is possible to achieve fast, multi-channel parallel computing architecture design [2–5]. In the optical synapse array, each optical synapse is implemented using a tunable optical switch to adjust the weights during neural network computation. Therefore, the performance of a single optical switch will significantly impact the computational energy efficiency and computational density of the optical neuromorphic network. In traditional research processes and engineering applications, volatile optical switches based on thermo-optic and electro-optic effects are the primary devices used to construct optical neural networks [2,3]. However, these optical switches require continuous external energy to maintain the switching state. Therefore, the optical neural networks constructed using these volatile optical switches need to consume a significant amount of energy during the training process. This limitation hinders the development of photonic neuromorphic computational networks.

Sulfur-based phase change materials, i.e., PCMs constructed with the three elements of Ge-Sb-Te, are characterized by high optical contrast ($\mathrm{\Delta }n>1$), nonvolatility (zero static power consumption), fast phase change speed ($\sim \mathrm{ns}$), and high stability, which provides a new opportunity for constructing low-power, energy-efficient, and highly integrated photonic devices [6,7]. They are used in reconfigurable photonic applications such as optical switches [8–14], optical routers [15,16], and metasurfaces [17–21]. Compared with traditional electronic switches, optical switches based on PCMs can sustain their switching state for ${10}^4\mathrm{s}$ without the need for continuous static energy supply. Therefore, it can greatly reduce energy consumption, especially in application scenarios that require frequent switching of the device state. However, the change in optical transmittance in different crystalline states is minimal due to the weak interaction between the waveguide mode and PCMs when the PCMs film is directly sputtered on top of the optical waveguide. Therefore, researchers have designed different waveguide structures such as the ridge–slot waveguide [22], sub-wavelength grating ridge–slot waveguide [23], surface plasmonic polariton waveguide [24,25], and metasurface mode convertor [26], to enhance interaction between the optical field and the PCM. In addition, Mach–Zehnder interference (MZI) [9,12,27] and micro-ring resonator [28–30] effects are utilized to enhance the modulation range of optical transmittance. However, their large footprints seriously impede the large-scale integration of optical neuromorphic networks. Therefore, constructing compact resonant structures to enhance the modulation of the optical field by PCMs is a key issue for the large-scale integration of nonvolatile optical switch arrays. The topological photonics construction of the TIS, topological insulators, and topological semimetals in the optical system can enable various novel device functions, such as unidirectional transmission and defect insensitivity [31–34]. For 1D topological photonic devices, splicing two photonic crystals or quasi-crystals with opposite signs of the imaginary part of the bandgap impedance can construct a compact resonant device [35]. The resonant modes excited by this topological device are bound at the photonic crystal interface, gradually decay on both sides, and are referred to as the TIS. The tightly bound optical field and transmission robustness of the TIS, similar to other topological modes, result in a smaller footprint and enhanced process robustness of photonic devices constructed based on the TIS. The modulation of the excitation wavelength of the TIS can be achieved by altering the structure of photonic crystals.

In this paper, we investigate the excitation of 1D TIS by designing the energy band structure of photonic crystals. The designed TPC consists of two quasi-1D PCs spliced with the same bandgap center frequency. The energy band structure of a quasi-PC can be modified by modulating the crystallization state of the PCM (${\mathrm{Sb}}_2{\mathrm{Se}}_3$). This modulation affects the excitation wavelength of the TIS, enabling the construction of a compact optical switching device similar to a micro-ring resonator. In the simulation results, the device IL is less than 2 dB, and the ER is greater than 18 dB within the 9 μm modulation length. The overall device footprint is only $0.5\mathrm{\mu m}\times 18\mathrm{\mu m}$. We believe that this nonvolatile optical switching device, based on TIS modulation, has greater research value and application potential in large-scale optical neural networks.

Consider a dielectric ABA layered structure distributed along one space dimension. A plane wave from free space is incident normally on the 1D PC and the reflection coefficient of the electric field $E_x$ is given by $r$. When the frequency of the incident wave is inside the bandgap of this system, the impedance $Z$ of the system and the reflection coefficient $r$ are related by $Z=(1+r)/(1-r)Z_0$, where $Z_0$ is the vacuum impedance, and $Z$ is purely imaginary. The condition for the presence of the TIS is simply $Z_1+Z_2=0$ [35]. To excite the TIS, two 1D photonic crystals, with the same bandgap center frequency but opposite impedance signs light, are spliced together, as shown in Fig. 1(a). A 1D TPC with the impedance of zero at a specific frequency can be constructed by adjusting the refractive index and width of the flat dielectric layers in the left and right 1D PCs. However, this 1D PC is impractical to fabricate due to its infinite width. We can create quasi-1D TPC by setting the effective refractive index of the fundamental mode in the waveguide cross-section equal to the material refractive index of the corresponding flat dielectric layer. Unlike 1D quasi-periodic structures, quasi-1D photonic crystals have a definite period in one direction in the Cartesian coordinate system (i.e., along the $z$ axis), but do not conform to the concept of infinite extension in the other two directions (i.e., along the $x$ and $y$ axes). Based on this, we can construct the quasi-1D TPC by modifying the effective refractive index of the fundamental mode of the waveguide through etching air holes or depositing PCMs on the silicon waveguide. By regulating the crystalline state of the PCM, we can control the excitation wavelength of the TIS, which subsequently influences the output optical intensity of the device. We designed two quasi-1D PCs consisting of the period structure of air holes-silicon (quasi-1D PC_L) and air holes-${\mathrm{Sb}}_2{\mathrm{Se}}_3$ (quasi-1D PC_R), respectively. The 3D structure diagram of the topological optical switch is shown in Fig. 1(b). The silicon ridge waveguide is fabricated on the silicon-on-insulator (SOI) wafer, which has a height of 220 nm. The height of the slab ($h_{\mathrm{slab}}$) and ridge ($h_{\text{ridge}}$) is 150 nm and 70 nm, respectively. The width of the ridge ($w_{\text{ridge}}$) is 500 nm. Etching periodic air holes and depositing ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ on the ridge waveguide form quasi-1D PCs, whose depth is the same as $h_{\text{ridge}}$.

In order to simplify the band structure calculation of the quasi-1D PCs in Fig. 1(b) into a 1D energy band calculation, we equate the mode effective refractive indices of the waveguide cross-section ($x-y$ plane) to the vacuum refractive indices of the different dielectric layers (A or B). Therefore, the correspondence between the refractive indices of different dielectric layers and effective refractive indices of different cross-sections of the ridge waveguide is $$\{\begin{array}{c}{n}_{A_1}=n_{\mathrm{eff},\text{air}\text{hole}}\\ n_{B_1}=n_{\mathrm{eff},\mathrm{Si}}\\ n_{A_2}=n_{\mathrm{eff},{\mathrm{Sb}}_2{\mathrm{Se}}_3}\\ n_{B_2}=n_{\mathrm{eff},\text{air}\text{hole}}\end{array}.$$(1)

Considering the fundamental transverse electric mode (quasi-TE mode) excitation condition, the normalized electric field distributions of different cross-sections of the ridge waveguide are shown in Fig. 2. The black line represents the outline of the cross-section geometry of the waveguide structures, while the white arrow indicates the polarization direction of the normalized electric field. For the cross-section of the waveguide structure shown in Fig. 2(a), the air hole is etched into the ridge waveguide with an etching depth of 70 nm (along the $y$ axis). Meanwhile, the width of the etching air hole is 200 nm (along the $x$ axis). Due to the small size of the etching air hole, the electric field is mainly restricted to the silicon region, which is different from the conventional slot waveguide. In the following content, we call this cross-section structure a ridge–slot waveguide. The indices of silicon and silica glass are 3.455 and 1.445, respectively. The refractive index of ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ thin film is measured using the ellipsometry device. The refractive indices of ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ in the amorphous and crystalline states are 3.328 and $4.058+0.005i$, respectively, at the wavelength of 1550 nm. Figure 2(b) illustrates the normalized electric field distribution for the quasi-TE mode of a conventional ridge waveguide. In Figs. 2(c) and 2(d), the ridge waveguide consists of two materials: silicon and a phase change material. The slab layer is silicon, while the ridge region is made of PCM. The difference between Figs. 2(c) and 2(d) is that the PCM is in different states (amorphous state and crystalline state). The effective refractive indices of the quasi-TE modes within different cross-sections are also indicated in Fig. 2. Combined with Eq. (1), we can determine the material refractive index of each flat layer of the 1D PC in Fig. 1(a).

In order to excite a TIS in a bandgap, the quasi-1D photonic crystals on the left and the right need to have impedances of opposite signs. In the bandgap, the absolute value of the impedance of the 1D photonic crystal is denoted as $\xi$. For the $n$th bandgap, the impedance of the 1D PC satisfies the following equation: $$\mathrm{sgn}[{\xi }^{(n)}]={(-1)}^{n+l}\exp \left(i\sum _{m=0}^{n-1}{\theta }_m^{\mathrm{Zak}}\right),$$(2)where the integer $l$ represents the number of crossing points of the energy band below the $n$th bandgap. ${\theta }^{\mathrm{Zak}}$ is the topological invariant of the $m$th band edge of the energy band, also known as the Zak phase, which is 0 or $\pi$. The topological invariant is $\pi$ when the band edge crosses a topological singularity and is 0 otherwise. It can be calculated by the following equation: $${\theta }_n^{\mathrm{Zak}}={\int }_{\frac{-\pi }{\mathrm{\Lambda }}}^{\frac{-\pi }{\mathrm{\Lambda }}}[i{\int }_{\mathrm{unit}}\epsilon (z)u_{n,q}^{*}(z){\partial }_q{u}_{n,q}(z)]\mathrm{d}q,$$(3)where $i{\int }_{\mathrm{unit}}\epsilon (z)u_{n,q}^{*}(z){\partial }_q{u}_{n,q}(z)$ represents the Berry connection. $\epsilon (z)$ denotes the dielectric function, and $u_{n,q}(z)$ is the periodic-in-cell part of the Bloch electric field eigenfunction of a state on the $n$th band with wave vector $q$. From Eq. (3), we can see that this formula cannot give the Zak phase for the zeroth-order edge (first band edge). The Zak phase of the lowest 0th band is determined by the sign of $1-{\epsilon }_a{\mu }_b/({\epsilon }_b{\mu }_a)$, i.e., $$\exp (i{\theta }_0^{\mathrm{Zak}})=\mathrm{sgn}[1-\frac{{\epsilon }_a{\mu }_b}{{\epsilon }_b{\mu }_a}].$$(4)

Here, ${\epsilon }_a$, ${\epsilon }_b$, ${\mu }_a$, and ${\mu }_b$ are the relative permittivity and permeability of slabs A and B, respectively. Combining Eqs. (1)–(4), the gap topological invariants of each gap for the left and right 1D PCs are obtained and labeled by blue when sgn $[\zeta ]>0$ and purple when sgn $[\zeta ]<0$. The Zak phase of each band edge which is encoded by red numbers is marked with green letters in Figs. 3(a)–3(c). Among them, Fig. 3(a) is the energy band structure of 1D PC_L, and Figs. 3(b) and 3(c) are the energy band structure of 1D PC_R when the PCM is in the amorphous state (${\text{a\_Sb}}_2{\mathrm{Se}}_3$) and crystalline state (${\text{c\_Sb}}_2{\mathrm{Se}}_3$), respectively. The first and third gaps of the 1D PC_L and 1D PC_R exhibit different gap topological invariants, indicating that the TIS exists in these photonic gaps when splicing the left and right 1D PC together. Taking the first bandgap as an example, the formation of the TIS can be visualized by observing the eigenmodes of the isolation bands above and below the bandgap. Figures 3(d)–3(f) represent the eigenmodes with $k_x=\pi$ of 1D PC_L and 1D PC_R on isolation bands 0 and 1, respectively. Considering the prevalent use of quasi-TE mode for transmission information in 3D on-chip waveguides, we limit our analysis to the in-plane $E_x$ component in the simplified quasi-1D photonic crystal simulation model. In the case of 1D PC_L, the eigenmode corresponding to isolation band 0 is an even mode, while the eigenmode corresponding to isolation band 1 is an odd mode. In contrast, for 1D PC_R, the eigenmodes corresponding to isolation bands 0 and 1 are the inverse of those observed in one-dimensional 1D PC_L. This means that the evolutions of the eigenmodes in the 1D PC_L and 1D PC_R systems are completely opposite processes. The above phenomenon can be regarded as an opposite process in the same system when 1D PC_L and 1D PC_R have the same band structure. In this case, the optical responses of the 1D PC_L and 1D PC_R will have a phase difference of $\pi$. It can be demonstrated that the splicing of two photonic crystals can result in high transmission in the bandgap, like the electromagnetically induced transparency. We use the finite element method (FEM) to simulate the transmission spectrum of the quasi-1D TPC consisting of two 1D PCs within 30 period numbers, as shown in Fig. 3(g). Resonance peaks are located in the center of the first gap, which corresponds to the TIS. Moreover, the wavelength corresponding to the TIS is shifted due to the change in refractive index of the PCM in different crystallization states. In this way, we realize the intensity modulation. Meanwhile, it is important to note that the frequency corresponding to the excitation TIS is related to the PC period and refractive indices by satisfying the following relationship: $${\omega }_m=\frac{k\pi c}{n_a{d}_a+n_b(\mathrm{\Lambda }-d_a)},$$(5)where $c$ denotes the wave speed in vacuum, $\mathrm{\Lambda }$ is the period of the 1D PC, and $k$ represents the gap number. The inset in Fig. 3(g) shows detailed information about the transmission spectrum of a 1D topological photonic crystal optical switch. The IL is less than 0.5 dB with an ER greater than 15 dB. Meanwhile, to set the center operation wavelength of the topological optical switching at 1550 nm, the periods of 1D PC_L and 1D PC_R are approximately 300 nm and 295 nm, respectively. Figure 3(h) shows the 2D transmission spectrum of the designed quasi-1D topological optical switch using the effective refractive index of the fundamental guide mode to approximate the refractive index of the dielectric flat layer. The excited TIS corresponds to a wavelength of 1550.8 nm, which is a slight deviation from the intended 1550 nm. The reason for this is the inability to accurately solve the energy band center frequency according to Eq. (5).

In order to verify the correctness of the aforementioned nonvolatile topological optical switch simplified model, we utilized the 3D time-domain finite-difference (FDTD) method to simulate the transmission and electric field distributions. Meanwhile, considering the challenge of controlling the period error within 5 nm during actual processing, the period of 1D PC_R is set to 300 nm. This small approximation does not result in the disappearance of the TIS, but rather in a shift in the excitation wavelength of the TIS, as illustrated in Fig. 4(a). Meanwhile, the ER of the topological optical switch is about 18.5 dB with a PCM modulation length of 9 μm ($300\mathrm{nm}\times 30\text{units}$) when the PCM is in different crystalline states. When the PCM is in an amorphous state, the topological optical switch operates in the “on” state, with an IL of approximately 1.92 dB. The reason for the greater IL in the 3D transmission model compared to the 2D simplified model is that the effective refractive index of the mode within a finite cross-sectional area is only approximated in the simplified model by replacing the refractive index of the flat plate layer. However, in the 3D real model, this cross-sectional area is expected to be infinite. Therefore, the results of this refractive index approximation are not entirely consistent with the 3D transmission process. Second, in the 2D approximate model, efforts are made to further reduce the computational complexity. We define the boundary condition along the $x$ axis as a continuous boundary. This represents that the boundary does not include lattice scattering caused by sudden refractive index changes. As a result, the IL of the 2D simplified model is almost zero, but this is challenging to achieve in the 3D transmission model.

Figures 4(b) and 4(c) represent the normalized electric field distribution of the TE polarization component of the topological optical switching device when the PCM is in amorphous and crystalline states, respectively, at an input wavelength of 1556.2 nm. It can be observed that when the PCM is amorphous, the maximum electric field strength is situated at the boundary of 1D PC_L and 1D PC_R and gradually decreases on both sides. This electric field distribution is one of the characteristics of the TIS. When the phase change material transitions from an amorphous to a crystalline state, the equivalent refractive index of the A2 flat plate layer changes in the 2D simplified model. Consequently, the energy band structure of 1D PC_R also changes. A small shift in the energy band center frequency can be observed in Figs. 3(b) and 3(c). Therefore, at the incident wavelength of 1556.2 nm, the phase change material cannot excite the TIS when it is amorphous, but it experiences a significant transmission loss. The optical field propagation is shown in Fig. 4(c).

Meanwhile, we analyzed the processing robustness of 1D topology optical switch. The TIS excitation wavelength, IL, and ER are evaluated by scanning parameters such as air hole width (width), duty cycle, PCM deposition width (PCM deposition error), and ridge waveguide etching depth (error of etching depth). Figure 5 illustrates the tolerance of the device’s performance to process errors. The excitation wavelength of the TIS will shift considerably when the etching width of the air holes is changed. This is because the change in the width of the air holes results in a significant difference in the effective refractive indices of the flat layers A1 and B2 in 1D PC_L and 1D PC_R, respectively. This, in turn, affects the energy band structure of the two 1D photonic crystals. This also proves that the modulation of the TIS excitation wavelength can be achieved by adjusting the width of the air holes, confirming the accuracy of the theoretical analysis. As the width of the air holes is changed, the IL of the device remains around 2 dB, and the ER is consistently greater than 16 dB. The bandgap center frequency, which satisfies Eq. (4), does not undergo a significant shift while the period length remains unchanged when the duty cycle of the device is changed. Therefore, in Fig. 5(b), the TIS excitation wavelength does not shift significantly with the change in duty cycle. In addition, there may be errors in the deposition width of the PCM during the processing of the PCM deposition area. The deposition error only affects the effective refractive index of the equivalent flat layer A2. Since the effective refractive index of the fundamental mode of the waveguide cross-section does not change significantly within the width error of 50 nm, the TIS excitation wavelength is not significantly shifted, as shown in Fig. 5(c). Also, the small effective refractive index change has no significant effect on the device’s IL or ER. In contrast, the etching depth has a significant impact on the device performance and the excitation wavelength of the TIS. For a ridge waveguide with a 150-nm-thick slab layer, an etching depth error of 20 nm can significantly impact device performance because it leads to a drastic change in the effective refractive index of the waveguide mode. And the smaller the etching depth of the air holes, the closer the normal ridge waveguide. This results in a rapid decrease in the IL and ER of the device. The TIS excitation wavelength is significantly shifted due to the substantial impact of the etching depth on the effective refractive index. The wavelength shift due to the error per unit etching depth (unit: nm) is about 0.5 nm. By analyzing the effect of processing errors on the device performance, this topological optical switch device does not have demanding requirements for processing accuracy. Therefore, we believe that the 1D topological optical switches involved have better processing robustness.

In this section, we furnish a brief presentation on the fabrication technology of photonic crystal topological interface state modulation for nonvolatile optical switching. The fabrication process flow is illustrated in Fig. 6. The device is fabricated on an SOI wafer with a 220-nm-thick top silicon (Si) layer and a 2-μm-thick buried silicon oxide (${\mathrm{SiO}}_2$) layer. First, clean the SOI wafer and add the photoresist coating on the silicon layer. The ridge waveguide with air holes was patterned by the electron beam lithography (EBL) process and then etched by the inductively coupled plasma (ICP) process after the developing process. After these processes, a second EBL exposure was performed in the open window region and etched out the PCM deposition region. Then, 70 nm ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ was sputtered on the top of the ridge waveguide. To control the crystalline state of the PCM, we sputtered the ITO film onto the PCM to construct an electric pulse excitation heater with a height of 50 nm. Meanwhile, the ITO film can also prevent the oxidation of the 70 nm ${\mathrm{Sb}}_2{\mathrm{Se}}_3$. Finally, the ${\mathrm{SiO}}_2$ cladding layer was deposited using plasma-enhanced chemical vapor deposition (PECVD). Two gold/titanium (Au/Ti) electrodes can be fabricated on the ITO layer to apply a direct current voltage and induce a change in the PCM crystalline state. Our designed nonvolatile optical switch relies on Joule heating in the ITO layer, which is driven electrically by Au/Ti electrodes formed on its two ends. When the ITO is heated and increases the environmental temperature of the ${\mathrm{Sb}}_2{\mathrm{Se}}_3$, ${\mathrm{Sb}}_2{\mathrm{Se}}_3$ will absorb the Joule heat and change its crystalline state.

In this paper, we propose a nonvolatile optical switch by modulating the TIS in the quasi-1D topological PC. The modulation of the energy band structure of quasi-1D topological PCs, and consequently the excitation wavelength of the TIS in quasi-1D topological PCs, is accomplished by controlling the crystallization state of the PCM. The designed 1D topological optical switch achieves a device performance with an IL of less than 2 dB and an ER of more than 18 dB at a modulation length of 9 μm. Moreover, the device footprint is about $0.5\mathrm{\mu m}\times 18\mathrm{\mu m}$, which is much smaller than that of nonvolatile optical switches based on structures such as slot–ridge waveguides, MZIs, and micro-ring resonators under the same material system and modulation length. However, the device we designed does not reduce the IL to a smaller level. This may be due to the scattering loss during the propagation of the quasi-1D PC. Moreover, due to the limitation of computational resources, the wavelength resolution in the transmission spectrum of the quasi-1D photonic crystal topological optical switch is only 0.1 nm. The IL obtained from the calculation will be slightly larger than the finer wavelength resolution. This work has great potential for nonvolatile optical switches and synthesizing photonic synapses with a high degree of integration, which benefits the realization of more efficient in-memory computing neuromorphic networks in the future.