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Abstract
In the development of integrated sensing, how to reduce losses and improve robustness has always been one of the key problems to be solved. The topological photonic crystal structure based on the quantum Hall effect has gradually attracted the attention of researchers due to its unique immune defect performance and anti-scattering performance. Here, we have successfully applied the valley photonic crystal structures to topologically manipulate the light within the band gap of 252 THz-317 THz in a silicon-on-insulator platform. We experimentally demonstrated that satisfactory transmission performance can be obtained using the valley-dependent topological edge states below light cone, even if there are structure defects such as lattice missing and lattice mistake near the interface between two kinds VPCs. Based on the features of topological protection, a triangular cavity consisting of three 10×a-length sides is proposed, and the Q factor value reaches 1.83×105 with little influence from defects. Finally, based on drying etching technology, a biosensor with cavity-coupled waveguide structure was prepared, and the RI sensitivity was 1228 nm/RIU.
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1. Introduction
Photonic crystal devices, as one of the typical optical sensors, have been widely used in various sensing fields [1–4]. However, conventional photonic crystals have inherent weakness, such as backscattering [5,6]. Especially when sharp corners and processing errors occur in the design of waveguide devices, scattering is particularly serious causing unnecessary losses and hindering the development and application of integrated sensing. In addition, for the high quality factor (Q) cavity of the sensing system, slight perturbations will cause greater disturbances to its optical properties. In complex biosensing environments, such as the detection of viruses and trace elements, the volume of the detection object is generally of the micro-nano scale or the changes are small, and only a slight change in refractive index (RI) can be produced. Therefore, even small machining errors can seriously interfere with inspection results and even lead to completely wrong conclusions. However, it is difficult to avoid the introduction of errors even with a high precision manufacturing process. It has become a a challenge in integrated sensing that reducing the impact of processing errors on the properties of the sensing structure and achieving high performance detection [7].
In recent years, inspired by the topological phase (a state of matter under the topological concept) in solid-state physics, topological photonics based on photon Hall effect and photon spin Hall effect is developing rapidly in integrated sensing due to its excellent sensing properties, including their novel edge states protected by the topological property [8–10]. Initially, to break the time reversal symmetry and achieve topological phase transition, the Spinning materials and magnetic materials are usually used [11,12]. However, the effective magnetic response of optical materials has been weak and difficult to apply to the optical frequency band.. In addition, this approach often relies on external magnetic field devices, which not only increases additional cost but also leads to oversized devices that are not conducive to integration. Later, the quantum spin Hall effect was applied to optical systems to achieve the corresponding topological phase transition, which quickly attracted the attention of many scholars [13–15]. However, the key to these schemes is the introduction of pseudo-spin degrees of freedom depending on the polarization or polarization properties of the light, which depends heavily on complex structures and delicate processes. In addition to the optical quantum spin Hall effect, the researchers also proposed the energy valley degree of freedom based on the valley Hall effect. Valleytronics based on the manipulation of valley degree of freedom in certain condensed matter systems has been proposed as computing electronics component [16,17]. Unlike the Hall effect of charge, for example, in the Haldane model [18], where Hall conductance is related to the current number, there is a chiral edge state at the system boundary according to the bulk-boundary correspondence. Furthermore, for the valley Hall effect or spin-valley Hall effect, there is no edge state at the sample boundary because the valley degrees of freedom is defined in the momentum space. Summing over the two valleys, we obtain the total system Chen number is zero, which indicates that there is no edge state. To achieve the bulk-boundary correspondence in the valley Hall effect and the spin-valley Hall effect, the usual approach is to consider the existence of an interface in a piece of bulk material with different topological numbers on each side of the interface [19]. Xiao et al. [20] revealed that there is an internal magnetic moment that closely resembles the Bohr magneton of electron spin and is related to the valley bottom index. Further, the broken inversion symmetry also allows a valley Hall effect. Recently, researchers have proposed topological photonic crystals with different lattice symmetry to achieve the double degeneracy of photons in a special wave vector, thus realizing topological phase transitions by opening the Dirac point of the double degenerate [21–26]. Different from the previous studies that require special materials and extremely precise processes, topological photonic crystals can be designed on the basis of ordinary dielectric materials without the restriction of special materials. One-way propagation with backscattering immunity can be realized on the boundaries of two different topological regions. The existence of the topologically protected edge state is of great significance for the application of integrated development. This property is particularly important in integrated sensing when cavities with sharp corners or high Q-factors are very sensitive to small disturbances [27]. Recently, a variety of novel of energy-valley-of-freedom photonic devices based on on-chip valley photonic crystal (VPCs) have been proposed, further enriching the topology regulation. He et al. realized topological transport in a SOI valley photonic crystal slab, and demonstrated that the topologically robust transport along two sharp-bend interfaces at subwavelength scales [28]. In 2020, Sabyasachi et al. proposed a topologically protected chiral nanophotonic resonator based on the topological edge states between two topologically distinct VPCs [29]. Mahmoud et al. realized a chiral quantum-optical interface by integrating semiconductor quantum dots into a valley-Hall topological photonic crystal waveguide using the topologically nontrivial optical modes and [30]. However, there are relatively few studies on the application of the excellent properties of topological photonic crystals to optical biomaterials sensors.
In this work, we designed and prepared a VPC biosnesor based on a SOI platform. Based on the analysis for optical properties of the designed VPC, we designed an Ω-shaped waveguide and a triangular cavity, which consist of an interface between two topologically different VPCs regions. The robustness and defect immunity of topological photonic crystal waveguides and topological photonic crystal microcavities were investigated, respectively. The exhibited robustness and high transmission of the designed structure can reduce the design and manufacturing technology requirements, and ensure the stability of optical devices, and the high Q value of the cavity is also significant for achieving integrated sensing. Base on this, combined with the dry etching technique, experiments show that the sensitivity of the topologically protected sensor with cavity-coupled waveguide structure is greatly improved to 1228 nm/RIU compared with the conventional photonic crystal RI sensor.
2. Design of the VPC and its topological properties
The starting point of our study is a triangular-lattice photonic crystal cell following the C6 symmetry, as illustrated in Fig. 1(a), where the lattice constant a is 575 nm. The substrate is the Si material with the RI of 3.6, which is attached on the SiO2 material with the RI of 1.45. The thickness of the Si layer (t) is 220 nm and the thickness of the SiO2 layer (T) is 2 µm shown in Fig. 1(b). The Fig. 1(c) shows the unit cell of a triangular-lattice photonic crystal structure in xy view, which can be seen as the result of a rectangle (d1 = 0.225a, d2 = 0.27a) rotated 60° around the center of the cell. The corresponding bandstructure along the boundary of the hexagonal Brillouin zone is shown in Fig. 1(d), which exhibits a double degeneracy points at the intersection of the lowest two TM bands along the hexagonal Brillouin zone, denoted by K and K’, and the dispersion of electromagnetic wave in air is represented by the red dashed lines. The detail calculation method can be seen in Supplement 1.
Fig. 1. Design of the valley photonic crystal. (a) Schematic of the crystal consists of the six-blade holey silicon in a hexagonal lattice. (b) The side view of the designed structure. (c) left: The top view of the unit cell. right: Schematic of the first Brillouin zone for the unit cells in reciprocal space. (d) Band structure of the unit cell and the corresponding double Dirac cone at the point K (K’).
By changing the length d2 = 0.27a of the rectangles spaced 120° to d2 = 0 (Fig. 2(a)), it can be seen that the inversion symmetry is broken and a bandgaps opens at K and K’ from 251 THz to 317 THz as illustrated in Fig. 2(b). In Fig. 2(c), we also plot the $|{{E_z}} |$ fields of the two degenerate states at the K (K’) valley in xy plane, where the white arrows represent the energy flux (Poynting vectors). As illustrated in the field diagrams, the electric fields mainly stay on direction of the rectangle with d2 = 0 for the first band at i, but shift to the the rectangle with d2 = 0.27a for the second band at ii. In addition, it can also be seen that the Poynting vector rotates in respectively opposite directions at the i and $ii$ points, and they are invariant under a rotation through 120°.
Fig. 2. Valley photonic crystal and its bulk band structure.(a) The xy view of the unit cell. The air hole consists of an inner hexagon with side length d1 = 0.225a and three rectangles with sides d1 = 0.225a and d2 = 0.27a with rotating angle of 120°. (b) Bandstructure of the unit cell after breaking inversion symmetry. The Dirac points at K and K’ are lifted. (c) The $|{{E_Z}} |$ filed diagrams and energy flux within each unit cell at K and K’. (d) Simulated phase profiles in xy view at the two lifted points.
Similar to the valley pseudo-spin in the condensed system, we refer to this vortex phenomenon as photonic valley pseudo-spin [20,31], whose characteristics can be described by the phase evolution. Figure 2(d) shows the phase profile in xy view, which clearly exhibits the counterclockwise and clockwise chirality.
Near K (K’), the Bloch states can be described by an effective 2D Dirac Hamiltonian [32,33]:
where ${\upsilon _D}$ is the Dirac group velocity of the conical dispersion, $({\delta {k_x},\delta {k_y}} )$ is the momentum deviation from the K (K’) point, ${\sigma _{x,y}}$ are the Pauli matrices. The Berry curvature of the first band along the Brillouin zone can be analytically calculated as [34]: where $\textrm{A}(\textrm{k} )$ is the Berry connection and ${\nabla _k} \equiv ({\partial {k_x},\partial {k_y}} )$. The berry connection of the first band is defined as $\textrm{A}(\textrm{k} )={-} i{u_k}|{\nabla k} |{u_k},$ where ${u_k}$ is the normalized Bloch wave function that can be obtained through simulation. As illustrated in Fig. 3, the Berry curvature of PC1 in the reciprocal lattice is mainly distributed near two valleys, i.e. singular sink at K’ while peak at K. On the contrary, the Berry curvature of PC2 is reversed with opposite signs at K’ and K.3. Design and discussion of topological VPC devices
3.1 Topological waveguide and its characteristics
Based on the obtained Berry curvature, the valley Chern number $\Delta {C^{K/K^{\prime}}} = C_{PC1}^{K/K^{\prime}} - C_{PC2}^{K/K^{\prime}} ={\pm} 1$ can be used to characterize the valley photonic crystal system, where ${C^K}({{C^{K^{\prime}}}} )$ are the integration of the Berry curvature near K and K’ points over the Brillouin zone. It is clear that the PC1 has negative $C_{PC1}^K$ and positive $C_{PC1}^{K^{\prime}}$ based on the obtained Berry curvature around K (K′), causing the negative valley Chern number ($\Delta {C^{K/K^{\prime}}} ={-} 1$). On the contrary, the PC2 has positive valley Chern number ($\Delta {C^{K/K^{\prime}}} = 1$). Therefore, based on the principle of the topological bulk-boundary correspondence, non-trivial edge states shall emerge in the first bandgap at the domain wall between PC1 and PC2 as shown in Fig. 4(a). This is verified by the numerically calculated photonic bandstructure shown in Fig. 4(b). The field plots in Fig. 4(c) show that the edge states are indeed strongly localized at the boundary between the PC1 and the PC2 with opposite valley Chern numbers (K and K’).
Fig. 4. Edge states of the designed VPC. (a) The interface formed by two VPC structures (PC1 and PC2) with opposite Chern number, and the boundary is marked by the red solid lines. (b) The calculated band structure of the boundary based on numerical method. (c) The $|{{E_Z}} |$ (rainbow map) distribution and the Poynting vector (white arrows) for the edge modes at K and K’.
In addition, in order to compare the anti-scatter performance of the topologically protected non-trivial linear TPCW in Fig. 4(a) and the linear defect PCW in Fig. 5(a), the field diagrams of the two types of waveguides can be obtained by simulation calculation, where the light source is set at A and B as shown in Fig. 5(b), respectively. It can be clearly seen that the conventional linear PCW has obvious backscattering, and its transmittance is about 12 dB - 28 dB with high losses. In contrast, the TPCW with topological protection achieves a backscattering transmittance of about 1 dB - 1.7 dB, which is almost close to lossless transmission. Therefore, the TPCW has very good lossless transmission during signal transmission and has a good application background in integrated development.
Fig. 5. A comparison of a straight waveguide with a mediocre topology and a non-mediocre topology. (a) The SEM of Common linear type PCW (b) Field plots of PCW versus TPCW for two waveguides.
To theoretically demonstrate the robust transport of the valley-dependent edge states based on the designed topological structure, we utilized the numerical calculation method to characterize the optical properties. As illustrated in Fig. 6(a), we designed a Ω-shaped topological interface with the corner angle of 60°. It can be seen that the light waves excited by the source can circumvent the sharp bends to achieve high transmission up to −0.5 dB without obvious backscattering. In order to evaluate the robustness of the waveguide, we introduce two types of defects near the interface. For the defect 1(lattice disorder) and the defect 2 (lattice missing), the light wave intensity at the output maintains high transmission values of −1.5 dB and −1 dB within the band gap, respectively, as shown in Fig. 6(d). The down illustrations of the Fig. 6(a)-(c) shows that the topologically protected light propagates smoothly around sharp bends with little disturbance from the defects. We also prepared Ω-shaped TPCW, whose SEM is shown in Fig. 6(e), and the transmission spectrum was experimentally obtained and compared with that of linear TPCW, as shown in Fig. 6(f). It can also be concluded that the existence of sharp corners does not have a large impact on the transmission mode protected by the topology. Therefore, the VPC-based waveguides can maintain robustness and high transmission to reduce design and fabrication technology requirements and ensure the stability of optical devices even in the existence of sharp corners.
Fig. 6. Topologically protected light wave transmission (a) Up:The top view of the Ω-shaped topological interfaces; Down: the corresponding filed plot at the wavelength of 1.04 µm. (b) Up: The top view of the Ω-shaped topological interfaces with a defect 1; Down: The corresponding filed plot at 1.04 µm. (c) Up: The top view of the Ω-shaped topological interfaces with a defect 2; Down: The corresponding field plot at 1.04 µm. (d): Transmission spectra for the Ω-shaped topological interfaces and with two kind defects. (e): The SEM of the Ω-shaped TPCW. (f): Comparison of linear TPCW spectra with Ω TPCW spectra.
3.2 Topological cavity design and analysis
We further construct the topological triangular cavity using edge states, and the structure of PC1 outside the cavity and PC2 inside the cavity is illustrated in Fig. 7(a). The proposed triangle cavity is arranged with three 10×a-length interfaces. The finite element simulation results of this resonator show the characteristic spectral mode structure as shown in Fig. 7(b), which lies within the topological band gap. Figure 7(c) show that the three filed plots of the three modes marked in Fig. 7(b), and it can be obviously seen that the light can be heavily confined in the whole edge even at the sharp corners in mode f2. In contrast, there are high reflection at the corners in the mode f2, f3. The three most prominent modes have high quality factor (Q factor) above 1.04×104 (ranging from 1.04×104 to 1.83×105).
Fig. 7. Optical properties of the proposed triangular cavity. (a) The schematic diagram of the triangular cavity with three equal 10×a-length sides. (b) The optical spectra of the cavity. (c) The field plots of the corresponding mode 1, 2, 3 at frequency of f1, f2, f3.
In addition, we further discuss the influence of the location of the point defects (the cells of PC1 in the three positions inside the boundary sequentially changes into the cells of PC2 as shown in Fig. 8(a)) on the cavity properties. Figure 8(b) shows the field plots of the mode at f2. From the field diagram, it can be seen that effect of defect 1 on the field distribution is weak whether the defect is located at the corner or away from the corner. Moreover, it can be found from Fig. 8(c) that the influence of defects at different positions on the intensity can be ignored by comparing the intensity, Q factor and resonant frequency position of the three modes. It can also be noted that all three Q values are above 1.82×105. Therefore, the light in the mode is topologically protected which has a great potential for applications in sensing.
Fig. 8. Optical properties of the proposed cavity in the case of defects at three different locations. (a) The schematic diagram of the cavity in the case of defects in three different locations marked with red box. (b) The field plots corresponding to three different cases with different defects locations. (c) The comparison of the optical spectra of the cavity with and without defects.
3.3 Design and analysis of the topological microcavity coupled waveguide structure
The effect of the distance between the waveguide and the microcavity on the coupling effect is first explored, using the crystal cell number N to represent the distance, as shown in Fig. 9(a). As shown in Fig. 9(b), the Q value of the resonant cavity reaches saturation when N is greater than 3. In other words, with this parameter, the resonant cavity and the waveguide are weakly coupled. In the experiment, we choose N = 3, and the preparation of all devices in this work is based on the dry etching technology, and the detail preparation process can be seen in Supplement 1. Finally, the surrounding refractive index n of the resonant cavity is changed from 1.33 to 1.36, corresponding to the refractive index nwater = 1.33 for water and nethanol = 1.36 for ethanol, respectively From the transmission spectrum as shown in Fig. 9(c), it can be seen that the resonant peak has been significantly shifted $\mathrm{\Delta }\lambda $. According to the simple definition of sensitivity S:
where the $\mathrm{\Delta }\lambda $ is the shift of the resonant wavelength, and the $\mathrm{\Delta }n$ is the change in refractive index. The sensitivity S of the RI sensing structure is calculated to be 1228 nm/RIU. Therefore, the device can be used to detect the concentration and volatilization level of ethanol solution with high sensitivity.Fig. 9. Topological microcavity coupled waveguide structure and its optical characteristics. (a) The SEM of the structure. (b) The Q values with different N. (c) the transmission spectral with different n.
In Table 1, the surface plasmon resonance sensor in Ref. [35] is mainly based on molecular adsorption for RI sensing. Compared with this work, its design is relatively complex, although the refractive index range is larger. In addtion, the sensitivity of our topological microcavity sensor is improved by two orders of magnitude compared to the optical fiber sensor in Ref. [36]. At the same time, compared with other photonic crystal sensors [37–39], it can be seen that our topological microcavity has a higher RI sensitivity in the desired RI range, which has great competitive in RI sensing.
Table 1. Comparison of the sensor performance parameters with other types of sensors
4. Conclusion
In summary, we proposed a six-blade valley photonic crystal structure based on a SOI slab with opposite Chern numbers near its Brillouin zone symmetry point to provide topological edge states Even with sharp corners, the Ω-shaped waveguide can obtain high transmission up to −1 dB, and it also exhibits a satisfactory high transmission value (<1.5 dB) stability when defects such as lattice missing and lattice disorder appear near the domain wall. In addition, we constructed a triangular cavity based on edge states and demonstrated that the cavity was capable of supporting robust modes with high Q-factors (up to 1.83×105) with interference from defects. Finally, the proposed highly sensitive microcavity-coupled waveguide biosensor was experimentally prepared and characterized based on dry etching technique. Therefore, the proposed topological semiconductor scheme provides a new approach for the study of valley-state photonic crystals and the development of integrated topological systems for robust optical transmission and biosensing.
Funding
National Natural Science Foundation of China (61771419).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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