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Abstract
Optical biosensor, which perceptively captures the variety of refractive index (RI) of the surrounding environment, has great potential applications in detecting property changes and types of analytes. However, the disequilibrium of light-matter interaction in different polarizations lead to the polarization-dependence and low sensitivity. Here, we propose a polarization-independent and ultrasensitive biosensor by introducing a one-dimensional topological photonic crystal (1D TPhC), where two N-period 1D photonic crystals (PhC1 and PhC2) with different topological invariants are designed for compressing the interaction region of the optical fields, and enhancing the interaction between the light and analyte. Since the strong light-matter interaction caused by the band-inversion is polarization-independent, the biosensor can obtain superior sensing performance both for TE and TM polarization modes. The sensitivity and Figure of Merit (FOM) of the designed biosensor are 1.5677×106 RIU−1 (1.3497 × 106 RIU−1) and 7.8387×1010 RIU−1deg−1 (4.4990×1010 RIU−1deg−1) for TM (TE) polarization mode, which performs two orders of magnitude enhancement compared with the reported biosensors. With the protection of the topological edge state, this biosensor has high tolerance to the thickness deviations and refractive index (RI) variations of the component materials, which can reduce the requirements on fabrication and working environment. It is anticipated that the proposed biosensor possesses excellent sensing performances, may have great potentials in environmental monitoring, medical detection, etc.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical biosensor has aroused intense interests for perceptively capturing the change of surrounding environment, and is widely used for environmental monitoring [1,2], medical diagnostics [3,4], food safety [5,6], and biochemistry applications [7,8]. According to different working principles, it can be classified into intensity, angle, wavelength and phase interrogations [9–12]. Due to the fast response speed and convenient operation, the intensity interrogation biosensor has attracted extensive attention [9,13–17]. The reported interrogation biosensors can be divided into surface plasmon resonance (SPR) [13,14] and waveguide mode [15–17]. SPR biosensors realized by coupling the evanescent wave and the surface plasmon wave (SPW) based on the method of attenuate total reflection (ATR), has a high sensitivity and simple structure [13]. However, SPR effect can only be activated by transverse magnetic (TM)-polarized light, and not suitable for transverse electric (TE)-polarized light [18]. In contrast, waveguide mode biosensors (such as guided-mode resonance and Fano resonance) can be achieved by both TE- and TM-polarized lights, may have wide applications in optical sensing [15]. However, limited by the different interaction intensities excited by polarizations and analytes, they are cumbersome to obtain high sensing performances both for TE and TM polarization modes [19]. Polarization-independence and ultra-sensitivity are two important properties of the optical biosensors. The polarization-independence affects the flexibility of the operation, while the ultra-sensitivity affects the accuracy and response speed of the analyte detection. Therefore, designing a suitable structure to enable the optical field to interact with the analyte strongly in both TE and TM polarization modes, is one of the keys to the further development of the optical biosensors.
Topological photonic crystals (TPhC) have aroused growing interests via its excellent properties of field confinement, robust propagation, and unidirectional propagation [20–25]. The field confinement provides a possibility to enhance the light-matter interaction, may has a high application in the optical biosensors. According to the spatial distribution of the material parameters, TPhC can be divided into one-dimension (1D), two-dimension (2D), three-dimension (3D) and multi-dimension (ND). In recent years, 2D TPhCs have been initially used to design the biosensors, including suspended slotted photonic crystal (SSPhC) [26] and valley-edge mode biosensor [27]. Compared to 2D TPhCs, 1D TPhC possess simple structure, which provides great convenience for the fabrication of integrated photonic devices. Recently, the topological interface state of 1D TPhC is controlled by adjusting the relation between the surface impedance and bulk-band geometric phases [28], the multiband perfect absorption is realized by combining graphene and 1D TPhC [29], and the unitary photonic topological pumps is implemented by 1D coupled waveguide arrays [30,31]. According to reported work, the 1D TPhC can be easily achieved by splicing two PhCs with different topological invariants, and the topological invariant is Zak phase, which is a special Berry phase defining the 1D bandgap [32]. When the Zak phases of two PhCs are not equal at a certain wavelength, the band-inversion will form the topological interface state [33,34]. And the topological interface state is available for producing strong field confinements [35]. Because the strong field confinements caused by the band-inversion is polarization-independent, it provides a possibility for obtaining strong light-matter interactions both for TE and TM polarization modes [35].
Based on the above superiorities, we propose and investigate a polarization-independent and ultrasensitive biosensor based on the 1D TPhCs, which is used to compress the interaction region of the optical fields into the interface between PhC1 and PhC2. As the strong field confinement is polarization-independent, the proposed biosensor has a superior sensing performance both for TE and TM polarization modes. By adjusting the number of periods, the sensitivity in TM (TE) polarization mode is optimized to 1.5677×106 RIU−1 (1.3497×106 RIU−1) corresponding to refractive index (RI) of 1.33 RIU, can obtain two orders of magnitude enhancement compared with the reported biosensors [15,19]. The sensitivity and FOM are still above 1.25×106 RIU−1 and 4.34×1010 RIU−1deg−1 even the RI varies from 1.33 to 1.335 RIU. Furthermore, due to the protection of topological edge states, the proposed biosensor is tolerant to the thickness deviations and RI variations of the component materials highly, which can improve the freedom of fabrication and working environment. These indicate that the proposed biosensor possesses high sensitivity and polarization-independence, which may have great potentials in environmental monitoring, medical detection, and biochemistry applications, etc.
2. Design consideration and theoretical model
The 3D schematic of the proposed biosensor is shown in Fig. 1(a). The proposed biosensor is composed of BK7 coupled prism, two N-period 1D photonic crystals (PhC1 and PhC2) with different topological invariants, and a sensing medium layer between PhC1 and PhC2 which is used to place the analyte. The PhC1 and PhC2 is consisted of TiO2 and SiO2 film, which are used to produce 1D TPhC, achieving the enhancement of the light-matter interaction [28,35]. Because the resonance curve of the proposed biosensor moves with the RI the sensing medium layer (ns), the analyte can be detected by measuring the shift of the reflectivity ΔR. As presented in Fig. 1(b), the structure of PhC1 is ‘BAAB’ while PhC2 is ‘ABBA’, the thickness of unit cell is Λ=dA + dB, where Λ=1.6 µm, dA = 0.75Λ, and dB = 0.25Λ. Since the designed sensor can be used to detect analyte with the RI of 1.33 RIU, which is the RI of the aqueous solutions of the biological macromolecules, it will have potential applications in biosensing.
Fig. 1. Structure of the proposed biosensor with 1D TPhC. (a) Three-dimensional schematic of the biosensor; (b) Unit cell of the TPhCs.
The 1D TPhCs is designed by TiO2 and SiO2 films, which are isotropic material, and their RI can be expressed as [36,37]
Here, we use the transfer matrix method (TMM) to simulate the biosensor. Each film is set with the thickness dk, dielectric constant ɛk, and refractive index nk. The relationship between the first tangential fields and the final boundary can be given as [38]
Hence, the reflection and transmittance coefficients can be inferred as [10]
For TE polarization mode, ${\textrm{q}_1} = \sqrt {{\mathrm{\varepsilon} _0}/{\mathrm{\mu} _0}} \cos \mathrm{\theta}$, ${\textrm{q}_\textrm{N}} = \sqrt {{\mathrm{\varepsilon} _\textrm{N}}/{\mathrm{\mu} _\textrm{N}}} \sqrt {1 - {{\sin }^2}\mathrm{\theta} /({\mathrm{\varepsilon} _\textrm{N}}{\mathrm{\mu} _\textrm{N}})}$, and for TM polarization mode, ${\textrm{q}_1} = \sqrt {{\mathrm{\mu} _0}/{\mathrm{\varepsilon} _0}} \cos \mathrm{\theta}$, ${\textrm{q}_\textrm{N}} = \sqrt {{\mathrm{\mu} _\textrm{N}}/{\mathrm{\varepsilon} _\textrm{N}}} \sqrt {1 - {{\sin }^2}\mathrm{\theta} /({\mathrm{\varepsilon} _\textrm{N}}{\mathrm{\mu} _\textrm{N}})}$. The reflectance (R) and transmittance (T) of the structure is given by
Because the resonance curve moves with the RI of the sensing medium layer (ns), the sensitivity of the biosensor can be defined as S = ΔR/Δns [19].
3. Results and analysis
3.1 Construction of the topological interface state
As shown in Fig. 1(b), topological interface state is constructed by shifting the inversion centers in the 1D PhC, and the inversion center of PhC1 and PhC2 are A and B, respectively. Thus, the band structure of a binary PhC can be determined by [28,39]
The Zak phase can be calculated by reflection phase as [40,41]
To determine the position of topological interface state, the sign of ς(n) is used to identify the band-inversion, which can be expressed as [28]
As shown in Figs. 2(a)-(b), the band structure of the PhC1 is similar to that of the PhC2. However, two PhCs have different topological properties due to the inverse arrangement of the unit cell. According Eq. (11) and Eq. (12), the Zak phase of every isolated band can be marked by green ‘0’ and ‘π’, indicating that the Zak phase of the PhC1 and PhC2 are different. To obtain the characteristic state, we mark each bandgap by purple when ς(n) > 0 and blue when ς(n) < 0 based on Eq. (13). Because the 1st and 3rd bandgaps of two PhCs have a good overlap while the signs of ς(n) are different, the topological interface state will generate and produce field confinement. Figure 2(c) shows the transmittance spectrum of the TPhC when the TE-polarized light incident vertically, where Λ=1.5 µm, dA = 0.7762Λ, and dB = 0.2238Λ, and we can see the TPhC has two transmittance peak in the wavelength of 548.5 nm and 633 nm. The corresponding normalized field distribution in the wavelength of 633 nm is shown in Fig. 3(a), indicating that the field confinement exists at the interface between PhC1 and PhC2, which can be used to realize the strong light-matter interaction. Because the topological interface state is polarization-independent, light-matter interaction also can be obtained in TM polarization mode, as shown in Fig. 2(d) and 3(b).
Fig. 2. Band structures of (a) PhC1 (b) PhC2, the Zak phases are marked by the green font in the center of the passband, the bandgap is marked by blue and purple to indicate the band-inversion; Transmission of 1D TPhC when the (c) TE-polarized (d) TM-polarized light incident vertically, there are two transmittance peaks in the wavelength of 548.5 nm and 633 nm, indicating that the field confinement exists at the interface between PhC1 and PhC2.
Fig. 3. Normalized field distribution in the wavelength of 633 nm when the (a) TE-polarized (b) TM-polarized light incident vertically.
3.2 Construction of the proposed biosensor
As shown in Fig. 1(a), the proposed biosensor is consisted of BK7 coupled prism, 1D TPhC and sensing medium layer. To satisfy the actual demand and reduce manufacturing difficulty, the thicknesses are changed to dA = 0.75Λ=1200 nm and dB = 0.25Λ=400 nm. From Fig. 4(a) and 4(b), the field confinement also can be given in 633 nm when the incident angle is almost 28° and the thickness of sensing medium layer is ds = 0 µm, which is chosen as the resonance wavelength of the proposed biosensor.
Fig. 4. Transmission of 1D TPhC when the (a) TE-polarized (b) TM-polarized light incident with 28°, the transmittance peak is obtained in 633 nm.
To consider the influence of PhC, we simulated the resonance effects of the proposed biosensor, PhC1-Sensing medium layer and Sensing medium layer-PhC2, the structures are displayed in Figs. 5(a)-(c). In the simulation, the number of periods of the TPhC is 6, the thickness of sensing medium layer is ds = 10 µm, the RI of BK7, TiO2 and SiO2 film are nBK7 = 1.5151, nA = 2.5836 RIU and nB = 1.457 RIU respectively. Figure 5(d) shows the resonance curve of the biosensor when TM-polarized light incident and the RI of sensing medium layer is ns = 1.33 RIU. It can be clearly seen that the resonance curve has 3 resonance dip of 27.069°, 28.869°, and 30.555°, the energy of light is greatly attenuated. In Fig. 5(e), the black and red solid lines are the resonance curves of PhC1-Sensing medium layer (SM) and Sensing medium layer-PhC2 respectively, their reflectivity is higher than 0.75, which cannot achieve the sharp attenuation of the optical signal. By the formula of $\textrm{R} = {\left( {\sqrt {{\textrm{R}_1}} \textrm{exp} (\textrm{i}{\mathrm{\phi}_1})/2 + \sqrt {{\textrm{R}_2}} \textrm{exp} (\textrm{i}{\mathrm{\phi}_2})/2} \right)^2}$, the resonance effect of the combination of PhC1-SM and SM-PhC2 can be calculated, where R1 and R2 are the reflectivities of PhC1-SM and SM-PhC2, ϕ1 and ϕ2 are the reflection phases. From the blue line, 3 resonance dip also can be found because the difference of the Zak phase between PhC1 and PhC2 at these angles is π, it is almost identical to that of the TPhC, indicating the resonance effect is caused by band-inversion of TPhC.
Fig. 5. Structure of (a) the proposed biosensor (b) PhC1-Sensing medium layer and (c) Sensing medium layer-PhC2; Resonance curve of the (a) the proposed biosensor (b) PhC1-Sensing medium layer and (c) Sensing medium layer-PhC2, the blue line shows the combination calculation of PhC1-SM and SM-PhC2.
As shown in Fig. 6(a), the resonance dip moves with the RI of the sensing medium layer increases from 1.33 RIU to 1.3301 RIU, manifesting that the biosensor is sensitive to the RI. According S = ΔR/Δns, the sensitivity of 9300 RIU−1 can be obtained at the resonance angle of 28.869°, which is large than the common biosensor, is shown in Fig. 6(b).
Fig. 6. (a) Change of the first resonance dip when the RI of the sensing medium layer increases from 1.33 RIU to 1.3301 RIU; (b) Sensitivity of the proposed biosensor when the number of periods is 6.
3.3 Effect of the number of periods
The number of periods (N) is an important parameter of 1D TPhC, which is independent of the band structure, but associated with the confinement effect of the light field. Thus, the number of periods has a positive effect on the performance. To obtain an optimum sensitivity, we discuss the influence of the number of periods. Figure 7(a) shows the relationship between the resonance curves and the number of periods. It can be seen that the width of the resonance curve will gradually narrow with the increase of the number of periods, which makes the reflectivity difference ΔR increase if the curve has a small movement. Thus, according to S = ΔR/Δns, the number of periods will affect the sensitivity directly. However, the larger the number of periods is not the better because the minimum reflectivity of the resonance curve will gradually increase. When we calculate the reflection spectrum at the corresponding resonance angle, it can be clearly seen that the width of the spectrum gradually narrows with the increase of the number of periods, but the resonance wavelength does not change, as shown in Fig. 7(b). Thus, the small movement of the resonance angle has little effect on the resonance angle under different number of periods, while the field confinement is enhanced. As shown in Fig. 7(c), with the number of periods increases from 1 to 25, the sensitivity increases rapidly at first and then drops. When the number of periods is N = 13, an optimum sensitivity of 1.5677×106 RIU−1 is obtained, which is higher than the reported biosensor [19,42].
Fig. 7. Shift of (a) the resonance curve (b) reflectance spectrum (c) the sensitivity with the increase of the number of periods, the polarization of the incident light is TM, the optimum sensitivity of 1.5677×106 RIU−1 is obtained in N = 13.
3.4 Tolerance of the thickness deviations and RI variations of the component materials
For traditional micro-nano devices, manufacturing deviations and environmental changes can affect the performance. Due to the protective effect of topological edge states, the designed optical biosensor may have a high tolerance. Since the direct reflection of fabrication deviations and environmental changes on the device are the thickness and the RI of the component materials, we will analyze the effect of these on the sensitivity.
Figure 8 shows the relationship between the sensitivity and the thickness variations of SiO2 and TiO2 layer ($\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}\textrm{ and }\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$). The thickness of SiO2 and TiO2 layer in the biosensor are ${\textrm{d}^{\prime}_{\textrm{Si}{\textrm{O}_2}}} = {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} + \mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ and ${\textrm{d}^{\prime}_{Ti{\textrm{O}_2}}} = {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} + \mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$ respectively, as shown in Fig. 8(a). Black-line (red-line) in Fig. 8(b) represents the sensitivity changes with the increase of $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ ($\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$) if $\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ nm}$ ($\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} = 0\textrm{ nm}$). The sensitivity gradually decreases with the increase of $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ ($\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$), but still higher than 1 × 104 RIU−1 even if $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} = 36\textrm{ nm}$ or $\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} = 23\textrm{ nm}$. When $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ and $\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$ are comprehensively considered, the sensitivity is shown in Fig. 8(c). As shown in Figs. 8(c)-(d), the sensitivity is higher than 1 × 106 RIU−1 when $0 \le \mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} \le 10\textrm{ nm}$ and $0 \le \mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} \le 10\textrm{ nm}$, and higher than 1 × 104 RIU−1 even if $0 \le \mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} \le 15\textrm{ nm}$ and $0 \le \mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} \le 15\textrm{ nm}$, but the resonance angle should be slightly adjusted. To measure the tolerance of single-layer defects on performance, we added two defect layers near the Sensing medium layer, their thicknesses are ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ and ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$ respectively, as shown in Fig. 9(a). Black-line (red-line) in Fig. 9(b) shows the relationship between the sensitivity and ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ (${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$) if ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ nm}$ (${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}} = 0\textrm{ nm}$). The sensitivity gradually decreases with the increase of ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ (${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$), but still higher than 1 × 104 RIU−1 even if ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}} = 240\textrm{ nm}$ or ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}} = 183\textrm{ nm}$. Figure 9(c)-(d) shows the sensitivity and resonance angle changes with ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ and ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$. The sensitivity is higher than 1 × 106 RIU−1 when $0 \le {\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}} \le 50\textrm{ nm}$ and $0 \le {\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}} \le 50\textrm{ nm}$, and higher than 1 × 104 RIU−1 even if $0 \le {\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}} \le 200\textrm{ nm}$ and $0 \le {\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}} \le 100\textrm{ nm}$, but the resonance angle also should be slightly adjusted. From Fig. 8 and Fig. 9, it is evident that the small thickness deviations cannot affect the performance, the proposed biosensor has an excellent tolerance for thickness deviations, and SiO2 layer is higher than TiO2 layer because the small RI.
Fig. 8. (a) Changes in the biosensor structure; (b) Sensitivity changes with the increase of $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ ($\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$) if $\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ nm}$ ($\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}} = 0\textrm{ nm}$); (c) Sensitivity (d) Resonance angle shifts when $\mathrm{\Delta} {\textrm{d}_{\textrm{Si}{\textrm{O}_2}}}$ and $\mathrm{\Delta} {\textrm{d}_{\textrm{Ti}{\textrm{O}_2}}}$ increase simultaneously, the polarization of the incident light is TM.
Fig. 9. (a) Changes in the biosensor structure; (b) Sensitivity changes with the increase of ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ (${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$) if ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ nm}$ (${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}} = 0\textrm{ nm}$); (c) Sensitivity (d) Resonance angle shifts when ${\textrm{d}^{\prime\prime}_{\textrm{Si}{\textrm{O}_2}}}$ and ${\textrm{d}^{\prime\prime}_{\textrm{Ti}{\textrm{O}_2}}}$ increase simultaneously, the polarization of the incident light is TM.
Figure 10 shows the relationship between the sensitivity and the RI of SiO2 and TiO2 layer (${\mathrm{n^{\prime}}_{\textrm{Si}{\textrm{O}_2}}}\textrm{ and }{n^{\prime}_{\textrm{Ti}{\textrm{O}_2}}}$), and the RI variations of SiO2 and TiO2 layer are $\mathrm{\Delta} {n_{\textrm{Si}{\textrm{O}_2}}}$ and $\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}}$ respectively. Figure 10(a) represents the sensitivity changes with the increase of ${\mathrm{n^{\prime}}_{\textrm{Si}{\textrm{O}_2}}}$ if $\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ RIU}$. The sensitivity gradually decreases with the increase of ${\mathrm{n^{\prime}}_{\textrm{Si}{\textrm{O}_2}}}$, but still higher than 7.5 × 105 RIU−1 even if ${\mathrm{n^{\prime}}_{\textrm{Si}{\textrm{O}_2}}} = 1.507\textrm{ RIU}$ ($\mathrm{\Delta} {\textrm{n}_{\textrm{Si}{\textrm{O}_2}}} = 0.05\textrm{RIU}$). From Fig. 10(b), it can be clearly seen that ${\textrm{n}^{\prime}_{\textrm{Ti}{\textrm{O}_2}}}$ has a slightly high impact on the sensitivity than ${n_{\textrm{Si}{\textrm{O}_2}}}$, but still higher than 1 × 104 RIU−1 even if ${\mathrm{\textrm{n}^{\prime}}_{\textrm{Ti}{\textrm{O}_2}}} = 2.6336\textrm{ RIU}$ ($\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}} = 0.05\textrm{ }RIU$). When $\mathrm{\Delta} {\textrm{n}_{\textrm{Si}{\textrm{O}_2}}}$ and $\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}}$ are comprehensively considered, the sensitivity is shown in Fig. 10(c). As shown in Figs. 10(c)-(d), the sensitivity is higher than 1 × 106 RIU−1 when $1.457 \le {\mathrm{\textrm{n}^{\prime}}_{\textrm{Si}{\textrm{O}_2}}} \le 1.477\textrm{ RIU}$ and $2.5836 \le {\textrm{n}^{\prime}_{\textrm{Ti}{\textrm{O}_2}}} \le 2.6036\textrm{ RIU}$, the RI variations is 0.02 RIU. Even if $1.457 \le {\mathrm{\textrm{n}^{\prime}}_{\textrm{Si}{\textrm{O}_2}}} \le 1.497\textrm{ RIU}$ and $2.5836 \le {\mathrm{n^{\prime\prime}}_{\textrm{Ti}{\textrm{O}_2}}} \le 2.6136\textrm{ nm}$, the sensitivity is higher than 104 RIU−1, but the resonance angle should be slightly adjusted. It is indicated that the small RI variations cannot affect the performance, the proposed biosensor has an excellent tolerance for RI variations, can reduce the requirements on fabrication and working environment.
Fig. 10. Sensitivity changes with the increase of (a) ${\mathrm{\textrm{n}^{\prime}}_{\textrm{Si}{\textrm{O}_2}}}$ if $\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ RIU}$ (b) ${\mathrm{\textrm{n}^{\prime}}_{\textrm{Ti}{\textrm{O}_2}}}$ if $\mathrm{\Delta} {\textrm{n}_{\textrm{Ti}{\textrm{O}_2}}} = 0\textrm{ RIU}$; (c) Sensitivity (d) Resonance angle shifts when ${\mathrm{\textrm{n}^{\prime}}_{\textrm{Si}{\textrm{O}_2}}}$ and ${\mathrm{\textrm{n}^{\prime}}_{\textrm{Ti}{\textrm{O}_2}}}$ increase simultaneously, the polarization of the incident light is TM.
3.5 Performance of the biosensor
To investigate the performance of the biosensor, the sensitivity and FOM are measured. Sensitivity is one of the fundamental parameters of the biosensor, which reflects the response speed to the analyte. Figures 11(a)-(b) illustrate the resonance curve and sensitivity for the TE-polarization mode. With the RI of sensing medium increases from 1.33 RIU to 1.3300002 RIU, the resonance dip moves from 25.00149° to 25.00151°, indicating that a small change of RI will cause the movement of resonance angle, and the biosensor is sensitive to the RI. As shown in Fig. 11(b), a sensitivity of 1.3497×106 RIU−1 can be obtained. Similar with TE-polarized light, the resonance dip moves from 28.86796° to 28.86797° when the polarization mode is TM, and a sensitivity of 1.5677×106 RIU−1 can be obtained. Comparing Fig. 11(b) and Fig. 11(d), the sensitivities of the biosensor are both higher than 106 for TE and TM polarization mode.
Fig. 11. (a) Resonance curve (b) Sensitivity curve when the polarization of the incident light is TE; (c) Resonance curve (d) Sensitivity curve when the polarization of the incident light is TM.
FOM is another critical parameter describing the detection accuracy, which can be expressed as FOM = S/FWHM, where the FWHM is the full width at half maximum. Figure 12 shows the sensitivity and FOM when the RIs of sensing medium layer are 1.33∼1.335 RIU. As shown in Fig. 12(a), the sensitivities corresponding to TE and TM polarization modes are above 1.25×106 RIU−1 and 1.3×106 RIU−1. The sensitivities of TM and TE polarization modes exceed 106, which performs two orders of magnitude enhancement compared with the reported biosensors [19,42]. From Fig. 12(b), the FOMs for TE and TM polarization modes are more than 4.34×1010 RIU−1deg−1, indicating the biosensor has a high detection accuracy.
3.6 Discussion
Table 1 presents the performance comparison of some reported biosensors. As is shown in Table 1, Yuan et al. designed a SPR-based biosensor by placing the black phosphorous-graphene hybrid structure on the gold films [43]. However, the SPR-based biosensor is polarization-dependent and can be only activated by TM-polarized light. To address this problem, Dai et al. constructed a guide-mode resonance (GMR) biosensor with 1D PhC, leading to a high sensitivity of 20683 RIU−1 in TM-polarized light, but is only 452 RIU−1 for TE polarization mode owing to the disequilibrium of light-matter interaction in different polarizations [19]. The new materials with high absorption may be an effective way to enhance the performance. Wu et al. increased the sensitivity by designed a lossy-mode-resonance (LMR) biosensor based on the strong coupling of perovskite, which performed the sensitivities of 11382 RIU−1 in TM and 21697 RIU−1 in TE polarization mode, but the performance enhancement is still limited [42]. Due to the excellent field confinement, TPhCs have been used to design biosensors in recent years. Gao et al. designed a suspended slotted photonic crystal (SSPhC) biosensor and obtained a sensitivity of 656 nm/RIU [26], Cheng et al. constructed a valley-edge mode biosensor and got a sensitivity of 1228 nm/RIU [27]. However, the reported TPhCs-based biosensor is wavelength interrogation and its design is based on two-dimensional silicon-based waveguide, which makes manipulation and fabrication inconvenient.
Table 1. Comparison of the sensitivity of the reported biosensors
The proposed biosensor in this work employs a 1D TPhC for compressing the interaction region of the optical fields into the interface, achieving strong interaction between the light and analyte. Compared to 2D TPhCs, 1D TPhC possess simple structure, which provides great convenience for the fabrication of the integrated photonic devices. Due to the polarization-independence of the strong light-matter interaction, the biosensor has a sensitivity above 106 both for TE and TM polarization modes, which is higher than the reported biosensors. Besides, the working wavelength can be flexibly regulated according to the actual requirements because the band-structure can be controlled by changing the thickness of the period and the ratio between A and B. With these excellent characteristics, the proposed biosensor will have a potential application in biosensing field.
To expand the interrogation modes of the proposed biosensor, the shift of the resonance curve under different RI is calculated. As shown in Fig. 13(a), with RI of sensing medium layer increases from 1.33 RIU to 1.330001 RIU, the resonance angle moves from 25.00149° to 25.00156°. By the formula S = Δθ/Δns for the angle interrogation biosensor, the sensitivity of 70°/RIU and the FOM of 2.33 × 106 /RIU when the polarization mode is TE. If the polarization mode is TM, the sensitivity of 60°/RIU and the FOM of 3 × 106 /RIU can be obtained, is shown in Fig. 13(b). Compare with the reported biosensor [10], the FOM is high while the sensitivity is slightly low, indicating the biosensor has high detection accuracy for the interrogation manipulation. Of course, the sensitivity also can be enhanced by adjusting the structure or introducing new materials [10,19,42].
4. Conclusion
In conclusion, we have proposed a novel biosensor based on 1D TPhC. With the strong field confinement and polarization-independence, the light-matter interaction is significantly improved, which affects the sensing performance directly. The results show that the proposed biosensor has a sensitivity of 1.5677×106 RIU−1 and a FOM of 7.8387×1010 RIU−1deg−1 for TM polarization mode, which are 1.3497 × 106 RIU−1 and 4.4990×1010 RIU−1deg−1 for TE polarization mode. The sensitivity and FOM are still above 1.25×106 RIU−1 and 4.34×1010 RIU−1deg−1 even the refractive index (RI) varies from 1.33 to 1.335 RIU. Furthermore, the high tolerance for the thickness deviations and RI variations in component materials makes it less demanding on the manufacturing and working environment. Compared with the reported biosensors, the proposed biosensor presents the excellent characteristics of polarization-independence and ultra-sensitivity, which may have great potential prospects in sensing technologies and optoelectronic devices.
Funding
Characteristic innovation projects of universities in Guangdong Province (2022KQNCX054); Scientific Key Research Fund of Guangdong Provincial Education Department (2019KQNCX099, 2019KZDXM061, 2020ZDZX2059); Basic and Applied Basic Research Foundation of Guangdong Province (2020A1515110488); China Postdoctoral Science Foundation (2021TQ0215, 402210053); National Natural Science Foundation of China (62105069).
Disclosures
The authors declare no conflicts of interest.
Data availability
The authors declare the data in this paper is true and available, can be generated and analyzed by commercial software MATLAB.
References
1. E. Mauriz, A. Calle, J. J. Manclús, A. Montoya, and L. M. Lechuga, “Multi-analyte SPR immunoassays for environmental biosensing of pesticides,” Anal. Bioanal. Chem. 387(4), 1449–1458 (2007). [CrossRef]
2. C. Hu, N. Gan, Y. Chen, L. Bi, X. Zhang, and L. Song, “Detection of microcystins in environmental samples using surface plasmon resonance biosensor,” Talanta 80(1), 407–410 (2009). [CrossRef]
3. J. W. Chung, S. D. Kim, R. Bernhardt, and J. C. Pyun, “Application of SPR biosensor for medical diagnostics of human hepatitis B virus (hHBV),” Sens. Actuators, B 111-112, 416–422 (2005). [CrossRef]
4. J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009). [CrossRef]
5. J. Homola, J. Dostálek, S. Chen, A. Rasooly, S. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Int. J. Food Microbiol. 75(1-2), 61–69 (2002). [CrossRef]
6. A. Rasooly, “Surface plasmon resonance analysis of staphylococcal enterotoxin B in food,” J. Food Prot. 64(1), 37–43 (2001). [CrossRef]
7. C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013). [CrossRef]
8. D. Conteduca, F. Dell’Olio, F. Innone, C. Ciminelli, and M. N. Armenise, “Rigorous design of an ultra-high Q/V photonic/plasmonic cavity to be used in biosensing applications,” Opt. Laser Technol. 77, 151–161 (2016). [CrossRef]
9. S. H. Choi, Y. L. Kim, and K. M. Byun, “Graphene-on-silver substrates for sensitive surface plasmon resonance imaging biosensors,” Opt. Express 19(2), 458–466 (2011). [CrossRef]
10. P. K. Maharana, R. Jha, and S. Palei, “Sensitivity enhancement by air mediated graphene multilayer based surface plasmon resonance biosensor for near infrared,” Sens. Actuators, B 190(1), 494–501 (2014). [CrossRef]
11. A. K. Sheridan, R. D. Harris, P. N. Bartlett, and J. S. Wilkinson, “Phase interrogation of an integrated optical SPR sensor,” Sens. Actuators, B 97(1), 114 (2004). [CrossRef]
12. J. Q. Zhu, Y. X. Ke, J. F. Dai, Q. You, L. M. Wu, J. Q. Li, J. Guo, Y. J. Xiang, and X. Y. Dai, “Topological insulator overlayer to enhance the sensitivity and detection limit of surface plasmon resonance sensor,” Nanophotonics 9(7), 1941–1951 (2020). [CrossRef]
13. L. M. Wu, J. Guo, H. L. Xu, X. Y. Dai, and Y. J. Xiang, “Ultrasensitive biosensors based on long-range surface plasmon polariton and dielectric waveguide modes,” Photonics Res. 4(6), 262–266 (2016). [CrossRef]
14. O. Salihoglu, S. Balci, and C. Kocabas, “Plasmon-polaritons on graphene-metal surface and their use in biosensors,” Appl. Phys. Lett. 100(21), 213110 (2012). [CrossRef]
15. B. X. Ruan, Q. You, J. Q. Zhu, L. M. Wu, J. Guo, X. Y. Dai, and Y. J. Xiang, “Fano resonance in double waveguides with graphene for ultrasensitive biosensor,” Opt. Express 26(13), 16884–16892 (2018). [CrossRef]
16. M. Gryga, D. Ciprian, and P. Hlubina, “Bloch SurfaceWave Resonance Based Sensors as an Alternative to Surface Plasmon Resonance Sensors,” Sensors 20(18), 5119 (2020). [CrossRef]
17. M. Gryga, D. Ciprian, L. Gembalova, and P. Hlubina, “Sensing based on Bloch surface wave and self-referenced guided mode resonances employing a one-dimensional photonic crystal,” Opt. Express 29(9), 12996–13010 (2021). [CrossRef]
18. L. M. Wu, Q. K. Wang, B. X. Ruan, J. Q. Zhu, Q. You, X. Y. Dai, and Y. J. Xiang, “High-Performance Lossy-Mode Resonance Sensor Based on Few-Layer Black Phosphorus,” J. Phys. Chem. C 122(13), 7368–7373 (2018). [CrossRef]
19. X. Y. Dai, H. Chen, C. Y. Qiu, L. M. Wu, and Y. J. Xiang, “Ultrasensitive Multiple Guided-Mode Biosensor With Few-Layer Black Phosphorus,” J. Lightwave Technol. 38(6), 1564–1571 (2020). [CrossRef]
20. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008). [CrossRef]
21. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008). [CrossRef]
22. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008). [CrossRef]
23. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013). [CrossRef]
24. L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014). [CrossRef]
25. G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, “Topological insulator laser: Theory,” Science 359(6381), eaar4003 (2018). [CrossRef]
26. Y. Gao, P. H. Dong, and Y. C. Shi, “Suspended slotted photonic crystal cavities for high-sensitivity refractive index sensing,” Opt. Express 28(8), 12272–12278 (2020). [CrossRef]
27. Q. Cheng, S. T. Wang, J. T. Lv, and N. Liu, “Topological photonic crystal biosensor with valley edge modes based on a silicon-on-insulator slab,” Opt. Express 30(7), 10792–10801 (2022). [CrossRef]
28. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems,” Phys. Rev. X 4(2), 021017 (2014). [CrossRef]
29. X. Wang, Y. Z. Liang, L. M. Wu, J. Guo, X. Y. Dai, and Y. J. Xiang, “Multi-channel perfect absorber based on a one-dimensional topological photonic crystal heterostructure with graphene,” Opt. Lett. 43(17), 4256–4259 (2018). [CrossRef]
30. P. St-Jean, V. Goblot, and E. Galopin, “Lasing in topological edge states of a one-dimensional lattice,” Nat. Photonics 11(10), 651–656 (2017). [CrossRef]
31. Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, “Topological States and Adiabatic Pumping in Quasicrystals,” Phys. Rev. Lett. 109(10), 106402 (2012). [CrossRef]
32. J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989). [CrossRef]
33. O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987). [CrossRef]
34. M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010). [CrossRef]
35. Y. M. Qing, H. F. Ma, L. W. Wu, and T. J. Cui, “Manipulating the light-matter interaction in a topological photonic crystal heterostructure,” Opt. Express 28(23), 34904–34915 (2020). [CrossRef]
36. J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41(6), 416–419 (1951). [CrossRef]
37. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965). [CrossRef]
38. W. N. Hansen, “Electric fields produced by the propagation of plane coherent electromagnetic radiation in a stratified medium,” J. Opt. Soc. Am. 58(3), 380–388 (1968). [CrossRef]
39. L. Xu, H. X. Wang, Y. D. Xu, H. Y. Chen, and J. H. Jiang, “Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals,” Opt. Express 24(16), 18059–18071 (2016). [CrossRef]
40. M. Xiao, G. C. Ma, Z. Y. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, “Geometric phase and band inversion in periodic acoustic systems,” Nat. Phys. 11(3), 240–244 (2015). [CrossRef]
41. W. S. Gao, M. Xiao, C. T. Chan, and W. Y. Tam, “Determination of Zak phase by reflection phase in 1D photonic crystals,” Opt. Lett. 40(22), 5259–5262 (2015). [CrossRef]
42. L. M. Wu, Y. J. Xiang, and Y. W. Qin, “Lossy-mode-resonance sensor based on perovskite nanomaterial with high sensitivity,” Opt. Express 29(11), 17602 (2021). [CrossRef]
43. Y. F. Yuan, X. T. Yu, Q. L. Ouyang, Y. H. Shao, J. Song, J. L. Qu, and K. T. Yong, “Highly anisotropic black phosphorous-graphene hybrid architecture for ultrassensitive plasmonic biosensing: Theoretical insight,” 2D Mater. 5(2), 025015 (2018). [CrossRef]
