Recently, to meet the growing demand of sensing platforms in the fields of biological, chemical and biochemical detection, photonic refractive-index (RI) sensors without fluorescent labeling have become a hot topic [1–8]. As typical photonic structures, photonic crystals (PCs) are powerful candidates for sensing applications, owing to the high sensitivity originating from their strong light-matter interaction between resonance modes and analyte. Generally the resonance modes can be generated by introducing line defects or point defects into perfect PCs. Therefore, many PC waveguide RI sensors [9–13] and PC cavity RI sensors [14, 15] have been designed in the near-infrared and midinfrared bands.

The midinfrared band, i.e. the wavelength range of 2–20 μm, has become more and more important in the realization of midinfrared devices. In fact, such a midinfrared band is an ideal wavelength range for the realization of absorption-based photonic sensors, because the absorption resonance peaks of many biochemical molecules fall in this spectral range. Recently, researchers have reported some optimized structures to achieve high performance RI sensors in the midinfrared band, such as slotted PC waveguides [16–19], a microtube PC [20], and PC nanocavities [21]. The operation principle of these studies is to find structures with strong modal confinement, which can enhance the interaction between the resonance modes and the analyzed samples. In [16] the proposed configuration was realized by introducing a T-shaped air slot into the PC slab. In the RI range of 1.05–1.10, the interaction between the slot-waveguide mode and the analyte produced an average RI sensitivity of 1040 nm/RIU (RI unit). In [21] the etching depth of air holes in PC nanocavities was optimized to detect the change in refractive index; the sensitivity was 322 nm/RIU, and the detection limit was 10^–3 RIU.

A coupled-cavity waveguide (CCW), which can be formed by placing multiple cavities in a row in a PC structure, should be another ideal choice for sensor applications, since the small group velocity that often emerges in this structure can enhance signal strength [22–27]. As a result, there may be stronger light-matter interaction and better sensitivity. In this paper, a midinfrared RI sensor is proposed for PC CCWs. To obtain strong modal confinement, some structural parameters, including the shape of the cavity, the width of the coupling cavity, and the size of the dielectric columns around the cavity, are fine-tuned. A high-sensitivity RI sensor based on the optimized PC CCW is then proposed and a sensitivity of approximately 2620 nm/RIU is obtained in the refractive index range of 1.0–1.4 [15, 20].

Silicon-on-insulator (SOI) can be used as an ideal platform for photonic sensors, because silicon is optically transparent in the midinfrared band. Generally, SOI has a high RI contrast between the silicon core and the cladding (air and SiO₂), which can effectively confine light within the silicon core. For these reasons, a PC CCW-based RI sensor is designed on a SOI platform in this paper. As shown in Fig. 1, the PC is created in a two-dimensional hexagonal lattice of dielectric rods with radius R = 0.3 a (where a, the lattice constant of the PC, equals 1 μm). The SOI platform consists of a 5-μm-thick silicon device layer and a 2-μm-thick silica buffer layer; the RIs of the silicon core and silica buffer layer are 3.42 and 1.45 respectively. According to the waveguide principle, the effective refractive index of transverse magnetic (TM)-like modes can be calculated as n_eff = 3.4 in the midinfrared band. The photonic band gap (PBG) of the PC lies between normalized frequencies 0.2248 and 0.309 (in units of 2πc/a) for TM polarization, according to dispersion analysis using the two-dimensional plane-wave expansion (PWE) method with the effective-RI approximation [28, 29].

Figure 1. Schematic representation of the PC CCW refractive index sensor with R = 0.3 a.

To form the CCW, three of every four rods in the central row are removed, forming coupled cavities distributed along the axis of the waveguide with a period of 4a. To study the dispersion properties of the CCW with original rod size (R = 0.3 a), the dispersion curve is calculated using the PWE method. As shown in Fig. 2, a unique CCW mode appears in the center of the photonic bandgap, represented by the green round-dotted line. In a realistic structure based on a slab waveguide, out-of-plane losses may be considerable; however, we focus only on the region of interest in reciprocal space where the CCW mode remains under the light line of the silica buffer layer (n = 1.45), thus mitigating such losses. Figure 2 also gives the distribution of the electric field component of the CCW mode at k = 0.5 (2πc/a), as shown in the inset. Evidently most of the localized modes are confined within the low-RI region of the CCW. When the analyte replaces air to fill the void space in the CCW, the analyte and the confined mode will be fully overlapped, which is very helpful to improve the sensitivity of the sensor.

Figure 2. Dispersion diagram for the PC CCW with R = 0.3 a; the inset shows the electric-field-component distribution for the CCW mode at k = 0.5 (2 πc/a).

It is worth noting that the CCW is designed in a rod-array-based PC. Compared to hole-array-based PCs, rod-array structures have several advantages for sensing applications. First, a rod array has a much larger air ratio. The large open space inside the CCW makes it much easier for analyte to fill the structure. Second, as seen from Fig. 2, the confined mode tends to be located more outside of the rods, which can enhance the light-matter interaction. For these reasons, the analyte fills in the void space of the CCW for RI sensing applications in this paper. The strong field confinement in the defect region makes the transmission characteristics of the CCW very sensitive to variation of RI among analytes. To explore the sensing performance of the CCW, dispersion and time-domain analyses are carried out using PWE and finite-difference time-domain (FDTD) methods [30].

The waveguide modes in the PBG region are demonstrated when the RI of the examined analyte (represented by n_s) changes from 1.0 to 1.4 in Fig. 3(a). It is seen that with increasing n_s the bands are pushed toward lower values. To verify the PWE results, numerical simulations are performed using the FDTD method with a boundary treatment of perfectly matched layers. In the simulation, the CCW sensor is illuminated by a broadband Gaussian pulse through the input channel, and the transmitted beam is detected at the output channel. The transmission length is 20 a. Figure 3(b) superimposes the transmission spectrum when the CCW is infiltrated by different analytes. Evidently the output transmission is subjected to a redshift with increasing RI of the infiltrated sample. These results are consistent with the dispersion analysis in Fig. 3(a). In addition, using the sensitivity parameter S (defined as S = Δλ/Δn, where Δλ represents the redshift of the transmission spectra and Δn represents the variation of refractive index), we show that the obtained shift corresponds to a sensitivity of 1437 nm/RIU.

Figure 3. Dispersion properties and transmission spectra for the RI sensor: (a) dispersion curves and (b) transmission spectra for the PC CCW sensor when the examined analyte’s n_s changes from 1.0 to 1.4.

The field-distribution diagram of the initial structure can be observed in Fig. 2, which shows that most of the energy is confined between the dielectric rods in the center of the waveguide and continuously propagates forward by coupling to the nearby evanescent Bloch waves. However, much energy dissipation still occurs near the waveguide. Therefore, in the proposed optimization method, first the two dielectric columns on either side of the waveguide with relatively concentrated energy in the figure are periodically removed, to ensure that more energy participates in the light-matter interaction, as shown in Fig. 4. Second, focusing on the energy in the middle of the dielectric column inside the waveguide, the area in which the sample is located is also the area that must be measured. Our goal is to make this area larger, which will significantly increase the area available for sensing in the central “high-field” regions, so that the sensitivity is steadily improved. Therefore, the structures on either side of the waveguide are shifted to the outside synchronously, with a shift of Δd.

Figure 4. Plane diagram of the CCW. The two structural parameters to be optimized are r and ∆d. r represents the radius of the central dielectric rods, and ∆d the synchronous outward shift of the structures on either side of the waveguide.

Next the optimization is o carried out on the two parameters Δd and r (i.e., the radius of rods in the center of waveguide). Considering the influence of these two parameters on the wavelength of the transmission peak, their numerical simulation is carried out simultaneously. As can be seen from Fig. 5(a), with decreasing r the sensitivity S generally increases. However, when r continues to decrease to 0.12 a and 0.10 a, the transmittance decreases obviously, as shown in Fig. 5(b). The reason for this may be that when r decreases the coupling effect between microcavities is weakened, and the energy transmission efficiency also decreases. Therefore, to ensure the performance of the sensor we determine the optimization range of r above 0.14 a. When Δd increases, S first increases and then decreases. This is because with increasing Δd the light-matter interaction is enhanced, as the area of the object to be measured increases. However, when Δd reaches a certain value, the mode part (i.e., the mode that is below the light line) that can be used for measurement disappears, and the remaining part of the transmission loss is very large, which ultimately reduces the sensitivity. The maximum sensitivity of 2400 nm/RIU is obtained by calculating a refractive index of 1.3–1.4 with Δd = 0.68 a and r = 0.14 a.

Figure 5. The sensitivity and transmission spectra for the CCW. (a) The sensitivity results for the CCW sensor with different ∆d and r; the range of ∆d is from 0 to1 a, and the range of r is from 0.14 a to 0.34 a. (b) Transmission spectra for r = 0.10 a, 0.12 a, and 0.14 a with n_s = 1.4.

Finally, it is necessary to study the sensing performance of the optimized CCW sensor with Δd = 0.68 a and r = 0.14 a when n_s varies from 1.0 to 1.4. Figure 6 shows the transmission spectra for some values of n_s. For the calculation of the sensitivity S, we determine the value of Δλ by investigating the shift of the rightmost peak, represented by the red dots in the figure. The results show that the highest sensitivity of 2620 nm/RIU can be obtained in the RI range of 1–1.2. and when the refractive index of analyzed samples changes from 1.0 to 1.4, the proposed sensor can maintain a high performance of greater than 2400 nm/RIU. From the mode-field diagram for n_s = 1.4, it can be seen that compared to Fig. 2, after removing the dielectric pillars on both sides the mode field energy is well limited within the waveguide. This may be the reason why the sensitivity has significantly improved. Table 1 compares some results from the recent literature with the work in this section. It can be seen from the results in the table that the sensitivity of the structure proposed in this paper is relatively high.

TABLE 1. Comparison of sensitivity from similar studies to that of the proposed sensor.

Sensor maximum sensitivity (nm/RIU)	Measurement range (RI)	Reference	Year
2280	1–1.06	[31]	2016
1040	1–1.3	[16]	2017
1720	1–1.01	[18]	2017
1450	1–1.5	[32]	2019
2400	1–1.4	Present work

Figure 6. Transmission spectra for the optimized PC CCW sensor with ∆d = 0.68 a and r = 0.14 when the RI of the examined analyte (represented by n_s) changes from 1.0 to 1.4. The inset shows the electric field distribution when n_s = 1.4.

In this paper, we have proposed the numerical design and analysis of a high-sensitivity midinfrared RI sensor based on a cavity-coupled photonic crystal waveguide. The highest sensitivity performance of up to 2620 nm/RIU was obtained around λ = 4 μm, by adjusting the width of the waveguide and the size of the central dielectric rods synchronously. In addition, when the refractive index of the analyzed sample changes from 1.0 to 1.4, the working performance of the proposed sensor can maintain a high performance of over 2400 nm/RIU. For the midinfrared band, the limitations of lithography technology are relatively low, which can greatly alleviate the manufacturing error of microcomponents such as a photonic crystal. This work provides valuable guidance for the realization of high-performance microscale integrated optical sensors.

This work was supported by the National Natural Science Foundation of China (No. 61605087).