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Abstract
Refractive index (RI) measurements are pertinent in concentration and biomolecular detection. Accordingly, an ultrasensitive optofluidic coupled Fabry–Perot (FP) capillary sensor based on the Vernier effect for RI sensing is proposed. Square capillaries integrated with the coupled FP microcavity provide multiple microfluidic channels while reducing the complexity of the fabrication process. The incoherent light source and spectrometer used during measurement facilitate the development of a low-cost sensing system. An ultrahigh RI sensitivity of 51709.0 nm/RIU and detection limit of 2.84 × 10−5 RIU are experimentally demonstrated, indicating acceptable RI sensing performance. The proposed sensor has significant potential for practical and low-cost applications such as RI, concentration, or biomolecular sensing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optofluidic microcavities have been widely used for the detection of various refractive indices (RIs) or concentrations because of their fast response time and ultralow detection limits (DLs) [1–4]. Some of the widely studied optofluidic microcavities include the Fabry–Perot (FP), whispering gallery mode (WGM), and photonic crystal microcavities [5,6]. Generally, the RI of a solution varies with its concentration, varying the effective RI (neff) of the resonance mode, resulting in a shift in the resonance wavelength (λ). The resonance wavelength is described as 2neff L = mλ, where L is the effective cavity length and m is a positive integer. Therefore, the RI or concentration can be measured by monitoring the resonance wavelength shift. Various parameters, such as RI sensitivity (S), mode spectral linewidth (full width at half maximum (FWHM)), DL, and figure of merit (FoM), are used to characterize sensing performance. The RI sensitivity is defined as S = δλ/δn. Accordingly, a high sensitivity indicates an acceptable ability to detect weak signals, and a narrower mode spectral linewidth indicates higher spectral resolution and quality (Q) factor. DL is defined as DL = 3σ/S, where σ is the background noise standard deviation. FoM is defined as FoM = S/FWHM, which indicates that a microcavity with significant S and narrow spectral linewidth has excellent sensing performance. Among the various microcavities, the FP microcavities have high sensitivity owing to their strong light-matter interactions [7,8]. In recent years, many efforts have been made to improve its DL by increasing the Q-factor [9–12]. However, difficulties in realizing a high Q-factor persist owing to the walk-off loss and low coupling efficiency [10,13,14]. The WGM microcavities have a larger Q-factor and smaller RI sensitivity. This is because most of the photons are constrained inside the cavity [15–17]. Furthermore, the maximum sensitivity is limited by the wavelength and RI of the analytes (Smax = λ/n) in a single microcavity. Recently, the Vernier effect has been combined with optical microcavities to further improve their sensitivity. The Vernier effect originates from the mode coupling of two cavities with different free spectrum ranges (FSRs), which induces a modulated spectral envelope. The magnification factor (M) is defined as M = FSR/ΔFSR, where ΔFSR is the FSR difference between the two cavities [18]. Theoretically, owing to the magnification effect, S can be improved without limitation. However, a high sensitivity simultaneously induces a small spectrum resolution. Therefore, M typically ranges from one to two orders of magnitude [19,20].
Coupled WGM microcavities based on the Vernier effect were previously used as laser sensors, realizing high RI sensitivities (5930 nm/RIU) [21–24]. However, the complicated detection system for lasing signals, bleaching effects of the gain medium, and poor repeatability limited their practical application. Therefore, coupled FP microcavities are used for RI sensing in passive schemes. Based on their structures, coupled FP microcavities can be categorized as fiber-based coupled FP interferometers (FPIs) and parallel-mirror-based coupled FP microcavities. For fiber-based coupled FPIs, various optical sensors have demonstrated ultrahigh sensitivities owing to the Vernier effect [25–27]. The advantages of fiber FPIs include easy and flexible integration in an entire fiber system. However, their complicated fabrication process and fragile structure limit their application. Additionally, their small and fragile fiber structure makes integration with microfluidic channels difficult. For parallel-mirror-based coupled FP microcavities, identical optical characteristics can be realized by cascading two FP microcavities [8]. Although their sensing structures are not flexible for integration in the entire fiber system, their fabrication process is simple and the microfluidic channels can be easily integrated. Additionally, optical sensing chips can be used to detect multiple microfluidic channels. Therefore, a high sensitivity optical RI sensor with simple fabrication process and multiple optofluidic channels is desirable.
In this study, novel compact optofluidic coupled FP microcavities based on the Vernier effect were developed for RI or concentration sensing. As shown in Fig. 1(a), two FP microcavities were constructed using three parallel-placement gold mirrors. The sensing cavity was integrated with square capillaries, and the medium was easily delivered using a combination of microfluidic technologies. The reference cavity consisted of two gold mirrors, and the cavity length was slightly different from the height of the square capillaries. The small difference between the FSR of the sensing and reference cavities resulted in the Vernier effect and magnification of S, showing in a form of modulated envelopes in the optical spectrum. Due to the RI is measured by monitoring the spectral envelope shifts rather than single transmission peak. The influence of non-parallel gold mirror inducing the broaden of single peak to the optical sensing performance is insignificant. Furthermore, measurement was realized using only an incoherent light source and a spectrometer, indicating a low-cost sensing system. The favorable optical characteristics of coupled FP microcavities such as multiple optofluidic channels, simple fabrication process and low-cost sensing system illustrate an attractive solution for practical applications in RI or concentration detection.
Fig. 1. Structure and parameters of a coupled FP microcavity. (a) Schematic of a coupled FP microcavity. (b) Cross section along the x-z plane.
2. Theoretical analysis
The x-z plane cross-section of the coupled FP microcavity is shown in Fig. 1 (b), consisting of multiple square capillaries and three gold mirrors. The sensing cavity was made of mirrors 1 and 2, and square capillaries, whereas the reference cavity was made of mirrors 2 and 3. The substrate thickness of mirror 2 was approximately 300 µm, similar to the height of the square capillaries required to generate the Vernier effect. When the light from an incoherent light source was incident on the coupled FP microcavity, the light that satisfied the resonance condition stably constrained inside the sensing and reference cavities. Owing to the difference in FSR, these two spectra superimposed and formed envelopes in the output transmission spectrum.
A numerical calculation was conducted to explain the sensing principle and provide instructions for further sensing performance optimization of the coupled FP microcavity. For a single FP microcavity, the normalization transmission spectrum is described as follows:
In the numerical simulation, L1 and L2 were set to 320 and 300 µm, respectively, the wall thickness of the square capillary was approximately 105 µm, reflectivity of the gold mirror was approximately 92% at 1550 nm, RIs of the quartz substrate and square capillary wall were 1.45, and RI of the analytes in the microfluidic channel was 1.33. The theoretically simulated transmission spectra are shown in Fig. 2, where (a) and (b) represent the transmission spectra of the reference and sensing cavities, respectively. Owing to the difference in cavity length and RI, FSR was different. FSR is defined as follows:
where λ is the resonance wavelength, and neff and Leff are the effective refractive index and cavity length of the FP cavity, respectively. The transmission spectrum of the coupled FP microcavity is shown in Fig. 2(c). The envelope of transmission was fitted using the Lorentz function [21,22].Fig. 2. Transmission spectra of separate FP cavities and coupled FP cavities. (a) Transmission spectrum of the reference cavity. (b) Transmission spectrum of the sensing cavity. (c) Transmission spectrum of the coupled FP microcavity.
Fig. 3. Numerical simulations of the transmission spectra for different microfluidic channel heights (L0). (a) and (c) Envelope shifts for different concentrations of dimethyl sulfoxide (DMSO) when L0 = 110 and 210 µm, respectively. (b) and (d) Wavelength shifts when L0 = 110 and 210 µm, respectively.
The RI of the solutions varied with respect to their concentration. To obtain different RI with a large range, dimethyl sulfoxide (DMSO) was chosen and dissolved into the deionized water, resulting in a RI range changes from 1.33 to 1.48. In the numerical simulation, the envelope shift was studied by setting different concentrations of DMSO inside the square capillary, as shown in Fig. 3(a). With the increase in DMSO concentration, the envelope in the transmission spectrum red-shifted owing to an increase in RI. The sensitivity was approximately 9505 nm/RIU, and its magnification was approximately 26, as shown in Fig. 3(b). To further optimize the sensing performance and increase the light-medium interaction strength, different wall thicknesses of the square capillaries were simulated. When the wall thickness decreased to 55 µm, the sensitivity increased to 69630 nm/RIU (M = 109), which was attributed to the increase in the M factor and light-medium interaction strength, as shown in Figs. 3(c) and (d). The difference between FSR1 and FSR2 decreased as the wall thickness decreased, resulting in an increase in the M factor. Moreover, the sensitivity limitation of the sensing cavity increased owing to a strong interaction between the analytes and light. The sensitivity limitation of the sensing cavity (Ssensing) is defined as follows:
The bulk S of the coupled FP capillary sensor is defined as follow:
According to Eqs. (6) and (8), the RI sensitivity is related with L0 and n0. Therefore, the effect of optofluidic can be considered into the numerical simulation model by changing the optofluidic channel height and its corresponding RI. Moreover, the RI sensitivity is limited by the microfluidic channel height, which directly affect the RI sensitivity of sensing cavity and M factor, as shown in Eq. (8). The bulk S under different L0 was shown in Fig. 4(a), wherein the sensitivity increased with decreasing wall thickness. The relationship between sensitivity and L0 was nonlinear, as shown in Fig. 4(b), owing to the Vernier effect of the coupled FP microcavity. A higher sensitivity induced a large envelope spectrum linewidth, resulting in a smaller resolution during sensing, as shown in Figs. 3(a) and (c). Therefore, a compromise between sensitivity and resolution was required for choosing a suitable square capillary wall thickness to fabricate the coupled FP microcavity.
Fig. 4. Numerical simulations of the RI sensitivity for different microfluidic channel heights (L0). (a) Wavelength shift for various L0 values of the microfluidic channel. (b) Relationship between bulk S and L0 of the microfluidic channel.
Fig. 5. Mode profile distributions with and without the Vernier effect. (a) and (b) Mode profile distribution for different liquid RI inside the square capillary when the reference cavity under resonance. (c) Mode profile distribution when the sensing cavity under resonance. (d) Mode profile distribution for separate FP microcavity.
The mode profile distribution with and without the Vernier effect is simulated with the Finite Element Method (COMSOL Multiphysics), as shown in Fig. 5. The photons are stably resonant in the reference cavity when the incident wavelength meets its resonance condition, as shown in Fig. 5(a). However, the incident wavelength does not meet the resonance condition of sensing cavity due to the small cavity length difference between sensing and reference cavities, resulting in a weak mode profile distribution is generated in the sensing cavity. With different RI inside the capillary, the resonance wavelength changes as well, as shown in Figs. 5(a) and (b). Figure 5(c) is the mode profile distribution when the sensing cavity is under resonant, whose resonance wavelength is different from Fig. 5(a). The resonance wavelength difference indicating the Vernier effect existed in the coupled FP microcavity sensors, resulting in the spectral superimposing in the transmission spectrum, as shown in Fig. 2(c). Figure 5(d) is the mode profile distribution for separate FP microcavity. The difference of mode profile distribution between coupled FP cavity and separate FP cavity also indicates the Vernier effect existed in a coupled FP cavity. During the simulation, the model was simulated with a smaller size to reduce the calculation time and computational memory. However, none of any difference exists compared with a larger coupled FP microcavity model to verify the Vernier effect.
3. Fabrication process and experimental setup
The fabrication process of the coupled FP microcavity involved several steps. First, multiple square capillaries of height 320 µm were fixed on the upper surface of the middle gold mirror using ultraviolet (UV) glue. The substrate thickness of the middle gold mirror was approximately 300 µm, which was close to the height of the square capillary required to generate the Vernier effect, as shown in Figs. 6(a) and (b). Accordingly, a square capillary with an initial wall thickness of 105 µm formed a microfluidic channel for analyte delivery. Subsequently, another gold mirror was fixed on the upper surface of the square capillaries using UV glue to form the sensing cavity, as shown in Fig. 6(c). Next, a third gold mirror (covered with a layer of UV glue) was fixed under the middle gold mirror to form the reference cavity, as shown in Fig. 6(d). During each fabrication step, a vertical stress was exerted on the capillary or gold mirror surface to ensure tight adhesion to another gold mirror surface. Therefore, the non-parallelism of three gold mirror can be greatly decreased. Finally, the two ends of the square capillary were connected to the microfluidic system to fabricate a bulk RI or concentration sensor.
Fig. 6. Fabrication processes and measurement experimental setup of the coupled FP microcavity. (a) A gold mirror with a silica height of 300 µm. (b) Square capillaries on the middle gold mirror. (c) Another gold mirror on the upper surface of the square capillaries to form a sensing cavity. (d) Third gold mirror below the middle gold mirror to form a reference cavity. (e) Schematic of the experimental setup. Abbreviations in image: beam collimator (BC), beam splitter (BS), objective lens (OL), and charge coupled device camera (CCD Camera).
Figure 6(e) shows a schematic of the experimental setup, consisting of the sensing (red) and imaging (cyan) paths of light. The sensing path was as follows: the light output from an incoherent light source (Energetiq-99X) entered the beam splitter after passing through a beam collimator. Subsequently, the light was coupled into the coupled FP microcavity via an objective lens. The transmission light from the coupled FP microcavity was collected by another objective lens and sent to the spectrum analyzer (Acton SpectraPro@SP-2750). The imaging path was as follows: the optical imaging information of the coupled FP microcavity was collected by an objective lens and sent to the charge coupled device (CCD) camera via a beam splitter, which was used to observe the position of the incident light and couple the lights in a square capillary region.
4. Results and discussion
4.1 RI sensing
When different concentrations of DMSO solution were injected into the sensing cavity, the transmission spectra of the coupled FP microcavity were detected using the experimental setup described in Section 3. Different concentrations of DMSO solution were obtained by mixing it with deionized water under specific volume ratio. As shown in Fig. 7, the Vernier effect was generated owing to the cavity length difference between the sensing and reference cavities, as shown in the transmission spectra in the form of envelopes. The uneven intensity distribution of the incident light source induces resonance peaks with significant or insignificant intensities in the transmission spectrum, as shown in Fig. 7(a). To reduce this influence and fit the envelope accurately, we first extracted the peak value of every resonant mode, as shown by the blue dots in Fig. 7(b). The envelope of the transmission spectra was obtained by fitting the peak value using the Lorentz fit function [21,22], as shown in Fig. 7(b) with a red line. Furthermore, the wavelength shifts were statistical average value by three different measurements, which further reduce such influence to the sensing performance. According to the theoretical analysis discussed in Section 2, a decrease in the wall thickness of the square capillary can further increase the RI sensitivity due to the increase in the M factor and interaction strength between the medium and light. Hydrofluoric acid (HF) solution with a concentration of 12% was used to decrease the wall thickness at a flow rate of 20 µL/min. By detecting the transmission spectra of the coupled FP microcavity every two hours under HF solution corrosion, S was measured, as shown in Figs. 7(c)–(e). S increased significantly with increasing HF solution corrosion time, and RI sensitivity of up to 51709.0 nm/RIU (R2 = 0.99381) was realized during the experiment, corresponding to an M factor of 84. Moreover, S increased nonlinearly with a decrease in wall thickness, owing to the Vernier effect, as described using the M factor. With a decrease in the cavity length difference between the sensing and reference cavities, the difference in FSR decreased, inducing a nonlinear increase in the M factor. The experimental results corelated with theoretical calculations. A compromise was to select an HF solution corrosion time of 7 h, resulting in larger RI sensitivity and a smaller spectrum resolution.
Fig. 7. Measured transmission spectra and its RI sensitivity for different HF corrosion time or L0. (a) Original output optical spectrum of the light source. (b) Measured transmission spectra of the coupled FP microcavity after 7 h of hydrofluoric acid (HF) solution corrosion for different concentrations of DMSO (0–0.5%). (c) Measured envelope center wavelength shift versus RI change in the DMSO solutions and linear fitting curve. (d) Measured envelope center wavelength shift versus RI change in the DMSO solutions and various HF corrosion times. (e) Measured sensitivity versus HF corrosion time and theoretical calculation results.
4.2 Practical RI resolution and biomolecular sensing
To evaluate the minimum RI resolution of the coupled FP microcavity, a smaller concentration of DMSO solution was injected into the square capillary. As shown in Fig. 8(a), a concentration of 0.02% was effectively distinguished using the coupled FP microcavity sensor, which corresponded to an RI change of 2.84 × 10−5 RIU. Figure 8(b) shows the fitting envelope for different concentrations of DMSO solution from 0–0.1%, illustrating the detection of a minimum concentration of 0.02% and corresponding wavelength shift of approximately 2.0 nm. The wavelength shift versus the low concentrations of DMSO solutions are shown in Fig. 8(c). The wavelength shifted by 8.2 nm when the RI changed from 1.33 to 1.330142, and the linearity (R2) was measured as 0.9952.
Fig. 8. Practical RI resolution evaluation. (a) Measured transmission spectra for smaller concentration DMSO solutions (0–0.1%). (b) Envelope for smaller concentration DMSO solutions (0–0.1%). (c) Wavelength shifts with RI for low concentration DMSO solutions.
Different concentrations of bovine albumin (BSA, Shanghai Sangon Biotech) solutions were further measured with the coupled FP microcavity sensor. Due to the ultralow practical RI resolution, the detection of low concentration BSA solution is feasible by the using of coupled FP microcavity sensor. During the experiment, the BSA solution with different concentrations were obtained by dissolving it into the phosphate buffer solution (PBS, diluted to 1x, Sigma Aldrich). As shown in Fig. 9, different concentrations of BSA solutions from 15 nM to 15 µM were measured. The low concentration detection of BSA solutions indicating the ultralow RI resolution of the coupled FP microcavity sensor. Furthermore, a series of RI sensors reported in recent years are listed in Table 1. Compared with existing and emerging RI sensors (surface plasmon resonance (SPR), WGM, Mach–Zehnder interferometer (MZI), coupler, FPI), the proposed coupled FP microcavity achieved higher optical RI sensitivity, FoM, and practical RI resolution. The optical sensing performance of the coupled FP microcavity implied significant potential for practical applications such as RI, concentration, or biomolecular sensors.
Table 1. Comparison of sensing performance among different types of sensors
5. Conclusion
A novel compact structure of square capillaries integrated with coupled FP microcavities based on the Vernier effect was proposed in this work, which is easy to fabricate compared with traditional fiber-based coupled FPIs. A benefit of the square capillary is the presence of multiple microfluidic channels easily integrated in the coupled FP microcavity, forming an FP sensing cavity, useful for the detection of multiple microfluidic channels. Furthermore, the incoherent light source and spectrometer used during measurement facilitates a low-cost sensing system. An ultrahigh RI sensitivity of 51709.0 nm/RIU, practical RI resolution of 2.84 × 10−5 RIU, and high FoM of 922 were experimentally demonstrated, indicating favorable RI sensing performance. The square capillary integrated coupled FP microcavity has potential for practical and low-cost applications such as RI or concentration sensors.
Funding
Open Foundation of Key Laboratory of Laser Device Technology, China North Industries Group Corporation Limited (KLLDT202108); National Natural Science Foundation of China (62175035); Natural Science Foundation of Shanghai (21ZR1407400).
Disclosures
The authors declare no conflicts of interest.
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.
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