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Abstract
A self-mixing interferometer combined with the photothermal spectroscopy is utilized as a remarkable sensor for highly sensitive trace detection, featuring the beneficial property of a He-Ne laser with back-mounted photodiode, to the best of our knowledge, acting as an excitation laser, also as a probe laser, and even more, as a detector. Utilizing the novel implementation of the photothermal self-mixing (PTSM) interferometer with an external cavity modulation, the concentration of the sample is directly measured by the PTSM parameter extracted from the PTSM signal. The metrological qualities of the PTSM interferometer were investigated by methylene blue trace detection. For a low excitation power of 5 mW, a 7.7 nM of the limit of detection was achieved with a relative standard deviation of ∼3%. The compact and simple structure with high sensitivity has guiding significance to a robust analytical tool for the analysis of photosensitive compounds and in the detection of aquatic product hazards in aquaculture.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photothermal spectroscopy(PTS) is the thermal state change of the sample induced by the absorption of radiation, which has been widely applied in many fields, such as analytical chemistry [1–3], biology and medicine [4], environmental protection [5, 6], physics for the Soret coefficients determination [7, 8] and hyperspectral imaging [9]. Typically, PTS setups have a two-laser arrangement, one is the excitation laser, which is used to heat the sample and induce the photothermal effect, and the other is the probe laser, which is used to detect the resulting changes of refractive index. Usually, this kind of PTS setups combined with an interferometer, which is used to sensitively detect the temperature-induced phase shift caused by the photothermal effect in the sample, are wonderful apparatuses for trace detection. Various types of interferometers have been applied, such as the Fabry-Perot configuration, Mach-Zehnder, and Jamin type [10–13]. Recently, H. Cabrera et al. firstly applied the self-mixing(SM) effect as a pump-probe in the photothermal system [14]. The SM effect, also known as self-mixing interference, generally happens when a laser is backscattered by an external object and re-entered back into the laser cavity, and mixes with the inside light field, resulting in a modulation in the spectra and the amplitude of the laser. Unlike traditional laser interference, the self-mixing interference does not need additional optical elements for inducing interference outside the laser cavity. Instead, the self-mixing effect occurs inside the laser cavity. Since the laser has a self-coherent nature, laser feedback systems are only sensitive to the laser reflected back to the laser cavity and only a small amount of light re-injected into the cavity can cause self-mixing effect. It is nowadays a well-established technique, because of the inherent simplicity, compactness and robustness as well as the self-aligning [15], and widely applied in different fields, such as displacement and vibration [16–19], absolute distance [20], angle [21], velocity [22], thickness [23], refractive index [24], motor runout [25], laser parameters [26], tomographic imaging [27], integral strain [28], acoustic fields [29], medical diagnosis [30]. The use of SM interferometry as a transducer for PTS offers a compact spatial structure for phase shift detection, and the amplitude of the resulting SM signal is proportional to the induced temperature change. Therefore, they used this system for trace detection in water samples [31]. The drawbacks of the basic two-laser arrangement PTS setups are that the energy of the selected probe laser should not be absorbed by the sample and the spot size of the probe laser must be smaller than that of the excitation laser beam to maintain the effectiveness of the parabolic approximation of thermal lens(TL) which results in complex optical path adjustment [32].
The simplest single-laser PTS setups, which are easy to build, align and manipulate. However, the major drawback is that most of them are based on far-field detection, which requires a long deflection path length of the order of a few meters [33]. And extraneous/parasitic mechanical vibrations can disturb the measurement which limited outdoor use. Additionally, high sensitivity is required for pollutants trace detection by applying low power and low-cost excitation light.
Regarding the issue above, the work aims to develop a simple and compact photothermal self-mixing (PTSM) interferometer for highly sensitive trace detection. The self-mixing interferometry is combined with the single-beam thermal lens effect. A He-Ne laser subject to a weak optical feedback regime is used to both excite the sample and simultaneously probe the thermal lens effect. The photodiode mounted in the back of the laser is used to detect PTSM signals for trace detection. An important advantage of the proposed method is that the He-Ne laser with back-mounted photodiode acts as an excitation laser, also a probe laser, even more, a detector. Having fewer components, which are only a laser, a chopper, a cell, and a mirror, allows for a highly compact experimental setup, which has an added benefit of lower cost. Moreover, the resistance against extraneous/parasitic mechanical vibrations and the sensitivity of the method are improved by external phase modulation. The metrological qualities of this novel method were demonstrated by methylene blue (MB) trace detection.
2. Principle
Figure 1 shows the diagram of the proposed photothermal self-mixing interferometer where the maximum power of the He-Ne laser is 5 mW. A chopper blade with a low-speed DC motor is used as an optical chopper to create periodic excitation. A mirror fixed on a high-precision nano-displacement piezoelectric transducer (PZT) is used to modulate the external cavity length.
As shown in Fig. 2(a), the propagation of the probe laser from its minimum beam waist ω0 at the plane of z = 0 to the mirror at z = L through the sample at z = d, then reflected back to the plane of z = 0, is calculated by the fundamental Gaussian-beam solution and the ABCD law for Gaussian beams. The size of the feedback beam is enlarged, and then the feedback-coupling coefficient is reduced. The fundamental Gaussian-beam solution q(z) is given by 1/q(z) = 1/R(z) – iλ/[πω2(z)], where R(z) is the radius of the laser wave front, ω(z) is the radius of the beam spot along the direction of laser propagation and λ is the wavelength of the laser. At the plane of z = 0, the radius of the minimum spot size is ω0, q0 = iπω20/λ = ib, where b is the confocal parameter of the laser beam. At the reflected plane of z = 0 with no TL effect, the Gaussian beam is described by
where
Fig. 2. Schematic for the Gaussian beam propagation of the photothermal self-mixing interferometer. (a) Gaussian beam propagation without TL effect and (b) Gaussian beam propagation with TL effect.
Then the laser beam is reentered into the laser cavity and formed the SM effect. According to the three mirror Fabry-Perot(FP) model, which is usually used to descript the principle of the SM effect [34], the equivalent FP model with a sample is shown in Fig. 3.
As can be seen from Fig. 3(a), the optical wave is firstly exited from M1, and then transmitted and reflected by M2. The related electric fields can be written as E1 = E0exp[-i(ωt+φ)], E2 = E0exp[-i(ωt+φ+kwnDLlaser)], and E3 = r2E0exp[-i(ωt+φ+kwnDLlaser)], respectively, where Llaser represents the cavity length of He-Ne laser, E0, ω, and φ are the amplitude, angular frequency and initial phase of the electric field, respectively. M1 and M2 are two facets of the He-Ne laser. kw = 2π/λp is the wave vector while λp is the wavelength of the probe laser. r2 is the reflection coefficient of M2. nD is the refractive index of the laser cavity.
The electric field of optical wave transmitted through M2 again, which is transmitted through the sample twice and reflected by the mirror, can be written as
As show in Fig. 3(b), the laser mirror M2, the sample and the mirror are combined into a single equivalent mirror. As reported in Ref [34]., the reflection coefficient of the equivalent mirror can be given by
The temperature gradient change in the sample causes the refractive index gradient change, which in turn causes the phase shift during the propagation of the probe laser. The phase shift can be expressed as [35]
The refractive index gradient change also causes the change in focal length of thermal lens, which in turn causes the change of the coupling coefficient of the feedback light in the PTSM system, that is the variation in modulation index m. Taking methylene blue in ethanol solution as an example; its thermal lens effect can be equivalent to a concave lens. As shown in Fig. 2(b), the size of the feedback beam is further enlarged, and then the modulation index is reduced. The Gaussian beam of the probe laser from its minimum beam waist ω0 at the plane of z = 0 to the mirror at z = L, through the thermal lens of focal length F, then reflected back to the plane of z = 0, is described by
whereThe difference in inverse focal lengths between the maximum heating and minimum cooling times is
According to the Beer law, the concentration of the sample is proportional to its absorption coefficient, α = K2C + α0, where K2 is a constant and α0 = 15.5×10−4 cm-1 is the absorption coefficient of ethanol [35]. dn/dT and k are the thermo-optic constants of the sample; and Pe, l, ω0, t1 and tc are constants of the system. We can get the linear relationship between the PTSM parameter and the concentration of the sample
The process is simulated and the simulation results are shown in Figs. 4 and 5. The corresponding parameters are shown in Table 1. The optical feedback is set in the weak optical feedback regime (the optical feedback level = 0.01).
Fig. 4. Simulation of signals for C = 0. (a) Inverse focal length, (b) PTSM signal ΔPFt, (c) and (d) Enlarged PTSM signal.
Fig. 5. Simulation of signals for C = 8.0×10−6 mol/L. (a) Inverse focal length, (b) PTSM signal ΔPFt., (c) and (d) Enlarged PTSM signal.
Table 1. Simulation parameters
As shown in Fig. 4, the concentration of the sample is 0. In other words, the sample is ethanol (99.9%). The magnitude of the inverse focal length difference is almost zero (∼7.14×10−6 m-1). As the laser irradiation, the amplitude of ΔPFt shown in Fig. 4(b) remains almost constant. When the chopper blocks the laser, the amplitude of ΔPFt suddenly becomes zero until the next laser excitation cycle. At the beginning of each excitation cycle, there is no TL effect. Therefore, the amplitude of ΔPFt at this moment is |ΔPF0|. At the end moment of each excitation cycle, the amplitude of ΔPFt at this time is |ΔPFt(at tt1)|. The difference between |ΔPF0| and |ΔPFt(at tt1)| can hardly be observed and the envelope amplitude of the PTSM signal in every excitation cycle is almost a constant. The reason is that the laser power is only 5 mW and the absorption coefficient of ethanol for laser with a wavelength of 632.8 nm is quite small. The PTSM signal is mainly affected by the chopper and changes periodically.
As shown in Fig. 5, the concentration of the sample is 8.0×10−6 mol/L. K2 = 6.9662×10−6 mol/(L·cm) measured by ultraviolet-visible spectrophotometer (Duetta, fluorescence and absorbance spectrometer, HORIBA). As shown in Fig. 5(a), The variation of the inverse focal length in one excitation cycle is about 7.4×104 times that of C = 0. It can be clearly observed from Fig. 5(b) that the envelope of the PTSM signal is modulated not only by the chopper, but also by the TL effect. At the beginning of each excitation cycle, there is no TL effect. Therefore, the amplitude of ΔPFt at this moment is the maximum, as shown in Fig. 5(c). As the laser irradiation, the laser beam is gradually diffused due to the TL effect and the amplitude of ΔPFt gradually decreases. At the end moment of each excitation cycle, the amplitude of ΔPFt at this time is the minimum. When the chopper blocks the laser, the amplitude of ΔPFt suddenly becomes zero until the next laser excitation cycle.
It’s shown that the PTSM signal of each excitation cycle is almost the same when M is greater than 25. Figure 6 depicts the simulated PTSM parameters S(M = 99) for the sample concentration ranging from 0.2×10−6 mol/L to 10.0×10−6 mol/L. The heating times are 1.0 s, 0.8 s, and 0.6 s, respectively. The excitation power of the upper four curves is 5 mW, and that of the lower three curves is 1 mW. The length of the sample for the top curve is 2 cm, and that of others is 1 cm. Solid and dashed lines are the least squares linear fitting of the simulation data. It’s shown that the relationship between S(M) and the concentration of the sample is linear. In addition, with the same excitation power, longer heating time and longer length of sample lead to a larger slope of the linear fitting curve, which means higher sensitivity. Higher excitation power also leads to a larger slope of the linear fitting curve. Therefore, if we use a longer sample cell, longer heating time, and higher power laser, the sensitivity can be improved.
Fig. 6. Simulated PTSM parameters for the sample concentration ranging from 0.2×10−6 mol/L to 10.0×10−6 mol/L with different excitation frequencies(R2 is the correlation parameter).
The frequency of the PTSM signal caused by the chopped excitation is
The self-mixing interference fringe frequency of the PTSM signal mainly caused by external cavity length modulation is To avoid frequency overlapping problems, fmF must be greater than twice ftlF. Therefore, the following relation should be satisfied: From Eq. (26) we can see that the minimum modulation frequency of external cavity length needed is directly inversely proportional to the modulation amplitude of external cavity length and proportional to the frequency of the chopped excitation. Considering only detecting the envelope of the signal and the details of the interference fringes are not used in the system, the modulation amplitude and frequency of the external cavity only need to meet Eq. (26). To make the phase shift caused by external cavity length modulation more obvious than that caused by thermal lens effect, and make the experimental phenomenon more obvious, ΔL ≥ λ/2 is set to obtain at least one complete self-mixing interference fringe in one heating cycle. Of course, the parameter limitation of PZT, which is used for external cavity length modulation, needs to be considered in the experiment.3. Experimental results and discussion
The experimental setup and measurement process for the photothermal self-mixing interferometer is shown in Fig. 7. The wavelength of the He-Ne laser is 632.8 nm, the radius of the minimum spot size is 0.085 cm, and the cavity length is 29.50 cm. The initial distance from the laser to the mirror is 35.00 cm. The distance from the laser to the cell is 22.00 cm. The radius of the entrance to the laser is 1.15 mm. A chopper blade with a low-speed DC motor is used as an optical chopper to create periodic excitation. The mirror is mounted on a linear stage (P-603, PI) and vibrated in a sine wave with amplitude of 2.373 μm and a frequency of 60 Hz. The PTSM signals are detected and amplified by the PD(PDA100, Thorlabs) mounted in the back of the laser. The output signals of PD are collected after 2 minutes of chopped laser excitation to get stable PTSM waveforms and converted into digital signals by a data acquisition board (USB-6361, NI) with a sampling rate of 51.2 KHz. And then the data are processed on a PC. Firstly, the PTSM signals are normalized and processed to extract the heating segments. And then the maximum and minimum value of the envelope of each segment (each laser excitation segment) are detected to calculate S(M). Seven measurements of the S(M) for the excitation cycle were performed and the average value with the standard deviation was registered.
Methylene blue is of great interest because it is frequently used to cure fish diseases in aquaculture practices and for transport around the world, which can cause harmful effects on the human body. Thus, accurate detecting approaches are vitally important for monitoring residual hazardous chemicals in fish tissues [36]. And methylene blue is also widely used as a redox indicator in analytical chemistry. Therefore we use the MB as an example for trace detection. We prepared the MB ethanol solutions in the range of 0.2×10−6 to 10.0×10−6 mol/L. The solution contained in a 1 cm quartz cuvette is used as a test sample.
Figure 8 shows the signals acquired for a sample without MB with a chopping period of 2 s and a heating time of 1 s. It has shown that the amplitude of the PTSM signal is modulated by a square wave, which is produced by the chopper and changes periodically, and the change of envelope amplitude in every heating cycle caused by TL effect can hardly be observed.
Fig. 8. Signals for C = 0. (a) The blue line is the PTSM signal and the red line represents the modulated excitation, (b) and (c) Enlarged PTSM signal.
Figure 9 shows the signals acquired for a sample of the concentration with 8.0×10−6 mol/L and other parameters are the same as those in Fig. 8. It’s shown that the measured PTSM signal is the result of the SM and TL effects. The feedback light passes through the sample with thermal lens effect twice and is reflected by the mirror. It is embedded with information of phase shift caused by the refractive index gradient change due to the TL effect and modulated by periodic motion of external cavity mirror. The feedback process brings the phase shift information back into the laser cavity. The contribution of this part is shown as self-mixing interference fringes in the PTSM signal. One fringe corresponds to the phase change of 2π. Furthermore, the beam is diffused by thermal lens. The light spot size increases gradually when the laser beam traverses the sample. Then the intensity of feedback light is modulated by the TL effect. The contribution of this part is shown as the envelope amplitude modulation of the self-mixing interference fringes in the PTSM signal. It’s shown that the envelope of the PTSM signal in every heating cycle decreases gradually during the laser excitation. In addition, during the next laser excitation cycle, it decreases gradually from the maximum value to the minimum value again. The shape of the envelope of the PTSM signal in every exciting period is characteristic of the thermal processes like the photothermal signals in the previously reported by single laser PTS, which indicates that the SM signal is modulated by the TL effect. This validates the proposed PTSM theoretical model.
Fig. 9. Signals for C = 8.0×10−6 mol/L. (a) The blue line is the PTSM signal and the red line represents the modulated excitation, and (b) Enlarged PTSM signal.
Figure 10 shows the relationship between the concentrations of MB in ethanol solution and the PTSM parameter S(M). It’s shown that the PTSM parameter S(M) changes linearly with the concentrations of MB in ethanol solution with the correlation parameter R2 =0.991. The relative standard deviations (RSD) are less than 3% as shown in the inset of the figure. The LOD of the proposed method was calculated as LOD = 3×SD0/Ms = 3×0.0003/(0.1170/(10−6 mol/L)) 7.7 nM, where SD0 is the standard deviation of S(M) for the blank signal and Ms is the slope of the linear fitting curve shown in Fig. 10 in red. At higher concentrations, nonlinearities are observed due to the very low SNR and an exciting power of only 5 mW. When the concentration is high, due to the sample's stronger absorption and TL diffusion, the beam feedback to the inner laser cavity is reduced to a very low value, resulting in a very small modulation index, and then the PTSM signal is drowned by noise. This makes it hard to obtain the S(M) parameter correctly. At lower concentrations, due to the stronger intensity of the feedback light and the help of external cavity modulation, the PTSM signal presents lower noise, especially compared with no modulation. This fact produces a low standard deviation in the blank PTSM signals and obtains the smaller LOD. Moreover, the linear fitting curve is linear through the whole range of concentrations enabling more reliable measurements. Although the LOD of our method is higher than that of the method by the ultra-sensitive surface-enhanced Raman spectroscopy coated with gold nanorods [36], our method is direct and convenient. This value compares favorably with those previously reported with PTS studies of MB (60 ng/mL) [37]. Moreover, our method uses much lower excitation power, shorter optical path length, and only one laser. And it is about 4 times lower compared to that determined based on the direct photothermal detection scheme in a flowing stream [38].
Fig. 10. Relationship between the concentrations of MB in ethanol solution and the PTSM parameter S(M) and the inset shows the RSD for each measurement point (n = 7).
Figure 11 shows the relationship between the concentrations of MB in ethanol solution and the PTSM parameter S(M) with a different heating period. The heating times are 1.0 s and 0.6 s, respectively. Solid lines are the corresponding linear fitting curves. It has shown that the longer heating time leads to a larger slope of the linear fitting curve, which means higher sensitivity in trace detection. Therefore, if we use a longer sample cell, longer heating time, and higher power laser, the sensitivity can be improved.
Fig. 11. Relationship between the concentrations of MB in ethanol solution and the PTSM parameter S(M) with a different heating period.
4. Conclusions
The paper illustrates high sensitive trace sensing by the newly developed photothermal self-mixing interferometer with an external cavity modulation. We deduced and demonstrated the linear relationship between the PTSM parameter S(M) and the concentration of sample; the capabilities of the method were demonstrated on the example of MB trace detection. With a low excitation power of 5 mW, a 7.7 nM LOD was achieved with an RSD of ∼3%. The novelty of this work is that the He-Ne laser with back-mounted photodiode acts as an excitation laser, also a probe laser, even more, a detector. This makes the sample with TL effect become a main component of the laser cavity, thus needing a very small amount of sample required for sensing. The proposed PTSM interferometer is simple, compact, and easy to operate, which can provide an application in the detection of aquatic product hazards in aquaculture, a possible application for the analysis of photosensitive compounds, or a technique as a detector for liquid chromatography.
Funding
Key Scientific Research Platforms and Projects in Guangdong Universities (2020ZDZX2055); National Natural Science Foundation of China (61705095); Natural Science Foundation of Guangdong Province (2019A1515011461); Special Projects in Key Areas of Rural Rejuvenation of Guangdong Higher Education Institutes (2019KZDZX2008); Science and Technology Program of Zhanjiang (2020A03003, 2020B01211, 2021A05042); Open Project Program of Guangdong Provincial Key Laboratory of Development and Education for Special Needs Children (TJ202001); Lingnan Normal University Natural Science Foundation (ZL1815); Overseas Scholarship Program for Elite Young and Middle-aged Teachers of Lingnan Normal University; Yanling Outstanding Yong Teacher Training Program Funded Project of Lingnan Normal University (YL20200102).
Acknowledgements
The authors thank Dr. E. E. Ramírez-Miquet and Dr. H. Cabrera for helpful discussions about the values of the thermo-optic constants of the samples.
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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