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Abstract
In this paper, an ultrahigh sensitivity sensing in aqueous solution for microfiber modal interferometer (MMI) is realized. The group refractive index (RI) difference between HE11 and HE12 mode will come down to 0 at a certain wavelength, resulting in ultrahigh sensitivity near this wavelength. MMI with different diameters have their individual ultrasensitive wavelength band, which indicates the broad range of optional probing wavelength and more liberal diameter condition on fiber fabrication. In the experimentation, infrared absorption band in water around 1360-1600nm is easy to keep away by adjusting the microfiber diameter. As a result, an ultrahigh sensitivity of 14.95 pm/ppm is realized for sodium nitrate at 1320nm, whose equivalent sensitivity is about 1.26 × 105-nm/RIU for RI, which is much higher than most of the existing naked sensors with magnitude of 102-104nm/RIU.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Micro- and nanofibers show numerous outstanding properties, such as compact size, flexible structure and strong evanescent field [1,2], which have attracted lots of attentions in recent years. Currently, relevant researches on micro- and nanofiber have been reported in a lot of optical fields, including nonlinear effect and supercontinuum generation [3,4], ultrafast modulation for laser and network [5,6], light velocity control [7], higher mode excitation and elimination [8,9], light coupling between different nanowires [10–14], surface plasma excitation [14–16], optically trapping and monitoring [17,18], and optical sensing [19–21]. In particular, micro- and nanofiber enables large evanescent field to interact with the surroundings directly, breaking through the limitations of the traditional sensing principles such as heat transfer and strain variation. Hence, micro- and nanofiber sensors have been widely used in various liquid and gas environments whose refractive index (RI) is lower than the fiber core, even some special medium with higher RI [22].
Water is the most widely used solvent and many researchers have devoted their efforts to microfiber sensing in various aqueous solutions, including sucrose [23], hexadecane [24], isopropanol [25], salinity [26], nitrate [27] and temperature [28,29]. Generally, all the above sensing applications are based on the RI change in aqueous solutions, and show RI sensitivity of 102-104nm/RIU and RI resolution of 10−4-10−7 RIU, which need to be further improved, especially in the detection of micro components in natural water, which play important roles in drinking water security and environment monitoring. For instance, nitrate, whose concentration in drinking water is less than dozens of ppm and generally shows an ultralow concentration with the magnitude of ppb in seawater, requires 10−7 RIU or lower resolution for sensors. In order to improve the sensing sensitivity, the existing researches mainly focus on sensor structure design and thus various sensors have been proposed and optimized, including microfiber ring resonator (MRR) [30,31], Fabry–Pérot interferometer (FPI) [32], and microfiber modal interferometer (MMI) [23,33]. Particularly, MMI, whose sensitivity is deduced to be able to reach infinity, has been proved to be only 1.08 × 104nm/RIU [34] due to the difficulty in controlling the fiber diameter and the operation of probing wavelength in the strong absorption band in water. In addition, sensitization materials, such as graphene [35,36] and polymers [21,37,38], are also introduced to enhance the performance of microfiber sensors. For instance, the thermal sensitivity of the N-isopropylacrylamide-coated in-line MZI shows two orders of magnitude higher than the naked one [21]. However, the use of sensitization materials may increase the manufacture difficulty and affect robustness of microfiber sensors.
In this paper, we demonstrate an ultrahigh sensitivity sensing for microfiber modal interferometer (MMI) in aqueous solution. Theoretical results show that MMIs with different diameters have their unique ultrasensitive wavelength band (covers about dozens of nanometers) where sensitivity is higher than 1 × 105nm/RIU. The ultrasensitive wavelength band moves to shorter wavelength and the band width narrows down with the decrease of diameter of MMI. In experiment, an ultrahigh concentration sensitivity of 14.95 pm/ppm, as well as a RI sensitivity of 1.26 × 105nm/RIU, is demonstrated at 1320nm in sodium nitrate concentration sensing. To the best of our knowledge, this is the highest sensitivity experimentally demonstrated for the existing similar in-line MMI. The sensor demonstrated here shows advantages of simple and robustness structure, easy fabrication, high sensitivity, and show great potential in detecting micro components in water, and even can be extended to other liquid surroundings, such as seawater and ethanol. Furthermore, the analysis method proposed here is also applicable for other modal interferometers and may provide theoretical basis for development of other ultrasensitive microfiber sensors.
2. Sensing principle and theoretical simulation
The schematic diagram of the naked MMI is shown in Fig. 1, which consists of the input and output single mode fiber (SMF), transition regions, and a waist region. Light launches into the input SMF in the form of fundamental mode, and then it will be excited to HE11 and higher mode HE12 in the non-adiabatic transition [8]. It must be pointed out that the higher mode cannot be always excited unless the transition meets the non-adiabatic condition. According to the theory for slowly varying waveguides [39], a non-adiabatic transition should meet the requirement of zt<zb, where zt and zb denote the local taper length and beat length, respectively, as shown in Fig. 2(a). The core diameter of SMF dco(0) is assumed as 8.2 μm, the cladding diameter of SMF is 125 μm, the RI of core, cladding, and water are 1.4506, 1.4467, and 1.3207, respectively, and the working wavelength is 1320 nm. The critical local taper angle can be obtained from [40]
where β1, β2 are the propagation constants of HE11, HE12 modes, respectively. The critical local taper angle for a taper is shown in Fig. 2(b), which is consistent with the previous works [40,41]. The critical local taper angle in water is slightly smaller than that in the air. The minimum critical local taper angle through the transition is 6.3 × 10−4 rad in water and 6.4 × 10−4 rad in the air. If the local taper angle of a taper is larger than the critical value somewhere, the non-adiabatic condition will be activated and the higher order mode HE12 can be excited.Then, HE11 and HE12 mode will propagate along the waist together and finally couple to the output SMF. The effective RI of HE11 and HE12 modes can be expressed as
where k0 is the propagation constant in vacuum. The propagation constants of the supported modes in microfiber can be calculated by first order mode eigenvalue equation [42]where J1 is the Bessel function of the first kind, K1 is the modified Bessel function of the second kind,, ,, and d is the microfiber diameter. ncore and ncladding are the RI of fiber core and cladding, respectively, which corresponds to the RI of silica [43] and water [44] in our model.The phase difference between HE11 and HE12 will lead to an interference pattern in transmission spectrum. Such a modal interference is similar to the double beam interference, and its interference dip can be characterized by
Here, ∆n = n1-n2 is the effective RI difference, L is the length of waist, and m is a positive integer, representing the order of interference dips.Once a small RI variation occurs in the aqueous solution, the effective RI of HE11 and HE12 modes will change as well, leading to the spectral shift. The RI perturbation can establish a new interference status, whose interference dip can be modified as
By comparing Eq. (4) with Eq. (5), it can be deduced that
In this new interference status, the variation of effective RI difference d(Δn) is affected by the variation of solution RI and wavelength shift. Therefore, Eq. (6) can be rewritten asFinally, sensitivity can be deduced as:
where is the group RI difference (GRD), n is the RI of pure water, and M is the concentration of analyte. In previous works, the dependence of sensitivity on microfiber diameter at 1550nm has been investigated [34,45]. However, due to the strong infrared absorption in water under this wavelength, the interference spectra usually deteriorates and thus thick MMIs have to be used to reduce absorption loss at the cost of sensitivity.To solve the contradiction between the strong absorption loss and ultrahigh sensitivity, sensitivity proposed in Eq. (8) is used to investigate the relation between sensitivity and wavelength, and finally realize ultrahigh sensitivity by performing the sensing in low-loss wavelength. By the broad range of optional ultrasensitive wavelength, not only the harsh diameter condition is broken, but also strong absorption band in water can be avoided, which will make the experiment implement much easier and the sensitivity much higher. It is necessary to point out that the sensitivity mentioned in Eq. (8) is established on the RI sensitivity and thus it is versatile for aqueous solutions with different solutes. It is obvious that Gm, denominator of Eq. (8), can greatly affect sensitivity, especially when Gm≈0.
In our model, the diameter of microfiber and temperature is assumed to be 3.5μm and 25C, respectively. The (effective) RI of fiber core, cladding, HE11, and HE12 mode are calculated and shown in Fig. 3(a). It can be seen that before 1700nm, HE11 and HE12 mode are supported synchronously, while HE12 mode is cut off after 1700nm. The effective RI difference of HE11 and HE12 mode is also calculated and shown in Fig. 3(a). From a mathematical point of view, ∆n is regarded as the function of wavelength λ. It can be seen clearly that ∆n(λ) is a non-monotonic function, which means that ∂(∆n)/∂λ (the derivative of the function) have a wider range of possible values than ∆n/λ. Undoubtedly, ∂(∆n)/∂λ and ∆n/λ will be equivalent at a certain wavelength. As shown in Fig. 3(b), the two curves for ∂(∆n)/∂λ and ∆n/λ intersect at 1482nm, indicating GRD is equivalent to 0 at 1482nm. Therefore, sensitivity tends to be infinite at 1482nm. It can be further calculated that sensitivity higher than 1 × 105nm/RIU will be obtained from probing wavelength of 1457nm to 1506nm. In addition, the sensitivity is positive from 1457nm to 1482nm, indicating a red shift with the increase of external RI, while a negative sensitivity should be obtained in the band from 1482nm to1506nm.
Fig. 3 (a) The calculated (effective) RI of core, cladding, HE11, and HE12 mode and the effective RI difference between HE11 and HE12 mode for microfiber with 3.5-μm diameter at 25C, and the insets are the electric field distributions of HE11 and HE12 mode, respectively. (b) The values of ∂(∆n)/∂λ and ∆n/λ, and the simulated RI sensitivity. The values of ∂(∆n)/∂λ and ∆n/λ are equivalent and the RI sensitivity tends to be infinite at 1482nm.
In general cases, the GRDs evolution of MMIs with different diameters are similar. Each MMI enables its GRD to be 0 at a certain wavelength, resulting from the wider range of value of ∂(∆n)/∂λ and smaller range of value of ∆n/λ. At this wavelength, the sensitivity tends to be infinite. MMIs with different diameters have their unique ultrasensitive wavelength band where sensitivity is higher than 1 × 105nm/RIU. Figure 4 shows the sensitivity level and their corresponding band for MMIs with different diameters. It can be seen that the ultrasensitive wavelength band is near the cut-off wavelength of HE12 mode. With the increase of microfiber diameter, the ultrasensitive wavelength band will shift towards long wavelength and the bandwidth will become larger.
3. Experimental setup and results discussion
Nitrate concentration in drinking water is one of the most concerns due to the fact that too high concentration of nitrate will bring pathogenic risks to human. The upper limit of nitrate for drinking water suggested by World Health Organization is 50 mg/L [46], and a more stringent standard, 10 mg/L counted as N content, has been implemented in China and US. The low level nitrate in drinking water brings a tough problem to the existing fiber sensors. Therefore, nitrate sensing is experimentally performed to demonstrate the theoretical results and provide a reference for micro components detection in aqueous solution.
First of all, the MMI is fabricated by a modified flame stretching method. According to the non-adiabatic condition in Section 2, the key to the fabrication of such an interferometer is the control of taper angle. It is easy to understand that the taper will be more abrupt if a smaller length is heated to the softening temperature during the stretching process. In other words, the critical factor to fabricate a non-adiabatic taper is the control of heating length. Here, this modified approach requires the SMF to locate at the edge of outer flame or slightly higher to ensure a small length to be heated to the softening temperature. In order to prove the above analysis and this modified method, the tapers fabricated under different heating length are shown in Fig. 5. Figure 5(a) shows the taper formed from the situation that a segment of 9-mm length of SMF is heated in the flame. Figure 5(b) and 5(c) shows the taper formed by our modified approach, and the average taper angles are estimated to be 7.7 × 10−4 rad and 8.9 × 10−4 rad, respectively, which are larger than the critical values in Fig. 2(b). In contrast, the SMF is also heated by a pair of electrodes in the fiber fusion splicer, due to the ultra-small heating length, a dramatically abrupt taper is obtained and shown in Fig. 5(d). It should be pointed out that the taper can meet the non-adiabatic condition and the angle is usually less than 1 × 10−3 rad by this modified flame stretching method.
Fig. 5 The microscope images of tapers fabricated by (a) heating 9-mm length of SMF in the flame, (b)(c) heating SMF at the edge of outer flame, and (d) heating an ultra-small segment of SMF by a pair of electrodes in the fiber fusion splicer.
The sensing system contains a supercontinuum light source (SuperK Compact), an optical spectrum analyzer (OSA, Yokogawa AQ6370C), two SMF (Corning SMF-28e) for light input and output, and an above mentioned MMI, as shown in Fig. 6. The MMI is fixed on a self-made U-shape metal support to enhance its robustness, as shown in the insets of Fig. 6, which is finally immersed in nitrate solution as a whole element. As a representative of nitrate, sodium nitrate is selected to be the solute, and the concentration is adjusted by changing the mass of sodium nitrate and pure water.
Fig. 6 The schematic diagram of sensing system for sodium nitrate. The insets, captured by a digital camera and an optical microscope, respectively, show a MMI with 2.93-μm waist diameter fixed on a U-shape metal support.
According to the theoretical results shown in Fig. 4, MMIs, whose diameters range from 2.9μm to 3.8μm, have the ultrasensitive wavelength from 1200nm to 1600nm (without consider any propagation loss). In fact, the transmission spectra will seriously deteriorate under the influence of infrared absorption in water. Figure 7 exhibits the transmission spectra in pure water of MMIs with 3.0- and 3.2-μm waist diameter. Obviously, the infrared absorption for evanescent field greatly affects the spectra in two respects. Firstly, the intensity decrease at 1450nm are estimated to be 7.7dB and 13 dB for the 3.0- and 3.2-μm MMI, respectively, which indicates an considerable power loss in the strong absorption band (1360nm-1600nm). It should be noted that the total loss of MMIs can be deduced as [47], where αguiding, αwater denote the guiding loss and attenuation coefficients in water, respectively, κ11, κ12 denote the power proportion of HE11 and HE12 mode to the total power (κ11 + κ12 = 1), respectively, and η1, η2 denote the ratio of the evanescent intensity in water to the total intensity of HE11 and HE12 mode (η1<η2), respectively. This equation means that the total loss of MMIs is the sum of loss of HE11 and HE12 modes, and the loss of each mode is made up of guiding loss and absorption loss. Obviously, the total loss of MMI is dependent on η1, η2, κ11, κ12, and L. It is well-known that η1 and η2 are determined by microfiber diameter. The coupling from the fundamental mode to the higher order mode (i. e., the power proportion of HE11 and HE12 mode) is highly dependent on the taper angle [40]. In other words, the total loss of MMI is simultaneously dependent on the microfiber diameter, the taper angle, and the length of microfiber. Compared with a smaller-diameter microfiber, a microfiber with larger diameter has smaller values of η1 and η2, and it will show smaller loss if they have the same taper angle and length of microfiber, it may also have larger loss if it has longer length and larger taper angle (i. e. κ12). Moreover, the ultrasensitive wavelength is near the cut-off wavelength of HE12 mode and thus the ratio of evanescent field and power loss for HE12 mode is much higher than those of HE11 mode, which leads to the deterioration of contrast ratio. More specifically, for the 3.2-μm diameter MMI, the ratio of the evanescent fields for HE11 at 1320 nm and 1450 nm is calculated to be 3.675% and 4.656%, respectively, and the ratio of the evanescent fields for HE12 at 1320 nm and 1450 nm is estimated to be 41.564% and 71.180%, respectively. Due to the fact that the absorption loss at 1450nm is about 10 times higher than that at 1320 nm [48], the absorption loss of HE11 mode at 1450 nm will be 12.7 times higher than that at 1320nm, and the absorption loss of HE12 mode at 1450 nm will be 17 times higher than that at 1320nm. Therefore, in the band from 1360nm to 1600nm, corresponding to an infrared absorption peak of water, the spectra in Fig. 7 show poor quality in spite of higher or lower input power, which are unsuitable for sensing application. In other words, it is hard to achieve ultrahigh sensitivity in strong absorption loss band because of the poor interference signal, as same as our estimation in Section 2. One possible solution to simultaneously improve the spectra quality and ensure ultrahigh sensitivity in strong absorption loss band is the combined use of circulating light path and amplifier. However, this solution will bring additional complexity to the sensing system. In contrast, the spectra show better quality in the band from 1200nm to 1360nm and thus the sensing below will be carried out in this band.
A MMI with 3.2-μm waist diameter theoretically have the ultrasensitive wavelength at 1338nm, and its experimental spectra in sodium nitrate solutions with different concentration are shown in Fig. 8(a). With the increase of concentration, interference dips shift toward long wavelength. The positions of dip1, dip2, and dip3, which are near 1207nm, 1254nm, and 1325nm, respectively, are tracked to plot the relation between dip position and concentration. Figure 8(b) shows the measured data and the linear fitting, indicating the sensitivity is obtained to be 2.30 pm/ppm, 3.40 pm/ppm, and 4.87 pm/ppm for dip1, dip2, and dip3, respectively. The RI rate of change with mass concentration dn/dM for sodium nitrate solution is measured to be 1.185 × 10−7RIU/ppm by an Abbe refractometer. Namely, the RI sensitivity can be achieved to be 19409.28nm/RIU, 28691.98 nm/RIU, and 41097.05nm/RIU for dip1, dip2, and dip3, respectively.
Fig. 8 (a) The transmission spectra of MMI with 3.2-μm waist diameter in sodium nitrate solution, and (b) the linear relation between dip position and concentration for dips near 1207nm, 1254nm, and 1325nm, respectively.
However, the achieved maximum sensitivity has a great gap to reach the magnitude of 105nm/RIU, which mainly caused by the negligence for the transition regions. In the above theoretical model and simulation for calculating sensitivity, MMIs are considered to be made up of the waist region and have uniform diameter. Actually, the minimum critical local taper angle lies in the middle segment of the transition, and the higher mode is most likely excited and coupled in the transitions indeed, which means that part of the transitions are also contribute to the sensing performance. Thus, the position of interference dip should be modified as:
where ∆n, a non-constant value here, is the effective RI difference of microfiber infinitesimal, L is the total contributing length between two SMFs. The contribution of transitions induces that the actual functional diameter is slightly larger than the measured waist diameter. In order to compensate this effect, it is necessary to slightly reduce the waist diameter.For this reason, a MMI with 3.0-μm waist diameter is fabricated and its transmission spectra are shown in Fig. 9(a). Similarly, 3 dips near 1230nm, 1270nm, and 1320nm, named as dip1, dip2, and dip3, respectively, are tracked to plot the relation between dip position and concentration, as shown in Fig. 9(b). As we predicted, a much higher sensitivity, 7.00pm/ppm, 10.54 pm/ppm, and 14.95 pm/ppm, as well as RI sensitivity of 59071.73nm/RIU, 88945.15nm/RIU, and 126160.34nm/RIU, respectively, are obtained. Assuming that this sensor does not have any error, and the OSA with 0.02-nm wavelength resolution can detect the minimum intensity regardless of any impact of noise, a 1.34-ppm limit of detection (for sodium nitrate) can be obtained, which means that this method is appropriate to detect nitrate in drinking water. By the use of OSA with higher resolution, this approach can be applicable for lower level, such as nitrate in seawater. In addition, MMI with 3.0-μm waist diameter theoretically have its ultrasensitive wavelength at 1284nm, so the actual transitions lead to a about 50-nm red shift to the theoretical results in Section 2.
Fig. 9 (a) The transmission spectra of MMI with 3.0-μm waist diameter in sodium nitrate solution, and (b) the linear relation between dip position and concentration for dips near 1230nm, 1270nm, and 1320nm, respectively.
4. Conclusions
In conclusion, an ultrahigh sensitivity sensing in aqueous solution for microfiber modal interferometer (MMI) is realized in this paper. A versatile sensitivity expression is deduced for the study on the relation of sensitivity on wavelength, and finally provide theoretical basis for the realization of ultrahigh sensitivity by avoiding the band with strong absorption loss.
Theoretical results show GRD will reach the value of 0 at a certain probing wavelength, indicating an infinite sensitivity. MMIs with different diameters have their unique wavelength to reach infinite sensitivity, as well as the band where sensitivity is higher than 1 × 105nm/RIU. The ultrasensitive wavelength band, showing the width of dozens of nanometers, shift towards short wavelength and the band width narrows down with the decrease of diameter. The analysis approach may also be extended to other modal interferometers.
Sodium nitrate, a typical nitrate, is used to experimentally demonstrate an ultrahigh sensitivity sensing and provide a reference for micro components sensing in aqueous solution. The reduction of waist compensates the influence induced by the transitions, which finally promotes to a 14.95-pm/ppm concentration sensitivity and a 1.26 × 105-nm/RIU RI sensitivity at 1320nm. This is much higher than that of the existing MMI with about 1.08 × 104-nm/RIU sensitivity [34]. By the use of OSA with higher resolution, this approach may be applicable for lower level, such as nitrate in seawater. The optimization approach eases the diameter condition and provides reference to avoid infrared absorption peak, indicating its potential to detect other micro components in water, even in other liquid or gas medium.
Funding
National Key R&D Program of China (2017YFC1405600); Natural Science Foundation of Shandong Province (ZR2017MD030).
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