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Abstract
We present here a detailed investigation into the sensitivity of the taper-based Mach-Zehnder interferometer as a function of external refractive index, with particular attention to the dispersion turning point (DTP) and possibilities for ultra-sensitive sensors. Our numerical simulation revealed that two DTPs exist with a decrease in the microfiber waist diameter; given this relationship, it is possible to obtain an ultra-sensitive operation. We then conducted experiments with fabricated devices with different waist diameters to achieve both positive and negative sensitivities at two DTPs. In particular, we achieved an ultrahigh refractive index sensitivity of approximately 95,832 nm/RIU at the second DTP when working with a diameter of 1.87 µm around the RI of air. These results show its potential for use in acoustic sensing and biochemical detection.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber Mach-Zehnder interferometer (MZI) has been the subject of great interests for its potential use in a variety of sensing applications like refractive index (RI) owing to their merits of small size and high sensitivity [1]. A number of methods have been proposed to fabricate the MZI, for instance, by pairing of wavelength-matched long period gratings (LPG) [2,3], assembling optical microfiber couplers [4,5], producing a misaligned spliced joint or the core mismatch [6,7], or tapering the microfiber mode interferometers [8–10]. Although the LPG-based interferometers are robust, they are typically plagued with a low RI sensitivity [3]. Even though past theoretical and experimental results have suggested that the RI sensitivity can be greatly enhanced by using microfiber LPG-based MZIs, it is difficult to manufacture LPG in thinner microfibers [11]. Regarding the MZI based on a cascaded microfiber coupler, the interference pattern is often very irregular and has high insertion loss [4,5]. In particular, by drawing a piece of standard single-mode fiber (SMF) and tapering down to a micro-size diameter with abrupt taper slopes [12–14], a taper-based MZI can be achieved where the interference spectrum depends strongly on the surrounding RI and the device is relatively insensitive to temperature changes [8,9,15]. In all the aforementioned MZI structures, knowing the sensitivity variation with respect to the physical parameters, including RI and others, is important. Moreover, both positive [8,9,15] and negative [6,7,10] sensitivities should be analyzed and the conditions of the occurrence of the maximum or minimum values should be investigated to guide future sensors design. At its foundation, this should also require reliable theoretical models and full experimental characterization as important precursors.
Recently, dispersion turning point (DTP) in highly birefringent microfiber Sagnac interferometer [16,17], microfiber coupler [18], LPG [19], trench fibers [20] and tapered SMF [13,21] has been observed and expected to show some notably different and potentially superior properties that may be exploited to achieve highly sensitive devices. For example, previous studies focusing on approaching an approximate DTP have suggested that the RI sensitivity can be greatly enhanced for the benefit of sensing applications [17,18,22]. These DTP results have illustrated sensitivity characteristics, both in terms of magnitude and sign variations with respect to conditions such as the fiber ellipse [17], diameter [18,21] and so on [16,19]. Consequently, greater effort will be required regarding DTP to provide a useful reference point for optimizing sensor performance.
In this paper, we present the first report toward the existence of dual dispersion turning points (DTP) by calculating the effect of the variation of the refractive index difference with wavelength at different diameters. Through careful design, we experimentally achieved both DTPs in transmission spectra, as well as the positive and negative RI response around two DTPs, well within expectations. Subsequently, we sought to systematically conduct an experimental investigation regarding the RI sensitivity that should dramatically increase when the dispersion factor approaches zero. Results show that the ultra-sensitive RI sensing in gaseous media, as well as the sensitivity limit in aqueous environments employing the device were demonstrated around both DTPs, showing that potentially numerous possibilities and options are available to meet different application requirements. With a relatively systemic investigation of the configuration, both in theory and in practice, this work may provide a reference model for the future design of DTP-based chemical or biochemical sensor.
2. Dual dispersion turning points of the taper-based modal interferometer
Figure 1(a) illustrates the schematic of the taper-based MZI. The transition has two abrupt diameter changes to break the adiabaticity, which allows for the coupling and recombination of waveguide modes. This allowed us to achieve a mode interferometer [13,14]. The transfer function can be expressed as
where Im (m = 1, 2) is the optical power of the interfering HE1m modes as described in [13,15]. φ=(2π/λ)ΔnL is the phase difference, in which Δn = neff1-neff2 represents the mode effective index difference between HE1m modes, L is the interaction length of the modes and λ is the input wavelength. By taking the partial derivative of the selected wavelength λ with respect to external RI next and using the phase difference φ, the RI sensitivity Sn can be expressed by [11]
Fig. 1. (a) Schematic diagram of the taper-based MZI; the inset presents calculated intensity profiles of the two modes, HE11 and HE12, respectively. (b) Simulated dispersion factor Γ and (c) RI sensitivity as functions of the fiber diameter. Calculated RI sensitivities for each diameter as a function of wavelength at (d) 2nd DTP (@Air) and (e) 1st DTP (@Water).
In view of the aforementioned results, there were two DTPs Γ=0 in Fig. 1(b) at fixed external RI, corresponding to the “turning point” of the phase matching curve for LPGs in [19]. We systematically calculated the properties of RI sensitivity of taper-based MZI at two DTPs with different diameters (2nd DTP shown in Fig. 1(d) and 1st DTP in Fig. 1(e)). The RI sensitivities for each diameter switched from positive to negative at the 2nd DTP, but switched from negative to positive at the 1st DTP, with increasing optical wavelengths, and reached the greatest value at these turning points. It is worth noting that, at the 1st DTP, a small variation in diameter or wavelength rapidly reduced RI sensitivity to 102 nm/RIU, and the region of high sensitivity was restricted to a small range. However, at the 2nd DTP, ultrahigh sensitivity of about 104 nm/RIU can be obtained easily over a wide wavelength range, which is promising for future sensing applications.
3. Responses to external refractive index at dispersion turning points
In order to verify this theoretical analysis, we conducted experiments to investigate the spectral and sensing characteristics of the taper-based MZI. First, we fabricated our proposed devices using different waist diameters by tapering a piece of SMF (Coractive, UVS-INT, NA = 0.20) using the flame-brush technique [12,15]. Figure 2(a) shows the transmission spectra recorded by an optical spectrum analyzer (OSA, Yokogawa AQ6370D) of the fabricated MZI with waist diameter of 43.6 µm in aqueous solutions. The extinction ratio could be higher than 30 dB if the length of the tapered transition region was carefully adjusted. A distinctive 1st DTP was clearly observed around a wavelength of 1410 nm, which was close to the simulation result obtained at a diameter of 42 µm. Subsequently, we used an aqueous sucrose solution with an index modified by distilled water to modulate across a small RI range (1.3324 to 1.4397) to test at the 1st DTP. By immersing the fabricated device into these solutions, we measured its spectral response. Specifically, the interference dips on both sides gradually shifted away from the DTP with increasing external RI; this was due to the negative and positive sensitivities, respectively. The broad center dip gradually split into two dips; additionally, another broad dip also appeared. With a slow shift of DTP to longer wavelengths, the broad dip split again into two dips. Taken together, these results agreed with those of our theoretical analysis regarding the change of the sign of Sn at the 1st DTP. The wavelength shifts of the interference dips on both sides are summarized and plotted in Fig. 2(b). Additionally, the corresponding RI sensitivities were calculated using a linear fit, with results showing that the larger the external RI, the greater the shift. At this diameter, the absolute value of ∂Δn/∂next was so small that the dispersion factor Γ hardly affected the sensitivity. Moreover, a small variation in either diameter or wavelength rapidly reduced RI sensitivity. Thus, while both positive and negative sensitivities were achieved near the 1st DTP, the highest sensitivity operated at only 846 nm/RIU.
Fig. 2. (a) Transmission spectra and (b) dip wavelength shifts of the fabricated MZI at 1st DTP with waist diameter of 43.6 µm, and (c) Transmission spectra and (d) dip wavelengths of the fabricated MZI at 2nd DTP with waist diameter of 3.21 µm placed in different liquid environments. (e) Spectra and (f) RI responses of the fabricated MZI near 2nd DTP but cut-off with different diameter and the inset indicates detailed structural parameters.
Subsequently, we tried to investigate the expected 2nd DTP with thinner waist diameters. Figure 2(c) shows the transmission spectra of the fabricated MZI with waist diameter of 3.21 µm. The cut-off point is clearly indicated on the right side of spectra, in which the interference between HE1m modes faded down and finally died away owing to the considerable power loss for HE12 mode in aqueous solution [22]. Nevertheless, from a practical point of view, it is still worthwhile to use the resonance dip outside the cut-off region for sensing implementation. So, we employed a set of standard RI liquids (Cargille Labs, Cedar Grove, NJ) to characterize the device performance in terms of RI sensing. With a high thermo-optic coefficient (-3.32×10−4RIU/°C for RI around 1.30, -3.36×10−4RIU/°C for RI around 1.32, -3.39×10−4RIU/°C for RI around 1.35, and -4.08×10−4RIU/°C for RI around 1.40). These certified refractive index liquids are allowed for temperature-dependent RI. Moreover, an electric temperature oven with a precision of 0.1°C was used to control the ambient temperature and change the external RI with great accuracy. We used this experimental set-up to detect the spectral response of the fabricated device. As shown in Fig. 2(d), a high sensitivity of approximately 17,603 nm/RIU (@1.319) was obtained using linear fitting. Owing to the intrinsic limitations on device performance, this was also the highest value a device with this diameter could produce around the RI of 1.319. However, the occurrence of cut-off point varies with different fiber diameters for different ambient RI. Therefore, we investigated the response of transmission spectra of the fabricated MZIs with other waist diameters (5.76 µm, 4.15 µm, and 2.94 µm) to different external RI using the standard RI liquid. The typical transmission spectra of these MZIs with various diameters are shown in Fig. 2(e). We observed that with the increase in the fiber diameter, the cut-off point occurred at a higher external RI. We experimentally characterized the RI sensitivities of these fabricated MZIs by tracing the interference dips that were closest to the respective cut-off points. As shown in Fig. 2(f), we also obtained and compared a series of RI sensitivities that served as the highest sensitivity corresponding to different external RI as well as different fiber diameters: 14,254 nm/RIU (@1.299) for 2.94 µm, 22,468 nm/RIU (@1.349) for 4.15 µm, and 27,455 nm/RIU (@1.408) for 5.76 µm were obtained and compared with each other by summarizing in Fig. 2(f). Even though there were cut-off condition in the liquid environments for the taper-based MZIs with small waist diameters, ultra-high sensitivities near the cut-off points were still experimentally achieved, indicating the great promise this approach has for applications in chemical and biochemical detection. Besides, experiments indicate that the polarization state has a negligible effect on the sensing performance (relative errors of RI sensitivity are below 0.1%).
Although the liquid media was unable to be used for complete implementation of 2nd DTP for ultra-high sensitivities, we were able to achieve such sensitivities in the surrounding medium with lower RI. We then experimentally verified and obtained the 2nd DTP in gaseous media using a fabricated MZI with waist diameter of 1.87 µm. Figure 3(a) shows the transmission spectra in which the HE12 modes were still far from cut-off around the RI of air. As shown, a distinctive 2nd DTP is clearly observed around 1320 nm, which is close to the simulation result for the diameter of 1.9 µm. Subsequently, to measure the capacity of gas sensing and obtain the RI performance at the 2nd DTP as directly and accurately as possible, we first examined the spectral responses to the relative pressure that has a definite functional relationship with the external RI in air at room temperature according to [23]. Briefly, experiments were conducted by sealing the fabricated MZI inside a hermetical chamber in which the pressure was controlled by a vacuum pump. The temperature was kept at 20°C in order to avoid extra negative features that might influence the measurement. Given this, the sensitivity to gas was tested by inducing air pressure changes from -90 to 0 kPa. As shown in Fig. 3(a), increasing relative pressures caused the interference dips on both sides of the 2nd DTP shift to gradually close in on the DTP. Since there should be a positive correlation between pressure and RI and as shown in Fig. 1(d), the spectral variation was in accordance with the simulated result of ${S_n}$ that switched from positive to negative at the 2nd DTP. Figure 3(b) gives the measured wavelengths of selected dip a-e as a function of relative pressure. These results were calculated using linear fit and indicated that the highest pressure sensitivity was approximately 255 nm/MPa; the corresponding RI sensitivity was approximately 95,836 nm/RIU and the figure of merit (FoM) was calculated to be 13,580 RIU-1, which are much higher than [18] and most SPR-based RI sensor [24]. By using numerical simulations, we calculated the theoretical results of RI sensitivity in air as indicated by the curves in Fig. 3(c), which were in good agreement with the experimental results as indicated by the dots.
Fig. 3. (a) Transmission spectra and (b) dip wavelength of the fabricated MZI at the 2nd DTP with waist diameter of 1.87 µm placed in different pressure environments. (c) Comparison of theoretically calculated and experimentally acquired RI sensitivities. (d) The typical spectra of the MZI with waist diameter of 2.12 µm in pure CO2 and N2. (e) Consecutive measurements of cyclically injected gasses.
Finally, we characterized the sensor device in terms of its ability to detect different kinds of gas by placing it in a hermetical gas chamber and consecutively exposing it to various gases. A fabricated MZI at the 2nd DTP with waist diameter of 2.12 µm was used and the chamber was filled with pure N2 and CO2 (three cycles in total). The typical transmission spectra of the MZI in both gases are shown in Fig. 3(d). As shown, a distinctive 2nd DTP is clearly observed around a wavelength of 1490 nm, which is close to the simulation results observed for a diameter of 2.1 µm. By tracing the shift of interference dips on both sides of the DTP, the response to both gases is summarized and plotted in Fig. 3(e) as a function of times. Both dips present obvious spectral shifts and the maximum value of approximately 4.36 nm was observed and is shown in Fig. 5(a). Considering the RI of the gases in the experiment were 1.00043970 RIU for CO2 [25] and 1.00029463 RIU for N2 [26], we achieved a high RI, experimental sensitivity of approximately 30,054 nm/RIU. This highlights this approach's continued promise for the practical detection of gases as well as its ability to meet most application requirement.
4. Temperature coefficient
To completely understand the characteristics of taper-based MZIs, the responses of the device to temperature at both DTPs were also investigated by placing the fabricated MZI into a resistance furnace. Figure 4 (a) and (c) show the recorded spectra, while (b) and (d) show the dip-wavelength shift of the fabricated MZI at different temperatures with waist diameters of 43.6 µm and 2.1 µm. As shown in Figs. 4(a) and 4(b), we obtained small temperature sensitivities of approximately -0.0564 nm/°C and -0.0812 nm/°C for the MZI at the 1st DTP. As shown in Figs. 4(c) and 4(d), we obtained higher temperature sensitivities of approximately 1.380 nm/°C and -0.9316 nm/°C on both sides of DTP for the MZI at the 2nd DTP. Similar to the pressure response, the dependence of the spectral response to surrounding temperature was mainly decided by the dependence between the external RI and surrounding temperature, in this case, thermo-optic and thermal expansion effects [9,27]. Both material effects worked together to impact the temperature sensitivity and the dominance of one effect over the other collectively depends on the practical shape and size of the microfiber [28].
Fig. 4. (a) Transmission spectra and (b) dip wavelength shifts of the fabricated MZI at the 1st DTP with waist diameter of 43.6 µm, and (c) transmission spectra and (d) dip wavelengths of the MZI at 2nd DTP with waist diameter of 2.1 µm placed in different ambient temperature.
5. Conclusion
In conclusion, we have shown that two DTPs exist in taper-based MZIs, where extremely high sensitivities can be achieved for the diameter-dependent dispersion factor close to zero. By fabricating devices with different waist diameters, we conducted experiments regarding external RI responses in different media. Results showed that in liquid environments, a clear 1st DTP was obtained when working with a large fiber diameter. While both positive and negative RI responses were experimentally obtained at the 1st DTP, limited RI sensitivities restricted the sensing capacity. Meanwhile, we characterized the device performance in terms of a thinner diameter and experimentally verified the sensitivity limit in the cut-off condition of liquid environments. The spectral responses of fabricated devices with small diameter in gaseous media were also investigated. The 2nd DTP as well as an ultrahigh RI sensitivity of approximately 95, 836 nm/RIU (@Air) were achieved, which indicated the great promises this approach has for future gas- and/or acoustic-sensing applications. In a word, the existence of dual DTPs in such a simple configuration gives us extendable application possibilities and more options when designing the DTP-based fiber sensor and the relatively detailed investigation presented here may serve as a useful reference tool. Ideally, not only is the theory of sensitivity characteristics of DTP applicable for the taper-based MZI, but it should be able to theoretically extend it to most types of in-line MZIs. It is hoped this approach will advance operational implementations of the devices employed for ultra-sensitive detection and facilitate continued, future improvements in novel fiber optic sensors.
Funding
National Natural Science Foundation of China (NSFC) (61705083, U1701268).
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