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We propose a novel all-fiber Mach-Zehnder interferometer (MZI) fabricated by infiltrating two separated liquid sections along a PCF. Due to the reduced effective index difference between the core region and the liquid-filled cladding region, the guided field in the liquid sections possesses a larger mode field area and can simultaneously induce the core mode and cladding modes of the empty PCF to form a MZI. The measured results demonstrate that very clear interference spectra can be obtained. By increasing the length of the MZIs, the decreased average fringe spacing can be observed. We have also measured the temperature sensitivity of our proposed PCF-based MZIs. Due to the existence of the two liquid sections, the temperature sensitivities can be enlarged to −0.176nm/°C and −0.53dB/°C.
© 2015 Optical Society of America
1. Introduction
Optical fiber sensors have been widely investigated and employed in chemical and biomedical applications due to their compact size, high sensitivity, and simple configuration [1–15]. In addition, compared to electronic sensors, optical fiber sensors possess the characteristics of immunity to electromagnetic interference, convenient operation, and cabability of distributed remote measurement, making them useful in structure strength monitoring and operation in harsh environment. There are several kinds of optical fiber sensors which are developed based on different mechanisms, such as D-shaped fibers [1], long-period fiber gratings [2,3], fiber Bragg gratings [4], tapered fibers [5], multimode fibers [6], Fabry-Perot interferometers (FPIs) [7,8], Mach-Zenhder interferometers (MZIs) [9–14], and Machison interferometers [15]. Among these fiber sensors, MZI-based fiber sensors are widely used in gas, temperature, strain, bending, and refractive index sensing due to they are very sensitive to environmental variations [9–14].
There are several ways to fabricate a MZI along a single-mode fiber (SMF). The commonly used method is to induce and recombine the core mode and cladding modes of a SMF by using core-offset splicing [9,10], taper regions [11,12], or long-period fiber gratings [13,14]. Recently, it was demonstrated that one can use femtosecond lasers to fabricate an air cavity along a SMF, which produce two different optical paths for the core mode, to form a MZI [16,17]. In spite of SMFs, MZIs can also be fabricated in photonic crystal fibers (PCFs) with air holes running along the entire fiber length. By using a commercial fusion splicer, one can easily collapse air holes [18–20] or making lateral core offset [20,21] at two splicing points of a PCF to obtain the interference of the core mode and cladding modes for sensing applications. However, the collapse of air holes may result in high propagation losses, and the core-offset splicing may weaken the strength of the fiber sensors during the measurement process.
In this paper we propose a novel structure of PCF-based MZI by introducing two liquid infiltrations into a PCF. Unlike the collapsing or offset-splicing method, no structure destruction is made and the MZI structure is robust. The two liquid sections can simultaneously excite the core mode and cladding modes of a PCF and combine them to form the interference pattern for sensing applications. The function of liquid sections and the interference properties of our proposed PCF-based MZI will be investigated and discussed.
2. Operation principle and fabrication
Figure 1(a) depicts the schematic diagram of our PCF-based MZI. There are two liquid infiltrations separated by a distance L along a PCF. As the incident light from the lead-in SMF propagates to the first liquid section of the PCF, the infiltrated liquid with higher refractive index than air will reduce the effective index difference between the core region and cladding region, which broadens the mode area of the core mode in the liquid section. When the broadened core mode leaves the first liquid section, it will simultaneously induce the core mode and cladding mode of the empty PCF as shown in Fig. 1(a). The induced core mode and cladding mode propagate along the empty PCF with different velocities and are recombined as they pass through the second liquid section. The recombined signals will be sent to an optical spectrum analyzer (OSA) to obtain an interference spectrum resulted from the accumulated phase difference between the core mode and the cladding mode.
Fig. 1 (a) Schematic diagram of the proposed PCF-based MZI with two liquid sections. (b) Side view of two fabricated PCF-based MZIs with the MZI lengths are 36mm and 9mm, respectively. The two liquid sections in each MZI are indicated with blue arrows.
The intensity of the output interference spectrum can be expressed as:
where Icore and Iclad are the intensities of the core mode and cladding mode, respectively. ϕ represents the accumulated phase difference between the core mode and cladding mode and can be obtained from:with Δneff denotes the effective index difference between the core mode and the cladding mode, L stands for the MZI length defined as the length of the empty PCF between the two liquid sections, and λ is the wavelength. As ϕ equals to (2m + 1)π where m is an integer, we can obtain an output dip due to the destructive interference, and the mth dip wavelength λm can be expressed as:As a result, one can detect the environment variations which influence the value of Δneff or L by measuring the shift of the dip wavelength.To fabricate the proposed PCF-based MZI with two liquid sections, we first spliced a section of PCF with a SMF. For the reduction of the mode-field mismatch and coupling loss, the PCF we employed is the commercial large mode area PCF (LMA-10) from NKT Photonics A/S with the air-hole diameter and the lattice constant are d = 3.1 μm and Λ = 7.1 μm, respectively. In addition, to enlarge the mode filed in the liquid section, the filling liquid we utilized is from Cargille Laboratories with the liquid index nq smaller but close to the silica index. To infiltrate the first liquid section, the PCF was fixed on an upper holder of a vacuum pumping chamber (Skiing Technology co.) with the filling liquid placed on a lower movable stage. After the chamber was vacuumed close to 0 cm-Hg, the liquid was raised up to touch the end face of the PCF to fill the liquid into the PCF by the capillary force. By carefully controlling the infusion time, the liquid length can be well controlled. We then moved down the liquid away from the PCF and slowly released the pressure to push the first liquid section up from the fiber end. After the first liquid section was pushed away from the end face of the PCF for a desired length, the liquid was raised up to touch the PCF again to perform the infiltration of the second liquid section. After finishing the infiltration of two liquid sections, the end face of the PCF was spliced to another SMF which was connected to an OSA to measure the interference spectrum properties. Figure 1(b) demonstrates the side view of two fabricated PCF-based MZIs with the MZI lengths are 36mm and 9mm, respectively. One can clearly observe the two liquid sections along each PCF as indicated in Fig. 1(b).
3. Interference properties
We first discuss the influence of the liquid sections in our proposed PCF-based MZI. As what we have mentioned, the liquid section should function as a coupler which can simultaneously induce the core mode and cladding modes. Therefore, the filling liquid should be chosen with its refractive index slightly smaller than that of pure silica. If the liquid index is larger than the silica index, the effective index of the liquid-filled cladding region will be larger than the core index, which makes the liquid section become photonic-band-gap-guiding (PBG-guiding) with larger losses. On the other hand, if the liquid index is much smaller than the silica index, light will be centrally confined in the core region and no cladding modes can be excited. By using a finite-difference time-domain (FDTD) simulation tool from Rsoft, Fig. 2(a) plots the field distributions from a SMF to a PCF with a liquid section as the liquid index nq is 1, 1.432, and 1.440. One can see that as the liquid index is close to the silica index (nSi = 1.45), we can have a guided mode with a larger mode field area in the liquid section to induce the cladding modes.
Fig. 2 (a) Calculated field distributions from a SMF to a PCF with a liquid section as the liquid index nq is 1, 1.432, and 1.440. (b) The measured transmission spectra for PCFs with no liquid section (black curve), with one liquid section (red curve), and with two liquid sections (blue curve).
Figure 2(b) shows the importance of the two liquid sections in our PCF-based MZI. The black curve represents the measured transmission of a PCF without any liquid infiltration. There is no interference can be observed due to the mode field is matched between the SMF-28 and LMA10 PCF. If we introduce only one liquid section, the induced cladding modes cannot be efficiently coupled back into the core region by another liquid section. As a result, interference with a very small extinction ratio is observed as the red curve in Fig. 2(b). On the contrary, the second liquid section can efficiently combine the cladding modes induced by the first liquid section with the core mode, and a very clear interference spectrum can be obtained as the blue curve in Fig. 2(b). Please note that lengthening the liquid length will slightly increase the power coupled to the cladding modes, which results in higher extinction ration in the interference spectrum.
We have also measured the interference spectra of our proposed PCF-based MZIs with different MZI lengths. Figures 3(a)–3(c) are the interference patterns as the MZI length L = 13.5 mm, 16 mm, and 26 mm, respectively. The length of liquid sections in each MZI is about 1 mm. One can see that, as we lengthen the PCF-based MZI, the fringe spacing is decreased due to the accumulated phase difference between the core mode and the cladding mode is increased with the MZI length L, which is consistent with Eq. (2). The average fringe spacing as a function of the MZI length is plotted in Fig. 3(d). The square dots represent the experimental results. An exponential relationship can be observed as the red curve in Fig. 3(d).
Fig. 3 The measured spectra of the PCF-based MZIs with two liquid sections as the MZI length L is (a) 13.5mm, (b) 16 mm, and (c) 26 mm. (d) The relationship between the fringe spacing and the MZI length L.
The interference spectra of PCF-based MZIs with L = 16 mm and L = 26 mm are transformed to the spatial frequency domain by using fast Fourier transform (FFT) as shown in Fig. 4. It can be seen that, except for the core mode, there is a main cladding mode appearing at 0.04 #/nm and 0.06 #/nm for L = 16 mm and L = 26 mm, respectively. Although we can also observe a small peak representing higher-order cladding mode at larger spatial frequency, the power is mainly distributed in the core mode and main cladding mode to construct the interference spectrum.
Fig. 4 The spatial frequency spectra of our PCF-based MZIs as the MZI length L = 16 mm (black curve) and L = 26 mm (red curve).
4. Temperature sensing properties
To measure the temperature properties, our PCF-based MZI with two liquid sections was placed on a heating stage to vary the operation temperature. Meanwhile, a thermo-coupler was employed for calibration. As the temperature was raised from 25°C to 50°C, the corresponding spectra were recorded as shown in Fig. 5(a) for the lengths of the liquid sections and MZI are 1.0 mm and 16 mm, respectively. It can be seen that the interference dip slightly shifts toward shorter wavelength with the increasing temperature as indicated in Fig. 5(a). Due to the thermo expansion coefficient of the liquid (9 × 10-4 oC−1) is larger than that of silica (5.5 × 10-7 oC−1) [8], the MZI length is reduced with the raising temperature. As a result, we can see a blue shift in the interference dip for the PCF-based MZI with two liquid sections. In addition, one can also observe that the extinction ratio of the interference spectrum gradually decreases with the raising temperature. As what we have mentioned, when we increase the temperature, the negative thermo-optic coefficient of the filling liquid reduces the liquid index and enlarges the refractive index difference between the core region and the liquid-filled cladding region. Therefore, along the liquid section, light propagates with a smaller mode area for higher temperature, which reduces the power coupled to the cladding mode of the empty PCF and the extinction ratio of the interference spectrum.
Fig. 5 (a) The measured spectra of the PCF-based MZI with two liquid sections at variant temperature. (b) Temperature dependence of the wavelength shift and the extinction ratio for the PCF-based MZI with two liquid sections.
Figure 5(b) demonstrates the temperature dependence of the wavelength shift and the extinction ratio of the interference spectrum. The square dots are the experimental results with the lines obtained from linear fitting. We can see that both the wavelength shift and the extinction ratio of the interference spectrum are linearly decreased with the temperature. The corresponding temperature sensitivities are −0.176nm/°C and −0.53dB/°C, respectively. For most PCF-based MZIs, the temperature sensitivity is relatively small due to that PCFs are composed of only silica and air. Both of these two materials are insensitive to temperature. Owing to the filling liquid, our PCF-based MZIs with two liquid sections possess higher temperature sensitivities and can be used in temperature sensing applications. Besides, instead of using core-offset splicing method or air-hole collapse method, our proposed PCF-based MZI is formed by filling two liquid sections along a PCF and is more robust, making it highly potential in sensing applications.
Please note that, unlike some temperature sensors formed by selectively filling highly temperature-sensitive materials, such as alcohol or index matching liquid, into specified air holes of PCFs [22,23] to form light interference channels, the liquid sections in our structure only function as couplers to induce interference. As a result, our proposed PCF-based MZI shows smaller temperature sensitivity. However, our device does not require complex selective filling methods or coupling techniques, and it still possesses comparable temperature sensitivity to PCF sensors filled with Fe3O4 fluids [24] or coated with quantum dots [25].
5. Conclusion
We have successfully fabricated a novel structure of all-fiber MZIs by introducing two separated liquid sections along a PCF. It is demonstrated that the liquid sections in our MZI structure possess a larger propagating mode area. The two liquid sections can function as a coupler to simultaneously induce the core mode and cladding mode of the empty PCF and recombine them into the output SMF to form an interference spectrum. From the experimental results, it is observed that the average fringe spacing is exponentially decreased with the MZI length. In addition, the temperature dependence of our fabricated PCF-based MZI is also measured. Very high temperature sensitivities of −0.176nm/°C and −0.53dB/°C are obtained due to the infiltration of the two liquid sections.
Acknowledgments
This work was supported by the National Science Council of Taiwan under Grants No. NSC 101-2221-E-110-074-MY3.
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