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A microfluidic assistant beat-frequency interferometer based on a single-hole-infiltrated dual-mode microstructured optical fiber (DM-MOF) is proposed and demonstrated. The interferometer is constructed by inserting a piece of fluid-filled DM-MOF into two sections of single-mode fiber with slight core-offset. The mode-mismatch induced interferences with high-frequency dips and low-frequency envelope are observed in the transmission spectrum. Theoretical and experimental investigations reveal that the beat-frequency spectrum works from the interferences between LP01 core mode and the components of LP11 core mode with close but different frequencies. The deliberately infiltrated liquid rod in the air hole located at the second ring near the core of the DM-MOF enhances the sensitivity of the envelope to temperature or axial force. However, it shows little impact on the high-frequency dips. The distinguishing sensitivities of −959.22 pm/°C (−70.59 pm/°C) and 24.26 nm/N (−3.14 nm/N) for the envelope (dips) are simultaneously achieved in experiment, allowing for dual parameter measurement in such a compact structure.
© 2014 Optical Society of America
1. Introduction
In-line Mach Zehnder interferometers (MZIs) based on microstructured optical fibers (MOFs), as the tunable photonic devices and high performance sensors, have attracted considerable interests for their excellent properties such as simple and compact structure, immunity to electromagnetic radiation, as well as high sensitivity and tunability. They can be employed in sensing applications of various physical parameters such as temperature, axial strain, bending, torsion, and the refractive index (RI) [1–6]. So far, a number of techniques have also been proposed to construct the MZIs with high performance, such as utilizing the fiber tapering [1], long period grating (LPG) pair [6], imbedded micro-cavity [7] and single-multi-single mode (SMS) splicing fiber structure [8]. These MZIs are divided into two groups involving in-core and core-cladding interferences, respectively. The MZIs based on the core-cladding interferences are highly adapted in sensing external parameters such as temperature (at dozens of pm/°C) and mechanical parameters [2]. However, it remains challenging to overcome the crosstalk between the temperature and mechanical parameters. Also, their unstable interference spectra and changeful contrast to environmental vibration restrict the sensing applications of these MZIs. Comparatively, those MZIs involving in-core interferences between fundamental core mode and higher order core modes possess higher spectrum stability, better resistance to the crosstalk but lower thermal responses [8].
Recently, several novel techniques are utilized to enhance the thermal responses of the in-core MZI interferences while overcoming the crosstalk, including LPG assistant two-mode fiber MZI [9], highly GeO2-doping fiber-based MZI [2] and fluid-filled photonic crystal fiber based MZIs [10,11]. Due to the difference in thermal-optical coefficients between the pure silica and GeO2, specific few mode photonic crystal fibers with a high GeO2-doping concentration were used to enhance thermal responses of the MZI with a high sensitivity of 94 pm/°C [2]. The fluid-filled interferometers stand out for the enhanced sensitivities and resistance to crosstalk for the confining propagation in the fiber core [10,11]. An all fluid-filled MZI based on in-core interferences is also proposed by infiltrating functional materials into all cladding holes of the microstructured optical fiber [11]. Its thermal response exceeds −340 pm/°C at 1480 nm, which is an order higher than the pure silica based fiber devices. Furthermore, the crosstalk between temperature and strain was restrained as a result of the significant differences in temperature and strain sensitivities for two different interference dips located at 1250-nm and 1480-nm wavebands, respectively.
In this paper, a novel microfluidic assistant beat-frequency interferometer with enhanced sensitivities is proposed and demonstrated. The interferometer is constructed by inserting a small piece of microfluidic-filled dual-mode microstructured optical fiber (DM-MOF) into two sections of standard single-mode fiber (SMF) with slight core-offset. The DM-MOF is achieved by selectively infiltrating a fluid with higher RI than that of the background silica into a single air hole located at the second ring near the core. The distinctive beat-frequency interferences with high-frequency dips and low-frequency envelope are observed in transmission spectra of the interferometer. The envelope possesses enhanced sensitivity while the dips are lowly sensitive to temperature and axial force. Theoretical and experimental investigations reveal that the periodic beat-frequency spectrum works from the interferences between the LP01 core mode and the components of LP11 core mode with close but different frequencies. Since the liquid is deliberately introduced in the DM-MOF, the degenerate modes of LP11 are further separated from each other because of the asymmetry. Slight changes in small effective refractive index (ERI) difference between components of LP11 mode enhance the thermal response of the envelope, while show little impact on high-frequency dips. The distinguishing sensitivities of −959.22 pm/°C (−70.59 pm/°C) and 24.26 nm/N (−3.14 nm/N) at 1500-nm waveband for the envelope (dips) are simultaneously achieved in experiment, allowing for dual parameter measurements in such a compact structure.
2. Structure and principles
Figure 1(a) illustrates the schematic experimental setup for investigating the transmission spectra and sensing characteristics of the proposed microfluidic assistant beat-frequency interferometer. The interferometer is fabricated using a piece of microfluidic-filled DM-MOF directly spliced between two sections of SMF with slight core offset. The light from a super-continuum source (SCS) (600.0 nm-1700.0 nm) is launched into the interferometer and the output transmission spectra are measured by an optical spectral analyzer (OSA) with a highest resolution of 0.02 nm. A polarizer and a polarization controller are inserted between SCS and interferometer for polarization analysis. The microfluidic-filled DM-MOF is achieved by selectively infiltrating a standard RI liquid (Cargille Laboratories, Inc.) into a single air hole located at the second ring near the silica core, as shown in Fig. 1(b). The original pure silica DM-MOF includes five rings of air holes arranged in a regular hexagonal pattern with a fiber diameter of 124 µm, supporting two core modes of LP01 and LP11 propagating with low loss. The diameter of air holes and the adjacent hole-spacing are 3.64 μm and 5.85 μm, respectively. Due to the slight core off-set from the SMF to DM-MOF as shown in Fig. 1(c), LP11 mode is excited at the first splicing joint as the result of mode mismatch, leading to a phase difference and the modal interferences between LP01 and LP11 at the second one.
Fig. 1 (a) Schematic diagram of the measurement system for the proposed interferometer; (b) Transverse cross-section of the refabricated DM-MOF; (c) Working mechanism of microfluidic assistant beat-frequency interferometer.
Since the deliberate introduction of the fluid, the symmetry of the DM-MOF is changed and the degenerate modes of LP11 are further separated from each other. Via adjusting the polarization controller, two degenerate mode and in a certain polarization are obtained. Also, there exists a phase difference between the components of and caused by their slight ERI difference, resulting in two sets of interferences with close but different frequencies. Therefore, the complex transverse electric field distributions of LP01 mode and the components of and are calculated using the Eq. (1) as follows:
where A1, A2 and A3 refer to the amplitude of the LP01 mode and the components of and , and ni and n'i (i = 1, 2, 3) denote their mode ERIs in the filled and unfilled part of the DM-MOF, respectively. The lengths of filled part and the unfilled part including both ends of the DM-MOF are defined as L1 and L2, just as that shown in Fig. 1(c). Therefore, the transmitted light intensity I of the interferences can be expressed as:where the ERI differences between two certain modes are represented by Δnij and Δn'ij (i< j = 1, 2, 3) in the filled and unfilled part of the DM-MOF. In order to simplify, supposing that the LP01 mode and components of and share the amplitudes as A1:A2:A3 = 2A:A:A, specific transformation of Eq. (2) is mathematically deduced for discussing the direct dependence of the interferences on ERI differences in Eq. (3):The wavelength-dependent ERI differences between LP01 mode and the components of LP11 mode are numerically obtained via analyzing the theoretical model of the fluid-filled DM-MOF using the full-vector finite element method (FEM). The infiltrated fluid possesses a material refractive index (MRI) of 1.4600 for 589.3 nm at 25 °C and a negative thermal-optic coefficient of −0.000387 RIU/°C. The material dispersion curve of the liquid is fitted by the Cauchy equation [12] with constants of 1.447924, 407435.7 and 4.15 × 1011, respectively. In addition, the material dispersion for the pure silica background of the DM-MOF is approximately satisfied by the Sellmier equation [13].
Given asymmetric cross-section of the microfluidic infiltrated DM-MOF, and mode with asymmetric electric field are utilized in our numerical simulation, which are easy to be excited and stable to propagate in the fiber core. According to the ERI curves obtained from numerical simulations (L1 = 2 cm, L2 = 6 cm), transmission spectrum of each separated factor D (black curve) or E (red curve) as well as the beat-frequency interference light intensity I (blue curve) are calculated and depicted in Fig. 2 without considering the insertion loss, respectively. Due to Eqs. (4) and (5) , a large phase difference between LP01 mode and LP11 mode in the factor D results in high-frequency interference dips, while the low-frequency envelope is caused by the slight phase difference between the components of LP11 mode in factor E.
Fig. 2 (a) Transmission spectrum of the factor D; (b) Transmission spectrum of the factor E; (c) The beat-frequency interference of the transmitted intensity I.
It is seen from Figs. 2(a) and 2(c) that the periodic beat-frequency interference possesses equivalent free spectral range (FSR) of 4 nm with that of the factor D, while the nodes of the periodic envelope corresponds to the dips of the factor E with a period of 133 nm. Thus, it can be concluded that the factors D and E play decisive roles of the beat-frequency interferences.
To validate the conclusion above, the thermal responses of dip1, dip2 and dip1' and node2' shown in Fig. 2 are also discussed and shown in Fig. 3. The two solid lines represent the thermal responses of the dip1 (black) and dip2 (red), respectively. Besides, the blue scatters nearby the solid lines indicate the wavelength shift of dip1' and node2' in the beat-frequency interferences of Fig. 2(c). Through numerical comparisons of the linear variations, a sensitivity of −693.3 pm/°C for dip2 in factor E agrees well with that for node2' of the envelope in transmission intensity I. Moreover, dip1 in factor D shows the same trend with dip1' in the beat-frequency interferences with a sensitivity of −60.5 pm/°C as well, except for a small deviation in the wavelength range. Thus, the spectral responses of the periodic beat-frequency interferences with high-frequency dips and low-frequency envelope can be approximately represented by that of the factors D and E, respectively. Their corresponding temperature sensitivities S1 and S2 are further discussed by taking derivative of the phase matching conditions for factors D and E as follows:
where k = L1/L2 is the length ratio between the filled part and the unfilled part of the DM-MOF. The Bgij (i< j = 1, 2, 3) refers to the group of ERI difference with a general expression:Fig. 3 Thermal responses for dip1 of factor D and dip2 of factor E as well as their corresponding high-frequency interference dip1' and low-frequency envelope node2' in the beat-frequency interferences.
It is seen from Eqs. (6) and (7) that S1 and S2 strongly depend on the operation wavelength λ, partial derivative of the ERI differences to temperature, the group of ERI difference in Eq. (8) and the length ratio k, which are investigated as following. Assisted by the microfluidic, the partial derivative ∂∆nij/∂T in the fluid-filled fiber becomes enhanced (10−5) an order higher than that of the silica background ∂∆nij'/∂T (10−6) in the unfilled part. To be more intuitive, S1 and S2 are numerically calculated and shown in Fig. 4 with the increment of the length ratio k.
The black and red curves in Fig. 4 demonstrate the k-dependent thermal responses S1 and S2 of the high-frequency dip and low-frequency envelope at 1550-nm waveband, respectively. When the pure silica DM-MOF is unfilled (k = 0), S1 and S2 is lowly sensitive to temperature because of the small thermal-optic coefficient of the pure silica. With the increasing length ratio k, S2 becomes enhanced a lot while S1 remains almost the same. Eventually, when the length ratio k increases high enough over 20, both S1 and S2 approach the saturation values of ~-233 pm/°C and ~-2453 pm/°C, respectively.
The increments of negative sensitivities indicate a blue-shift direction of the interference spectra and the way to improve the sensing performance via increasing the length ratio k. However, length ratio k is limited as well since the unfilled DM-MOF should be retained long enough to avoid high transmission loss caused by fusion splicing with the organic liquid.
On the other hand, the photo-elastic effect slightly reduces the MRI of the silica core when the force is axially loaded along the microfluidic assistant interferometer at a constant temperature [14]. In this case, the envelope exhibits a red shift to the axial force increment, happening to be opposite to thermal responses. Due to the opposite spectral responses of the dip and envelope, a method for dual parameter measurements may be achieved in this microfluidic assistant beat-frequency interferometer.
3. Experimental results
In our experiment, an air hole at the second ring of the hexagonal pattern in a 7.85 cm-long DM-MOF was infiltrated with a ~2.1 cm-long liquid rod with a standard RI of 1.4600, by the direct manual-gluing method described in detail in [15]. Then, this piece of fluid-filled DM-MOF (k = 0.365) was fusion spliced to the SMFs with slight core offset and placed inside a temperature chamber to investigate its sensing characteristics.
Figure 5(a) shows the transmission spectra of the microfluidic assistant interferometer at the temperature of 20 °C and 30 °C. The high-frequency interference dips with an FSR of 4 nm and the low-frequency envelope with a period of 136 nm appear in the spectral range from 1200.0 nm to 1700.0 nm. A certain interference fringe in the detailed spectra near 1460.0 nm is defined as the dip with slight blueshift alongside the increasing temperature shown in Fig. 5(b). However, the fringe of the envelope with the lowest contrast is defined as the node with obvious blueshift as well. Seen from the Fig. 5(c), the thermal response of the node is approximately linear and approaching about −959.22 pm/°C, which is an order higher than −70.59 pm/°C of the dip. Compared with the sensitivities of −764.6 pm/°C and −65.3 pm/°C for k = 0.365 in Fig. 4, the experimental results agree well with the numerical simulation. The deviations may result from the imprecise measurement of the filling length and the inaccurate theoretical model for cross-section of the DM-MOF. Furthermore, sensitivities observed in our experiment exceed 10 times larger than that in [2], which also trebles that of the all fluid-filled MZI in [11]. In addition, the experimental sensitivities of the node and the dip can be further improved via increasing the length ratio k.
Fig. 5 (a) The transmission spectra of the proposed microfluidic assistant interferometer at the temperature of 20 °C and 30 °C; (b) Detailed fringes of the high-frequency interference dips in a small spectral range; (c) The linear fitting curves for thermal responses of dip and node.
Figure 6(a) demonstrates the spectral responses of the beat-frequency interference to axial force at a constant temperature of 25 °C. The node exhibits a red-shift in response to axial force increment, happening to be opposite to the thermal responses. As shown in detail of Fig. 6(b), the high-frequency dip shows slight blue-shift still. The distinguishing sensitivity of the node reaches 24.26 nm/N (29.11 pm/µɛ), which is −7 times as large as the dip of −3.14 nm/N (−3.77 pm/µɛ). The spectral responses to axial force (axial strain) achieve a high level, which is 14 times larger than that in [11] and 20 times larger than LPG in SMF. Moreover, this microfluidic assistant mechanism not only provides a flexible method to control the waveguide properties using beat-frequency interferences, but also allows for the applications in dual parameter measurement utilizing opposite spectral responses and different sensitivities. When temperature and axial force show co-effects on the beat-frequency interferences, their variations are simultaneously decoupled by finding inverse matrix and solving it below:
Fig. 6 (a) The transmission spectra of the proposed microfluidic assistant interferometer at the axial force of 0.0294 N and 0.2646 N; (b) Detailed fringes of the high-frequency interference dips in a small spectral range; (c) The linear fitting curves for axial force responses of dip and node.
In the matrix, ΔT and ΔF are the temperature and force variations, and ΔλD and ΔλE represent the wavelength shifts of the dip and envelope.
4. Conclusion
In conclusion, a microfluidic assistant beat-frequency interferometer based on a single-hole-infiltrated DM-MOF is proposed and demonstrated. The mode-mismatch induced modal interferences with the high-frequency dips and low-frequency envelope are observed in the transmission spectra of this interferometer. The beat-frequency mechanism is theoretically and experimentally explained by two sets of interferences between the LP01 mode and the components of LP11 mode with close but different frequencies. The deliberate introduction of the liquid rod enhances the sensitivities of the envelope to temperature and axial force. However, it shows little impact on the high-frequency dips. Moreover, a flexible method to control the DM-MOF properties and further improve the sensitivities is also proposed by increasing the length ratio k. In addition, the opposite wavelength-shift directions and distinguishing sensitivities of −959.22 pm/°C (−70.59 pm/°C) and 24.26 nm/N (−3.14 nm/N) for the envelope (dips) are simultaneously achieved in our proposed interferometer, allowing for dual parameter applications in physical, chemical and biochemical sensing with such a compact structure.
Acknowledgments
This work was supported by the National Key Basic Research and Development Program of China (Grant No. 2010CB327605 and 2011CB301701), the National Natural Science Foundation of China (Grant Nos. 61322510, 11174154 and 11174155), and the Tianjin Natural Science Foundation (Grant No. 12JCZDJC20600). The authors thank Yangtze Optical Fiber and Cable Co. Ltd. (Wuhan, China) for providing the MOF.
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