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Abstract
In this paper, a novel sensitivity amplification method for fiber-optic in-line Mach-Zehnder interferometer (MZI) sensors has been proposed and demonstrated. The sensitivity magnification is achieved through a modified Vernier-effect. Two cascaded in-line MZIs based on offset splicing of single mode fiber (SMF) have been used to verify the effect of sensitivity amplification. Vernier-effect is generated due to the small free spectral range (FSR) difference between the cascaded in-line MZIs. Frequency component corresponding to the envelope of the superimposed spectrum is extracted to take Inverse Fast Fourier Transform (IFFT). Thus we can obtain the envelope precisely from the messy superimposed spectrum. Experimental results show that a maximum sensitivity amplification factor of nearly 9 is realized. The proposed sensitivity amplification method is universal for the vast majority of in-line MZIs.
© 2017 Optical Society of America
1. Introduction
In the past few decades, fiber-optic in-line Mach-Zehnder interferometer (MZI) sensors have attracted great attention for their application prospects in various areas such as physical, chemical and biological sensing, due to their advantages of simple, compact structure, good stability, and low cost compared to traditional MZIs [1]. Similar to traditional MZIs, light splitting and recoupling configurations are essential. Many special structures have been proposed for the constitution of in-line MZIs such as: offset splicing [2–4], abrupt taper [5, 6], up-taper [7, 8], spherical structure [9, 10], micro bending [11, 12], air core collapse of photonic crystal fiber (PCF) [13, 14], 3dB long period fiber grating (LPFG) [15, 16] and so on. In addition, multimode microfiber [17], multicore fiber [18], femtosecond laser micromachining [19] and mode field mismatch of different fibers [14, 20, 21] have also been applied to in-line MZIs.
In general, working mechanism for most of the in-line MZIs is summarized as follows. When light transmits through the light splitting structure, part of the light energy in the transmission fiber core will be coupled into the cladding and some cladding modes are excited. Most of the cladding mode energy will couple back into the core of receiving fiber after passing though the light recoupling structure. As we know, because of the large attenuation of cladding modes, length of the in-line MZIs are usually set to be short in order to reduce the loss of the sensor while maintain a high fringe contrast. In addition, since the effective refractive index difference between the core mode and cladding modes are small, free spectrum range (FSR) of the in-line MZIs are always large (around 10nm or even bigger). Moreover, for in-line MZIs, several cladding modes may be excited and the excitation efficiencies are different, which lead to the messy interference spectrums. Large FSR and multi-mode interference are the characteristics of in-line MZI sensors compared to other interferometric fiber-optic sensors.
Vernier-effect was firstly employed by vernier caliper and barometers to enhance the accuracy of length and air pressure measurement. Recently, Vernier-effect has also been employed to fiber-optic sensing for the magnification of spectrum shift. The optical sensors consist of two cascaded two-beam interferometers (or high fineness multi-beam interferometers) such as high-Q micro-ring resonators [22–25], fiber rings [26–28], Fabry-Perot interferometers (FPI) [29–33], Sagnac interferometers (SI) [34] and even MZI or Michelson interferometers (MI). Just as the vernier caliper, the two interferometers must have a small fringe interval difference. Sensitivity can be amplified by an order of magnitude through implementing wavelength interrogation with a curve fitting method of the superimposed spectrum envelope. However, arising from the spectrum characteristics of in-line MZIs mentioned above, no obvious envelope is observed from the superimposed spectrum of cascaded in-line MZIs. So, Vernier-effect is scarcely applied to in-line MZI sensors to the best of our knowledge.
In this letter, we propose a novel sensitivity amplification method for fiber-optic in-line MZI sensors based on optimized Vernier-effect. Spectrum feature of the traditional optical Vernier-effect is analyzed in frequency domain theoretically and experimentally. Envelope of the superimposed spectrum of optical Vernier-effect can be obtained accurately from the frequency spectrum. Frequency component corresponding to the envelope is extracted and taken Inverse Fast Fourier Transform (IFFT) to restore the envelope from the messy superimposed spectrum of cascaded in-line MZIs. Two in-line MZIs based on core offset splicing of single mode fiber (SMF) are utilized to verify the effect of sensitivity amplification. Results of temperature and curvature measurements indicate that a maximum sensitivity amplification of nearly 9 times can be realized, which is consisted with the theoretical calculation. The proposed algorithm is a universal sensitivity amplification method for most of the in-line MZIs.
2. Operation Principles
2.1 Traditional Vernier-effect
For traditional Vernier-effect, the sensor consists of two cascaded two-beam interferometers or multi-beam interferometers. Here we take the sensor based on two cascaded MZIs as an example for the calculation of the superimposed spectrum. As shown in Fig. 1, Dj (j = 1, 2, 3, 4) are the normalized coefficients which denote splitting ratio and attenuation of the interference arms. ΔLR and ΔLS are the interference arm length difference of the reference and sensing interferometer. Interference spectrum of the reference and sensing interferometer are written as
Where A1 = D12 + D22, A2 = D32 + D42 and B1 = 2D1D2, B2 = 2D3D4 represent the DC component and fringe contrast of the interference spectrum, respectively.Electronic field of the cascaded structure can be deduced asCalculated output light intensity of the cascaded MZIs isFrom Eq. (1) and Eq. (3), we conclude that output light intensity of the cascaded MZIs can be regarded as the multiplication of IR and IS. It should be noted that, cascaded spectrum of the sensors composed of other kinds interferometers can also be deduced by the analogous method.Operation principles of the traditional sensors are mainly based on spectrum interrogation which is given in Fig. 2. FSR difference between the sensing interferometer (FSRS) and reference interferometer (FSRR) must be small to employ Vernier-effect. The cascaded superimposed spectrum is consisted of comb-like fine spectrum and large envelope. In order to improve the resolution and eliminate the measuring error introduced by power fluctuation at the same time, the envelope is acquired by a curve fitting method [25, 28, 29]. And the period of the envelope (FSRC) is given by
Compared to the wavelength shift of sensing interferometer, the shift of the cascaded sensor is magnified by a factor of
Fig. 2 Working mechanism of the traditional spectrum interrogation of Vernier-effect. (a) Spectrum of the sensing interferometer; (b) Spectrum of the reference interferometer; (c) Superimposed spectrum of the cascaded sensors.
In conclusion, for the traditional curve fitting method, the following conditions must be satisfied in order to obtain the envelope precisely. Firstly, in the limited wavelength span of the light source, at least a complete period of envelope must be observed. This requires that FSRs of the interferometers as well as the sensitivity magnification factor should be small. Secondly, the cascaded superimposed spectrum must be regular and cyclical. Namely, interference fringe of the both cascaded interferometers need to be periodic. Thirdly, fringe contrast of the two interferometers must be high enough.
2.2 Modified Vernier-effect
As we discussed above, traditional Vernier-effect based on curve fitting interrogation scheme is inefficient when applied to in-line MZIs, due to their spectrum characteristics of large FSR and non-periodic interference fringe. Here we propose a new and effective way to extract the envelope. To study the operation principle of Vernier-effect quantitatively, the cascaded spectrum should be analyzed in frequency domain. We can see from Eq. (3) that the superimposed spectrum is composed of four frequency components: fS, fR, fS + fR and |fS –fR|, where fS and fR are the spatial frequency of sensing and reference interferometer. The frequency components fS, fR and fS + fR are the comb-like fine spectrum, while the frequency component |fS –fR| is the large envelope. So the envelope function is expressed by
To verify our derivation, as shown from the inset in Fig. 3(b), two MIs based on 1:1 fiber couplers and Fresnel reflections of fiber end faces are cascaded to generate Vernier-effect. FSRs of the two MIs are controlled around 1 nm by precisely cutting of the fiber tips. Measured superimposed spectrum and the corresponding spatial frequency spectrum are shown in Figs. 3(a) and 3(b), respectively. Three clusters of spatial frequency can be seen from the frequency spectrum which indicate frequency components of |fS –fR|, fS & fR , and fS + fR, respectively. The multi-frequencies observed may result from the harmonic frequency components of single MI. In order to acquire the envelope, the frequency of |fS –fR| is filtered out by a Gaussian first-order type filter with the corresponding central frequency of 0.062 nm−1 and the 3 dB bandwidth of 0.02 nm−1 [35]. Then the envelope is extracted and recovered by means of IFFT as presented in Fig. 3(a).
Fig. 3 (a) Superimposed spectrum of the cascaded sensors based on two MIs constructed with 1:1 coupler and Fresnel reflection of fiber end face. And the red curve represents the envelope extracted by IFFT of the |fS –fR| frequency component; (b) Spatial frequency spectrum of the Superimposed spectrum. Inset Schematic configuration of the cascaded MIs.
For the interferometric sensors, interference spectrum reaches its valley position when the following condition is satisfied
Where ΔLS is the interference arm length difference, m is the interference order, and n is the effective refractive index difference. When the optical path difference (OPD) changes with external environment such as strain, temperature or curvature, the resonant wavelength λm changes accordingly asIn the equation, Δn and δΔLS are the change in n and ΔLS induced by the fluctuation of environmental physical parameters. We can see that Δn/n and δΔLS/ΔLS depend only on the intrinsic property of fiber [36]. Take the temperature measurement as an example. The factor Δn/n and δΔLS/ΔLS depend only on the thermo-optic and thermal expansion coefficient of fiber, respectively. So the sensitivity of single interferometer can be regarded as a constant and have no dependence on the interference arm length difference.However, as for the sensor based on the optimized Vernier-effect, the active-length of the sensor that response to the fluctuation of environmental physical parameters is ΔLS, while the actual interference length is | ΔLR -ΔLS |. The interference dip is calculated by λm = 2n| ΔLR -ΔLS |/(2m + 1). So, the resonant wavelength λm variation is rewritten as
Therefore, sensitivity amplification factor of the modified Vernier-effect can be approximated as ΔLS/| ΔLR -ΔLS| [36], which is equal to the result of traditional Vernier-effect.2.3 Vernier effect for in-line MZI
Different from traditional interferometers and all fiber FPIs, the interference spectrum of in-line MZIs is a result of multimode interference. Interferences between the fundamental core mode and several cladding modes are observed in the interference spectrum. However, among the cladding modes participated in the interference, only one cladding mode is dominant. As a result, we can see one main and several weak frequency components from the FFT of interference spectrum. For the majority of in-line MZIs reported, their transmission spectrums are usually formed by two primary frequency components among which one is much stronger than the other. To analyze the superimposed spectrum of cascaded in-line MZIs, interference spectrum of sensing and reference interferometer can be express as
Where Bj is much bigger than Cj, which means that ωS1 and ωR1 are the two dominant angular frequencies. From the calculation described above, the superimposed spectrum IC is calculated as IC = IS.IR. So frequency spectrum of the cascaded in-line MZIs is mainly consisted of 12 frequency components which are denoted as follows: ωS1, ωS2, ωR1, ωR2, ωS1 + ωR1, ωS1-ωR1, ωS1 + ωR2, ωS1-ωR2, ωS2 + ωR1, ωS2-ωR1, ωS2 + ωR2, ωS2-ωR2. They are divided into three clusters according to their value. The first cluster includes ωS1, ωS2, ωR1, ωR2, the second cluster includes ωS1 + ωR1, ωS1 + ωR2, ωS2 + ωR1, ωS2 + ωR2, and the third includes ωS1-ωR1, ωS1-ωR2, ωS2-ωR1, ωS2-ωR2. Here ωS1-ωR1 is the envelope frequency need to be extracted. So frequency components in the third cluster should to be discussed in detail. Amplitude of these four frequency components are 0.5B1B2, 0.5B1C2, 0.5B2C1, 0.5C1C2, respectively. We can see that, there is a certain difference between the value of ωS1-ωR1 and ωS1-ωR2, as well as ωS2-ωR1. In addition, amplitude of the envelope frequency is bigger than that of these two frequencies. Although the value of ωS1-ωR1 and ωS2-ωR2 are similar, it is obvious that amplitude of ωS1-ωR1 is much bigger than ωS2-ωR2. As a result, we can easily distinguish frequency component of the envelope from the frequency spectrum. Thus, according to the frequency picked out, the envelope can be precisely obtained by taking IFFT of the selected frequency.3. Experiment and discussion
3.1 Fabrication of the sensor and Envelope extraction
Two in-line MZIs based on core offset splicing of SMF are fabricated to verify sensitivity amplification effect of the modified Vernier-effect. The core offset splicing joints are made by a commercial fusion splicer (FSM-60S) under manual mode [2]. Fiber tips are manually controlled to ensure that offset occurs only in y axis while keeping alignment in x direction during the splicing process. The transmission spectrum is monitored by an optical spectrum analyzer (OSA AQ6370C) throughout the fabrication process. Figure 4 illustrates the experimental setup of the sensing system.
For the first splicing joint, the offset is precisely adjusted to obtain a spectrum attenuation of about 3dB with the help of OSA. Then, the fiber is cut at a specific length. Finally, another end of the SMF is spliced with the lead out fiber. Adjust the core offset carefully until good fringe visibility is observed. Phase difference of the MZI can be written as
Where neffco and neffcl-i is the effective refractive index of the fundamental core mode and the i-th cladding mode. And L is the length of the offset spliced SMF.Due to the large attenuation of the cladding modes, in order to get a high fringe contrast while keep a relative small attenuation, length of the spliced SMF should not be too long. Meanwhile, to realize a considerable magnification factor in the restricted wavelength span of the light source, the FSR may not be too large, namely the length need to be a little longer. Taking fringe contrast, attenuation and magnification factor into consideration, length of the sensing and reference MZIs is controlled around 4.5 and 5 centimeters, respectively.
Transmission spectrums of the two MZIs as well as FFT of the spectrums are depicted in Fig. 5(a). We can see from the transmission spectrums that FSRs of the two MZIs are around 11.5 nm and 12.5 nm. The interference spectrums are mainly consisted of two cladding modes among which one is dominant. Primary spatial frequency of the sensing and reference MZIs are 0.081 nm−1 and 0.092 nm−1. Spatial frequency of the in-line MZI depends on L and the effective refractive index difference, which is given by [3]
Fig. 5 (a) Spatial frequency spectrum of the two MZIs, inset is the corresponding transmission spectrum. ; (b) Spatial frequency spectrum of the cascaded two MZIs, inset is the corresponding superimposed spectrum.
According to the length we choose and the FSRs we estimate, the designed magnification factor is 9 and FSR of the envelope may be around 100nm. However, there may be error in the control of L. Moreover, the dominant cladding mode participated in interference may be different for the two MZIs, which results in the slight disparity of effective refractive index difference. So, experimental result may have a small difference with the theoretical prediction.
To analyze the optical spectrum properties of the proposed sensor, light emitted from a broadband source is launched into the cascaded MZIs as sketched in Fig. 4. Measured superimposed spectrum of the cascaded in-line MZIs is shown in Fig. 5(b). Just as we have assumed, due to special spectrum features of the in-line MZI, no obvious envelope can be observed in the cascaded spectrum. From spatial frequency spectrum shown in Fig. 5(b), we can see that there are three clusters of frequency components in the FFT outputs, located near 0.01 nm−1, 0.1 nm−1 and 0.2 nm−1, respectively. As discussed in previous investigation, the smallest frequency component near 0.01 nm−1 is the envelope frequency that needed to be picked out. The frequency is filtered out by a Gaussian first-order type filter with the corresponding central frequency of 0.011 nm−1 and the 3 dB bandwidth of 0.004 nm−1. Then the envelope is recovered by means of IFFT. Superimposed spectrum as well as the filtered envelope are depicted in Fig. 6. FSR of the envelope is about 98 nm.
Fig. 6 Superimposed spectrum of the cascaded sensors based on two in-line MZIs. And the black curve represents the envelope extracted.
3.3 Experimental result
Temperature and curvature measurements of single MZI and cascaded MZIs are carried out to verify the feasibility of the proposed spectrum shift amplification mechanism. Temperature response of the sensor is investigated by means of placing it onto a semiconductor based TEC temperature controller with a stability of ± 0.1 °C. Temperature adjusting range of the TEC is from 20 °C below room temperature to 80 °C.
Firstly, temperature response of the single sensing MZI is tested. Temperature of the TEC rises gradually from 10 to 75 °C with a step of 5 °C, and then maintains about 3 min at each temperature. When the external temperature rises, due to the fact that thermo-optic coefficient of the Ge-doped silica core is higher than that of the cladding, the effective refractive index of the core mode shows a larger change than that of the cladding modes. In addition, as a result of thermal-expansion effect, L increases accordingly [36]. So, as shown in Fig. 7(b), the attenuation dip exhibits a red shift with the increasing of external temperature. Relationship between the temperature increment and the corresponding wavelength shift of the single sensing MZI is shown in Fig. 7(c). Temperature sensitivity of the attenuation dip near 1556 nm is about 45.36 pm/°C.
Fig. 7 (a) Transmission spectrum of the sensing MZIs with different temperature; (b) Wavelength shift of the attenuation dips near 1556nm; (c) Dip wavelength versus temperature and the fitted line.
Then the sensitivity amplification is test by cascading the sensing MZI with the reference MZI. The sensing MZI is placed on TEC while the reference MZI is kept at room temperature (about 30 °C). Envelope is acquired by the method mentioned above. Wavelength shift of the extracted envelope with the increasing of temperature is illustrated in Fig. 8. Temperature sensitivity of the sensor under modified Vernier-effect is about 397.36 pm/°C. So, a sensitivity amplification factor of about 8.7 is obtained, which is consistent well with the theoretical calculation.
Fig. 8 (a) Wavelength shift of the envelope extracted from the superimposed spectrum under different temperature; (b) The relationship between the center wavelength shift of the envelope dip peak and the temperature.
As a supplement, curvature respond of the sensor is also implemented. Two ends of the fiber sensing head are clamped in a straight state by two fiber holders. One of the holders is fixed and the other is movable. Displacement of the movable holder is controlled by a computer. Initial distance of the two holders is 16 cm. During the experiment, displacement with a resolution of about 2 μm is applied on the structure. As a reference, the other interferometer is kept in straight by clamping two ends of it on fiber holders fixed on the optical platform. Firstly, curvature sensitivity of the sensing MZI is tested. Then, the reference MZI is connected to realize the Vernier-effect.
The transmission spectra of the single sensing MZI with different curvature applied are shown in Fig. 9(a). The resonant dip experiences a blue-shift as the curvature increases. Resonant wavelengths of the dip near 1556 nm under different curvature are depicted in Fig. 9(b). From linear fitting of the experimental results, a curvature sensitivity of −4.55 nm/m−1 is obtained. It should be noted that, curvature sensitivity of the offset splicing structure relies greatly on the relative positional relationship between the bending direction and the offsetting axis. In addition, the dominant cladding mode excited also has influence on the curvature response.
Fig. 9 (a) Interference fringe patterns of the sensing MZI with different curvature; (b) Relationship between dip wavelength and the curvature.
Curvature measurement of the sensor after the connection of reference MZI is carried out then. Just like the sensing of temperature, the extracted envelopes under different curvature are shown in Fig. 10(a). Valley wavelengths of the attenuation dips and the corresponding fitted line are presented in Fig. 10(b). We can see that from the experimental result, the sensitivity is enhanced to about −36.26 nm/m−1 with a magnification factor of about 8.
Fig. 10 (a) Wavelength shift of the envelope extracted from the superimposed spectrum under different curvature; (b) The relationship between the center wavelength shift of the envelope dip and the curvature.
The modes of a curved optical fiber are usually analyzed through a conformal transformation. Effective refractive index of the fundamental core mode has much weaker dependence on curvature compared to cladding modes which can be regarded as a constant. As curvature rises, effective refractive index of most cladding modes will increase. The rates of effective refractive index change for each cladding modes are different. So the attenuation dips will exhibit a blue-shift with the increasing of curvature. However, on the contrary, effective refractive index of some cladding modes may keep almost the same or may even decrease. Responses of cladding modes to curvature depend on the horizontal distribution of the mode field [37]. Moreover, it should be emphasized that, curvature may influence the attenuation of cladding modes and result in the change of attenuation dips intensity. For the transmission spectrum of in-line MZIs, different attenuation dips may result from different cladding modes. So the responses of these dips to curvature are different. Some dips show obvious wavelength shift while some experience considerable intensity fluctuation.
4. Conclusion
In this work, we propose and demonstrate a novel sensitivity amplification method based on optimized Vernier-effect which is universal for the majority of fiber-optic in-line MZI based sensors. Both the theoretical analysis and experimental verification are implemented. Frequency component corresponding to the envelope is extracted and taken inverse FFT to restore the envelope of the cascaded superimposed spectrum. Extraction of the envelope is demonstrated with two cascaded Michelson interferometers. Two in-line MZIs based on core offset splicing of SMF are adapted for the experimental verification of the sensitivity amplification of the modified Vernier-effect. Experimental results of temperature and curvature measurement indicate that a maximum sensitivity magnification factor of nearly 9 can be achieved.
Funding
National Natural Science Foundation of China (NSFC) (No. 61775070, 61290315, 61290311); Fundamental Research Funds for the Central Universities (No. 2017KFYXJJ032).
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