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We propose and demonstrate a Fabry-Perot (F-P) optical fiber tip sensor for high-resolution refractive-index measurement fabricated by using 157-nm laser micromachining, for the first time to our knowledge. The sensor head consists of a short air F-P cavity near the tip of a single-mode fiber and the fiber tip. The external refractive index is determined according to the maximum fringe contrast of the interference fringes in the reflective spectrum of the sensor. Such a sensor can provide temperature-independent measurement of practically any refractive index larger than that of air and offers a refractive-index resolution of ~4×10-5 in its linear operating range. The experimental data agree well with the theoretical results.
©2008 Optical Society of America
1. Introduction
Fiber-optic refractive-index (RI) sensors, such as surface plasma resonance (SPR) RI sensors [1,2], grating-based RI sensors [3–8], and interferometric RI sensors [9–11], have attracted considerable interest in recent years, because of their many excellent characteristics, including corrosion resistance, immunity to electromagnetic interference, high precision, etc. These advantages are important for applications in areas like biomedical measurement and environmental protection. However, there are still some drawbacks that need to be overcome with these sensors. SPR RI sensors can offer advantages of high accuracy (generally 10-4~10-7) and real-time responses [1, 2], but they are relatively expensive to implement. Because the SPR absorption peak of the commonly used metal (such as silver and gold) is located in the wavelength range 300–1000 nm, the light source and the fiber used in a SPR sensor are incompatible with the low-cost 1550 nm optical communication technology. In addition, SPR RI sensors are highly sensitive to the ambient temperature. It is also difficult to coat a sufficiently thin silver or gold film to a high quality on a fiber to form the sensing element. On the other hand, grating-based fiber-optic RI sensors [3–8] can operate in the 1550 nm band with comparable resolution of 10-5~10-6, but their performance is in general sensitive to the temperature variation. RI sensors based on long-period fiber gratings are further limited by their nonlinear characteristics and can offer a high sensitivity only over a small range of RI [3–5,7]. Conventional Fabry-Perot (F-P) interferometric sensors [8,9], which rely on the modulation of the phase of a F-P fiber interferometer in response to a change in the physical parameter to be measured, can in principle provide relatively low-cost absolute RI measurement with a low thermal sensitivity. In spite of the fact that F-P fiber sensors have been commercialized successfully, their reliability in RI measurement can be affected seriously by contaminants deposited on the F-P cavity during the liquid-filling process. Nevertheless, a micrometric F-P fiber sensor for RI measurement has been demonstrated, which was formed with a single-mode fiber spliced to a short section of a multimode fiber with an etched cladding [10]. The sensor, however, shows rather poor optical performance because of the small index difference between the two spliced fibers. The sensor is also sensitive to the ambient temperature and has a nonlinear response to the RI variation.
In this paper, we present a simple in-line F-P fiber sensor that measures the RI of a liquid at a fiber tip and avoids the need of filling any small fiber cavity. The sensor consists of a short air cavity produced near the tip of a single-mode fiber by 157-nm laser micromachining. The light reflected from the fiber tip thus interferes with the light reflected from the air cavity. By measuring the fringe contrast of the interference pattern from the reflected spectrum, we can determine the RI of the liquid accurately. The sensor can provide temperatureindependent measurement of practically any refractive index larger than that of air with a good linearity and a high resolution.
2. Sensor configuration and analysis
The structure of the sensor head is shown schematically in Fig. 1(a), which contains an in-fiber air cavity near a cleaved end of a single-mode fiber. The fiber end is supposed to be dipped into the medium whose RI is to be measured.
Fig. 1. (a). Structure of the sensor head, showing an in-fiber air cavity introduced near a cleaved fiber end, where the numbers “1”, “2”, and “3” label the three reflection surfaces in the structure. (b) The field amplitudes at the three reflection surfaces (the dashed arrows and the expressions within the boxes are for the case n′>n 0), where the symbols are defined in the text.
As shown in Fig. 1(a), there are three reflection surfaces in the sensor head, labeled as “1”, “2”, and “3”, respectively. Reflection surfaces 1 and 2 form a short cavity, denoted as cavity 1, while reflection surfaces 2 and 3 form another cavity, denoted as cavity 2. Cavity 3 is formed by reflection surfaces 1 and 3. The lengths of cavity 1, cavity 2, and cavity 3 are L 1, L 2, and L 1+L 2, respectively. The refractive indices of the fiber and the liquid are denoted as n 0 and n′, respectively. The power reflection coefficients at surfaces 1, 2 and 3 are R 1 and R 2 and R 3, respectively. The cavity lengths of L 1, L 2 and RI of the fiber n 0 can be regarded as constants over the normal range of the operating temperature of the sensor because the thermo-optic coefficient (6.3×10-6/°C) and thermal expansion coefficient (0.55×10-6/°C) of the fiber are quite small. The power reflection coefficients R 1 and R 2 at surfaces 1 and 2 are both equal to (n 0-1)2/(n 0+1)2=0.034≤1, while the reflection coefficient R 3 at reflection surface 3 depends on the liquid index as (n 0-n′)2/(n 0+n′)2, which is also much smaller than unity in practical situations.
Figure 1(b) shows the electric fields at the three reflection surfaces. The total reflected field from the sensor is given approximately by the sum of the first-order reflected fields from the three surfaces. The total contribution from the high-order reflections is less than 0.1% because of the low reflection coefficients and therefore can be neglected. The total reflected electric field, Er, is thus given by
where Ei is the input field, A 1, A 2, and A 3 are the transmission loss factors at reflection surfaces 1, 2, and 3, respectively, which are due to the surface imperfections (e.g., roughness), β is the propagation constant of the guided mode of the fiber, and α is the loss factor of cavity 1, which is mainly caused by diffraction in the air cavity. We ignore the loss in cavity 2, which is just the fiber loss over a short distance. For the sake of simplicity, we also ignore the effects of the surface imperfections on the reflection coefficients. The effects are practically the same for the three surfaces and cause mainly a change of the background light intensity. There is a π-phase shift at reflection surface 2, since light is reflected from an optically denser medium. When n′>n 0, there is also a π-phase shift at reflection surface 3.
From Eqs. (1) and (2), we obtain the normalized reflection spectrum RFP(λ) as follows:
Equations (3) and (4) describe the interference pattern of the reflected light from the sensor head for n′≤n 0 and n′>n 0, respectively. The key point of this work is to obtain the interference pattern and determine the value of n′ from the fringe contrast. It should be noted that only the reflection coefficient R 3 depends on the RI to be measured.
The measurement based on Eqs. (3) and (4) is independent of the power of the input light. Since both the thermal expansion coefficient and the thermo-optic coefficient of the fiber are very small, the measurement should be insensitive to the temperature variation. No temperature compensation is therefore needed for the sensor designed.
To show how the interference pattern varies with the fabrication parameters of the sensor, we calculate the reflection spectra of the sensor for different cases. The physical parameters of the sensor used in the calculation are summarized in Table 1. Figure 2(a) shows the reflective spectra calculated for the cavity losses α=0.02, 0.05, and 0.1 with the transmission loss factors A 1=A 2 fixed at 0.4, assuming n′=1.0 (air). As shown in the figure, each reflective spectrum consists of a large number of fine fringes, which are due to the long cavity 3. In the absence of cavity 3, i.e., by setting R 3=0 in Eqs. (3) or (4), these fine fringes disappear and only broad fringes due to the short cavity 1 remain, which are marked by the “envelope line” in the figure. A close-up of the fine fringes in the range where their fringe contrast is the largest is shown in Fig. 2(b). As expected, the contrast of the fringes increases with a decrease in the cavity loss. Nevertheless, a small cavity loss does not affect significantly the contrast of the fringes. Figure 2(c) shows the reflective spectra calculated for the transmission loss factors A 1=A 2=0.4, 0.5, and 0.6 with the cavity loss α fixed at 0.02, respectively. Figure 2(d) shows a close-up of the fine fringes. As shown in the figures, the contrast of the fringes increases with a decrease in the transmission loss factor. Therefore, to achieve a high fringe contrast, it is necessary to minimize both the cavity loss and the transmission loss.
Table 1. Values of the physical parameters of the sensor used in the calculation
As shown in Fig. 2, the contrast of the narrow fringes is not uniform across the reflective spectrum. To achieve the highest RI measurement resolution, we should always use the fringe that has the maximum fringe contrast. To locate this particular fringe, we first locate the dip of the fringe envelope from the reflective spectrum, as shown by the dashed box in Fig. 2(a) or Fig. 2(c). Within the dip of the fringe envelope, we then identify the fringe that gives the maximum fringe contrast, which can be done by locating the absolute minimum dip (λ 1) and the adjacent peak (λ 2), as shown in Fig. 2(b) or Fig. 2(d). The corresponding fringe contrast is given by V=|10 log10[RFP(λ2)/RFP(λ1)] for n′≤n 0, and V=|10 log10 [R′FP(λ1)/R′FP(λ2)] for n′>n 0, respectively, which is the maximum fringe contrast to be obtained.
The variation of the maximum fringe contrast V with the external RI n′ is shown in Fig. 3(a) for the cavity losses of α=0.02, 0.05, and 0.1, assuming A 1=A 2=0.4, and in Fig. 3(b) for the transmission loss factors A 1=A 2=0.4, 0.5, and 0.6, assuming α=0.02. As shown in the figures, the maximum fringe contrast V decreases with an increase in n′ for n′≤n 0. On the other hand, V increases with n′ for n′>n 0. The sensor can provide a measurement of practically any RI larger than that of air, as long as it is not very near the fiber index n 0, at which the fringe contrast goes to zero. It is easy to show that, as n′ approaches n 0, i.e., (n 0 -n′)/(n 0+n′)≪1, the maximum fringe contrast V (in dB) varies linearly with n′ as
with and
where the plus and minus signs are for n′≤n 0 and n′>n 0, respectively (See appendix).
Fig. 2. (a). Reflection spectra calculated for the cavity losses 0.02, 0.05, and 0.1, respectively, with A 1=A 2 fixed at 0.4. (b). Close-up of the fringes in (a). (c). Reflection spectra calculated for the transmission loss factors 0.4, 0.5 and 0.6, respectively, with α fixed at 0.02. (d). Close-up of the fringes in (c). The parameters of the sensor are given in Table 1 and n′=1.0 (air).
Fig. 3. Variation of the maximum fringe contrast with the external refractive index (a) for the cavity losses α=0.02, 0.05, and 0.1, assuming A 1=A 2=0.4, and (b) for the transmission loss factors A 1=A 2=0.4, 0.5, and 0.6, assuming α=0.02. The parameters of the sensor are given in Table 1.
The average RI sensitivities over the two ranges of the sensor (1.0≤n′≤1.45 and 2.15≥n′>1.45) are summarized in Table 2, where the numbers in the brackets are the RI resolutions obtained by assuming a fringe contrast resolution of 0.001 dB (typical value of an optical spectrum analyzer, and the power fluctuation of the light source is ignored in theory). The results in Table 1 confirm the need of minimizing the cavity loss and the transmission loss for the achievement of a high RI sensitivity.
Table 2. Dependence of the RI sensitivity on the sensor parameters, where the numbers in the brackets are the RI resolutions obtained by assuming a fringe contrast resolution of 0.001dB
Discrimination of the RI range of n′≤n 0 and n′>n 0, can be easily realized because there is a π-phase shift between the cases of n′≤n 0 and n′>n 0 due to existence of the half-wave loss. In practical operation, external refractive range of n′ is determined by comparing the real-time positions of peaks and dips of the interference fringes with that of the sensor in air. For n′≤n 0, the peak position of the sensor are the same as those of the sensor in air, while for n′>n 0, the peaks of the sensor are converted into the dips, as shown in Fig. 4.
3. Experimental results and discussion
To fabricate the sensor head, we first produced a circular hole with a depth of ~23 µm and a diameter of ~56 µm at the center of the cross section of a single-mode fiber by using a 157-nm laser micromachining system, which consisted of a 157-nm pulsed laser (Coherent, LPF202), an optical focusing system (with 25 times demagnification), an observing system, and a precision translation stage. The pulse energy density, pulse width, and pulse repetition rate used were 12 J/cm2, 15 ns, and 20 Hz, respectively. We used 160 pulses to produce the hole, which took only 8 seconds to complete. The hole was larger than the core but smaller than the cladding, as shown in Fig. 5(a). We next spliced the micromachined fiber to another fiber to enclose the air hole, so that an air cavity was formed. Finally, we cleaved the fiber at a short distance from the air cavity to complete the sensor. A microscopic image of the fabricated sensor head is shown in Fig. 5(b). The length of the air cavity was 29 µm and the distance from the air cavity to the fiber end was 1014 µm. The experimental setup of the sensor is shown in Fig. 5(c). In our experiments, the sensor head was dipped into a glycerin solution (for n′<1.45) or a solution of carbon bisulfide (CS2) and alcohol (for 1.45 <n′<1.62). The RI of the solution was controlled by changing the concentration of the solvent. An optical spectrum analyzer (OSA) (Agilent, 86142B) provided a broadband light source for the sensor and at the same time measured the reflective spectrum of the sensor.
Fig. 5. (a) Microscopic image of the micromachined hole introduced on the fiber cross section. (b) Microscopic image of the fabricated sensor head. (c) Experimental setup for refractive-index sensing.
Fig. 6. (a). Reflection spectrum of the sensor measured in air. (b) Close-up displays of the fringes for n′=1.0 (air), 1.33, and 1.404, respectively.
The sensor was tested with RI varying from 1.0 to 1.62. The reflection spectrum of the sensor in air is shown in Fig. 6(a). A close-up of the fringes is shown in Fig. 6(b) for several values of RI: n′=1.0 (air), 1.33 (water), and 1.404 (glycerin solution), from which the fringe contrast can be determined. The experimental spectra shown in Fig. 6 agree well with the theoretical ones shown in Fig. 2. The variation of the measured fringe contrast with the RI is shown in Fig. 6(a) with an expanded scale shown in Fig. 6(b). The fringe contrast decreases with the increase in the RI, as predicted. Over the RI range from 1.0 to 1.441, the fringe contrast variation is 16.5 dB, which corresponds to an average RI sensitivity of ~37 dB/RI (assuming a linear response). Over the range from 1.33 to 1.441, the fringe contrast varies almost linearly and the total change is ~3.0 dB, which corresponds to a RI sensitivity of ~27dB/RI. Over the range from 1.45 to 1.62, the fringe contrast also varies almost linearly and the total change is 3.9 dB, which corresponds to a RI sensitivity of ~24dB/RI. The RI resolution is limited by the amplitude resolution of the OSA i.e. 0.001 dB and the short term stability of the light source since the light power could be calibrated during testing, etc. With a fringe contrast resolution of 0.001 dB, the RI resolutions are ~3.7×10-5 and ~4.2×10-5 for the linear RI ranges from 1.33 to 1.441 and from 1.456 to 1.62, respectively. As shown in Fig. 7, the experimental results agree closely with the theoretical results, which are calculated with A 1=A 2=0.4 and α=0.
Fig. 7. Variation of the fringe contrast with the refractive index for the range (a) from 1.0 to 1.62, and (b) from 1.33 to 1.62, showing close agreement between experimental and theoretical results.
Two experiments were added for investigating power stability of the light source and the accuracy of the sensor. It was found that the power stability of the light source is ±0.001dB, similar to the amplitude resolution of the OSA, as shown in Fig. 8(a). The accuracy of the sensor is investigated as shown Fig. 8(b). The sensor was put into pure water for ~2 hours. It was found that the fluctuation of the fringe contrast of the sensor is ~±0.003dB, corresponding to a RI accuracy of ±12×10-5. Such an accuracy of the sensor is limited by the stability of the light source, the amplitude resolution of the OSA, and the noise of the photodetector and electric circuit, etc. The accuracy can be further improved by averaging to reduce random noise.
The temperature dependence of the fringe contrast measured in air is shown in Fig. 9, which confirms that the fringe contrast stays practically constant over the temperature range from 10 to 70 °C.
4. Conclusions
A novel laser-micromachined F-P fiber tip RI sensor is proposed and demonstrated, for the first time to our knowledge. The sensor provides temperature-independent measurement of any RI larger than that of air and offers a RI resolution of ~4×10-5 in the linear operating range. The sensor exhibits many desirable characteristics, including wide RI sensing range, good linearity, high resolution, easy operation, low thermal sensitivity, low fabrication cost, potential for mass production, small size, good reliability (no cavity filling), etc. The performance of the sensor can be further improved by increasing the fringe contrast, which can be achieved by improving the quality of the reflection surfaces to reduce the transmission loss factors through optimizing the operation parameters of the 157-nm laser micromachining system. The use of an A/D converter with a higher resolution for the spectrum analysis can further improve the fringe contrast resolution and hence the RI resolution. The sensor could find a broad range of biomedical applications, such as DNA sequence detection and antigen-antibody binding monitoring. The long, thin geometry of the sensor head would allow applications to human bodies with minimal invasion.
Appendix for Eq. (5)
Within the dip of the fringe envelope, we then identify the fringe that gives the maximum fringe contrast, which can be done by locating the absolute minimum dip (λ 1) and the adjacent peak (λ 2), as shown in Fig. 2(b) or Fig. 2(d). The corresponding fringe contrast is given by V=|10 log10[RFP(λ2)/RFP(λ1)] for n′≤n 0, and V=|10 log10 [R’FP(λ1)/R’FP(λ2] for n′>n 0, respectively, which is the maximum fringe contrast wanted.
for n′≤n0
for n′>n 0
where
When considering using the principle of determining the maximum fringe contrast, we get:
Eq. (A.1) can be simplified as Eq. (A.2)
for n′≤n 0 and n′>n 0, respectively.
When n′ approaches to n 0, (n 0-n′)/(n 0+n′) ≪1, the 2nd order factor could be ignored. Eq. (A.2) is then simplified as Eq. (A.3)
We modify the form of Eq. (A.3) into Eq. (A.4)
Eq. (A.4) is simplified to Eq. (A.5) by using when x→0.
where the plus and minus signs stand for n′≤n 0 and n′>n 0, respectively.
Acknowledgment
This work is supported by the key project of National Natural Science Foundation of China under Grant No 60537040.
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