We report in this paper a high thermal sensitivity (78 pm/°C) modal interferometer using a very short Photonic Crystal Fiber stub with a shaped Germanium doped core. The Photonic Crystal Fiber is spliced between two standard fibers. The splice regions allow the excitation of the core and cladding modes in the PCF and perform an interferometric interaction of such modes. The device is proposed for sensitive temperature measurements in transmission, as well as in reflection operation mode with the same high temperature sensitivity.
©2013 Optical Society of America
In the past years a wide range of fiber optic sensors using modal interferometry have been developed. Especially, many different applications have been explored using modal interferometry with microstructured fibers or Photonic Crystal Fibers (PCF). The PCF fiber sensors were used to measure different parameters such as strain , temperature , refractive index , pressure and torsion . Fiber optic sensors in general provide considerable advantages in application such as compact size and immunity to electromagnetic fields and to microwave radiation.
Y Jung et al demonstrated in 2006  a new interferometer arrangement using a coreless fiber spliced between two multimode fibers to measure refractive index. Recently, a new technique to create a modal interferometer with PCF fiber was demonstrated consisting of splicing a piece of PCF between standard mode fibers (SMF), where in the collapsed region of the PCF the voids are fully collapsed . PCFs were also exploited as strain sensors in contrast to sensors avoiding a temperature cross [7,8]. Such devices were studied as strain sensors with lower temperature dependence. H. Y Choi showed in 2008 a hybrid sensor with a PCF fiber and a Fabry Perot Interferometer to measure temperature . However, the low thermal sensitivity (~1.2 pm/°C) limited the application of such a sensor concept. Another temperature sensor was described using two short stubs of a multimode fiber (MMF) for excitation of the modes in a SMF fiber . The device was used especially to measure in the high temperature range. At the same time, M. J. Kim showed an interferometer using the same principle  with a PCF fiber to measure temperature. The low sensitivity and the transmission operation made this sensor unviable for practical applications. Villatoro et al demonstrated in 2009  a sensor using a commercial PCF with two collapsed regions to measure temperature, with a medium thermal sensitivity (~8 pm/°C). The device operated in transmission and required a long thermal treatment. In 2009 B. Larrion et al  demonstrated a sensitive temperature sensor using a PCF fiber with a very high sensitivity (~0.14 nm/°C). This device, however, requires a metal deposition in PCF and is limited to applications in low temperature regions (<80°C). Recently, a temperature sensor with high sensitivity (~73 pm/°C) was demonstrated and low strain sensitivity (0.93 pm/με) was shown . However, the device needs 40 cm of PCF fiber to operate, which makes applications difficult. Another interesting temperature sensor was demonstrated in 2012 , showing a very high thermal sensitivity (~6.6 nm/°C), albeit with the requirement to use ethanol inside the PCF voids, which makes fabrication difficult. A. Bozolan et al.  reported a temperature sensor using a colloid core PCF with a thermal sensitivity of 70 pm/°C.
We report in this paper a miniature temperature sensor with a very high thermal sensitivity of 78 pm/°C based on a very short PCF stub (~1.7 mm) with a shaped double Germanium core. The high Germanium concentration provides the high temperature sensitivity for the interference of the fundamental mode and a higher order mode, and achieves a wide free spectral range at very short lengths of the interferometer. In addition, the device is shown to operate in transmission and reflection mode with the same thermal sensitivity.
2. Fiber arrangement for modal interference
The sensor setup is based on the combination of a piece of a special PCF spliced between two single mode fibers, as presented in Fig. 1(a). A cross section of the PCF used is shown in Fig. 1(b) with a high Germanium doped core surrounded by a silica glass structure. The fusion splices were performed with the splicing device ‘Sumimoto T36’. The discharge arc parameters were chosen to fully collapse the PCF voids. The two collapsed regions are 150 ± 20 μm in length, and the total head sensor length is 1.71. ± 0.1 mm.
The first collapsed region [Fig. 1(c)] has the function of exciting the fundamental core mode and cladding modes in the PCF. The second collapsed region has the function of recombining the PCF modes, as was reported in . The combination of the fully collapsed regions, PCF geometry and a small lateral off set in the PCF can adjust the intensity ratio of the interfering modes and can optimize, therefore, the value of fringe contrast, as was demonstrated in . The lateral off set was made using the splice machine manual steps only to improve the quality of the signal (value of the fringe contrast bigger). The interferometer can be manufacture without lateral off set. A result of the fully collapsed regions, a lateral off-set, and PCF mode properties is an interference pattern in the spectral transmission signal.
The Germanium-doped core of the PCF is designed to guide only a single fundamental mode at the operation wavelengths between 1500 and 1600 nm. Since the PCF is used without a coating, light can also be guided in the cladding region. In contrary to conventional step-index fibers, this fiber exhibits two cladding regions: a micro-structured and a homogeneous one.
Conventional solid fibers do exhibit a continuous spectrum of radiation modes with an effective refractive index below the cladding index. However, micro-structured fibers with a periodical arrangement of rods or air holes usually show fluctuations in the eigenvalue distribution of these modes, also referred to as density of states (DOS). The lowest order solution of the infinite triangular lattice of air holes is called the fundamental space-filling mode (FSM). These eigenvalues have been calculated using a commercial full-vectorial finite element method . The DOS are calculated from the eigenmodes of a hexagonal unit cell of the PCF cladding following the procedure presented in . Table 1 shows the geometric parameters of the PCF which we used for these simulations.
It is found that modes can propagate in a lattice defect (core) of this microstructured fiber, although no strict bandgap (DOS equals zero) is present . This effect occurs at local minima of the DOS, sometimes also called pseudo-bandgaps . These modes are leaky and their (complex) effective refractive indices are below the FSM. Figure 2 shows the DOS of the PCF cladding (red) together with the refractive indices of selected modes.
The high DOS region on the right hand side corresponds to the FSM (with the refractive index nFSM). The fundamental core mode (FM), which is plotted in Fig. 3(a), always has a higher refractive index than the fundamental space filling mode (neff>nFSM). Furthermore, a distinct higher-order mode (neff<nFSM), denoted as HOM, was identified, which is a leaking cladding mode and is not guided by the effective refractive index difference between core and microstructured cladding. Although there is no bandgap present, the mode is still able to propagate over short distances because it is located in a local minimum of the DOS. The intensity pattern of this mode is plotted in Fig. 3(b) in comparison to the fundamental core mode [Fig. 3(a)].
Although other minima in the DOS plot are visible, no other defect modes exhibit a strong confinement in the core area, which would be necessary for an interaction with the fundamental mode. For such an interferometric interaction a sufficient overlap of the modes is required in the core region of the fiber.
As a criterion for the determination of the defect modes which can efficiently interfere with the fundamental core mode, we used the guided power (Pcore) within the first ring of air holes.
The overlap of the fundamental mode - shown in Fig. 3(a) - with the doped core area is 71% and the power which is guided within the first ring of air holes is almost 100%. The defect mode shown in Fig. 3(b) carries 6% of its power in the doped core and 35% within the first ring of air holes. For all other defect modes the power fraction within the first ring of air holes was equal to or below 10%.
Such types of weakly guiding modes have been described by Eggleton et al using a similar fiber for the inscription of fiber Bragg gratings (FBG) . It was found that these defect modes, in contrast to cladding modes, are insensitive to external refractive index changes .
3. Analysis of thermo-optical properties
The thermo-optical properties are influenced by the material in the core as well as by the structural properties. Bulk silica material (without doping) has a thermo-optical coefficient (TOC) of δn/δT = 1.06∙10−5K−1. This bulk TOC increases by 1.07∙10−7 K−1 per mol% of Germanium in case of doping . The mismatch of the expansion coefficients between core and cladding due to the different material properties induces a mechanical stress. This mechanical stress leads to a change in the refractive index due to the stress-optical effect and adds an additional component to the TOC. Since the used fiber has a very high GeO2 concentration in the core, which can be verified by the refractive index measurement of the core rod used for fiber drawing, see [Fig. 4(a)] this effect cannot be neglected. The molar concentration was calculated backwards from the refractive index values using a value of δn/δc = 1.5∙10−3/mol% .
As can be seen in Fig. 4(a), the core has a butte-like shaped concentration profile with approximately 32 mol% Germanium concentration at its top and 13 mol% at the maximum of the pedestal. The mechanical stress has been measured using a setup which is described elsewhere . The obtained axial stress distribution is shown in Fig. 4(b) (blue line). As the plain-strain theory implies, the integralEq. (1), an offset of approximately 36 MPa was added, which can also be seen in Fig. 4(b) (red line). The resulting change of the radial refractive index Δnr is as high as −1.3∙10−3 in the inner region of the core, which exhibits 32 mol% of GeO2 concentration. This value decreases with increasing temperature until it vanishes typically at a temperature of approximately 1000°C. Based on this stress-optical effect, it is possible to estimate a maximum change of the thermo-optical coefficient (TOC) inside the core to δn/δT = 0.4∙10−7 K−1 per molar percent of Germanium concentration caused by the mechanical stress. We derived the final thermal stress in the PCF caused by the stress in the preform using a finite element method. In this case, the stress-optical effect causes a change of the refractive index, which can be approximated by12]. Similar result was published for Y. Geng et al  where the TOC found also is bigger than pure silica TOC due the doping in the fiber composition and consequently the temperature sensitivity is higher than pure silica fiber. The devices using doped fibers can be useful in the future to monitoring temperature. In special, our case, with a 32 mol% germanium doping concentration the TOC is higher by 44%. This effect enables very short sensor lengths for the interferometer temperature fiber sensor and high temperature sensitivity can be found when compare with temperature sensor manufactured with pure silica.
4. Interferometric operating principle
The interferometric measurement principle is based on the interaction of core and cladding modes. Inside the lattice defect in the center of the microstructured cladding the fiber has a highly Germanium doped region. Figure 5(b) shows the GeO2-concentration profile as well as the corresponding refractive index difference of the Ge-core compared to bulk silica, which was calculated from the preform data using the diffusion equation.
The calculated concentration profile of the GeO2-doped core can be approximated by the analytical function,
The general interference of two modes in a fiber can be described very easily using the equationEq. (2)
The refractive index difference between the modes can be assumed to be constant over the wavelength range for a constant temperature. It can be calculated using the distance between two consecutives peaks in the transmission spectrum at the wavelengths λ1 and λ1:
The wavelength shift of a single transmission dip can be written as a function of the refractive index variation of the temperature:
ΔT is the temperature variation and ∂Δneff/∂ΔT is the variation of the effective refractive index difference of the guide modes with temperature. The influence of the thermally induced length change is equal for both modes and therefore has no influence on the wavelength shift.
From these data a high wavelength sensitivity of 94 pm/°C can be expected for such a fiber sensor. A temperature difference of 500 °C would therefore result in an interference pattern shift of about 46 nm.
5. Experimental results and discussion
The experimental setup consists of a broadband source (ASE) and an Optical Spectrum Analyzer (ANDO AQ6317). The total loss measure in the device when operated in transmission was 5.8 dB. The first test involved heating the device up to 500° C and measuring the thermal characteristics in transmission. The sensor head was placed in an oven and heated at a rate of 10°C /min. The temperature was kept constant at 500°C for 10 min, then cooled down to room temperature. A thermocouple PT100 was placed beside the PCF inside the oven to monitor the temperature.
Figure 6 shows the interference pattern of the transmission spectrum of the device before the thermal cycle (black line) and after the thermal cycle (green line). The wavelength shift came back to the same point after heating and cooling with almost no hysteresis. In the spectrum it is possible to see the high value of fringe contrast in the interference pattern of more than 27 dB. The transmission signal of our device has a free wavelength range of~60 nm, which is large enough for a temperature range of about 600°C. The thermal sensitivity was measured in a thermal cycle with temperature steps of 50°C.
The result of the temperature cycle is shown in Fig. 7 (left). The equation of fitting for the temperature dependent wavelength shift (in nm) is: −1.29 + 0.0434*T + 6.94x10−5*T2, with a very good correlation factor of R2 = 0.99996. The wavelength shift of interference patterns for a temperature variation of 500°C for the best linear fit is found to be Δλ/ΔΤ = 78 pm/K. This is similar to the result shown in , however applicable for much shorter PCF length (~0.5% of the length), and the value found is little less than the estimated result of 94 pm/K. The device has less temperature sensitivity when compare with liquid filled interferometers [14,15], but has the advantage of be easier to manufacture, a temperature range of operation bigger, and probably has more robustness.
This sensor device could be also arranged for a reflection measurement in a simple way. To this end a thin film of gold is deposited at the end of standard fiber (SMF28). The film has a thickness of about 100 nm. When compared with the signal of the Fresnel reflection only at the end fiber of about 4% in the silica-air interface, the signal is increased by 13 dB.
The modified experimental setup of the device operating in reflection is shown in Fig. 8, where ASE (HP83438A) is a broadband source light, OSA is the Optical Spectrum Analyzer, and FOC is the Fiber Optical Circulator. The spectrum in reflection maintains the same interference pattern, only the value of fringe contrast increases (>40 dB) when compared with the signal in transmission (Fig. 6). A thermal cycle was repeated for this configuration and the results are shown in Fig. 7 (right). The measured sensitivity curve can be described with the following fit parameters −1.29 + 0.0451*T + 6.39*10−5*T2 and with a correlation factor of R2 = 0.99991. As expected, the wavelength shift of 78 pm/°C of the interference pattern with temperature variation for the best linear fit is equal to the value measured in transmission. We believe that such a sensor would be especially interesting in the reflection arrangement for local high temperature measurements, due to its small length in combination with its high temperature sensitivity.
We described in this paper the mode interference in a PCF fiber interferometer for a fiber with high Ge-core concentration and a structured cladding. An explanation about the density of states in the cladding of that fiber was explored, and the modes which can propagate and which may interfere with the core mode were calculated.
The fabrication and characterization of a very short PCF interferometer temperature sensor based on such a highly doped core fiber has been demonstrated. The fabrication of the device is simple and requires only a few steps. A short PCF stub was spliced between standard mode fibers. It was demonstrated that the device can operate in reflection and transmission without changing the thermal sensitivity. A high thermal sensitivity was measured due to the use of highly Ge doped silica (>78pm/°C). A great free spectral range was achieved even with a relatively short length with a specially shaped core structure. A high fringe contrast was measured of > 27dB in transmission and > 40 dB in reflection. We believe that the device demonstrated could have a great potential for application, since the device is very short and operates in transmission and reflection.
Funding by the Thuringian Ministry of Education, Science and Culture and the European EFRE program is gratefully acknowledged.
References and links
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