We report on the sensing characteristics of rocking filters fabricated in two microstructured fibers with enhanced polarimetric sensitivity to hydrostatic pressure. The filter fabricated in the first fiber shows a very high sensitivity to pressure ranging from 16.2 to 43.4 nm/MPa, depending on the resonance order and features an extremely low cross-sensitivity between pressure and temperature 28 ÷ 89 × 103 K/MPa. The filter fabricated in the second fiber has an extreme sensitivity to pressure ranging from −72.6 to −177 nm/MPa, but a less favorable cross-sensitivity between pressure and temperature of 1.05 ÷ 3.50 × 103 K/MPa. These characteristics allow using the rocking filters for pressure measurements with mbar resolution.
© 2012 OSA
Hydrostatic pressure measurements using optical fibers have attracted a lot of interest for many years. Several sensing concepts have already been developed and tested, including temperature compensated polarimetric sensors based on conventional birefringent fibers for static  and dynamic pressure measurements , Bragg gratings in conventional  and in side-hole fibers for simultaneous measurements of pressure and temperature  and a wide range of membrane based interferometric pressure sensors . The latest development of a new class of microstructured fibers has opened new possibilities for fiber based pressure sensing. These new opportunities stem from the freedom to engineer the sensing and the transmission properties of microstructured fibers. More particularly, birefringent microstructured fibers with very high polarimetric sensitivity to pressure and low sensitivity to temperature have already been successfully fabricated . These fibers possess a germanium doped core to allow for Bragg grating fabrication and for differential interrogation of the two Bragg peaks related to the two polarization modes. As the differential sensitivity of the Bragg grating is directly proportional to the polarimetric sensitivity of the fiber KX:7], by fabricating a Bragg grating in microstructured fibers with Kp exceeding 120 rad/MPa × m at 1.55 μm, it is possible to obtain a differential sensitivity of the grating of about 33 pm/MPa, which allows for hydrostatic pressure measurements with a resolution of a fraction of a bar.
In this paper we demonstrate that with rocking filters fabricated in similar microstructured fibers we can significantly increase the sensitivity of hydrostatic pressure measurements. The first rocking filters in conventional birefringent fibers were manufactured by using periodic twisting  and point-by point UV inscription technique . A rocking filter fabricated in a microstructured fiber by periodic mechanical twisting and heating with a scanned CO2 laser beam was first demonstrated in . Moreover, we have already shown in  that the displacement of the resonance wavelength in the rocking filter is related to the polarimetric sensitivity of the fiber by the following expression:
The concept of using rocking filters elliptical core and side-hole fibers for hydrostatic pressure measurements was studied earlier in  and , respectively. The sensitivity to pressure reported for the filter in the elliptical core fiber was only 0.5 nm/MPa. The sensitivity of the rocking filer in the side-hole fiber was about 100 nm/MPa at 720 nm. However, due to the small birefringence of this fiber, the filter length was about 1 m, which made it unpractical for actual applications. Moreover the low birefringence deteriorated the resonance depth and limited the measurement resolution.
The rocking filters described in this paper feature several advantages compared to those already reported in literature. These include an extremely low cross-sensitivity between pressure and temperature exceeding 104 K/MPa, a reasonable length of only a few centimeters, and a high quality of the resonances, which allows determining the resonance wavelength with 10 pm resolution. These advantages, combined with the sensitivity exceeding 100 nm/MPa, make our filters excellent sensors for temperature insensitive high resolution pressure measurements.
2. Microstructured fiber used for rocking filter fabrication
The cross-sections of the birefringent microstructured fibers used for fabricating our rocking filters are shown in Figs. 1 -2 . The fibers were manufactured using a conventional stack and draw technology. Appropriately balanced pressures applied to respective sections of the microstructured cladding during the drawing process allowed to achieve significant differences in the holes’ diameters. The holes in the outer part of the microstructured cladding are distributed in such a way that the mechanical properties of both fibers are significantly different along their symmetry axes. Therefore and similarly to conventional side-hole fiber , the symmetrical load induced by hydrostatic pressure applied to the fiber cladding produces a nonsymmetrical stress distribution in the core region which results in a significant change of the birefringence. An 2.4 mol% GeO2 doped inclusion in the core region helps reducing the confinement and splice losses. In the first fiber shown in Fig. 1 the inclusion has an elliptical shape. The orientation of the ellipse induces a birefringence that counteracts that induced by the cladding microstructure. Since both birefringences have an opposite sign they compensate each other in the short wavelength range. Moreover, as shown in Figs. 3 -4 , the polarimetric sensitivity to temperature of this fiber (measured without coating) is very low and equals KT = 0.007 rad/K × m at λ = 1.55 μm, while the phase and group modal birefringence at this wavelength are equal to B = 0.17 × 10−3 and G = −0.39 × 10−3, respectively. As shown in Fig. 4(b), the polarimetric sensitivity to hydrostatic pressure Kp decreases against wavelength according to the term 1/λ because dB/dp is almost non-dispersive. Kp reaches −29.9 rad/MPa × m at λ = 1.55 μm, while Kp/KT = 4300 K/MPa at this wavelength. The negative sign of the pressure sensitivity indicates that the stress birefringence induced in the core region by an applied pressure has an opposite sign with respect to the initial fiber birefringence.
Finite element simulations evidence that the major contribution to the birefringence in the first fiber stems from the asymmetry of the holes surrounding the core. This is confirmed bythe elliptical shape of the mode field distribution whose longer axis is oriented vertically, parallel to the row of small cladding holes. In order to obtain a positive sign of the phase modal birefringence, which is defined as the difference between the effective indices of the x- and y-polarized modes, we have chosen the x-axis along the vertical orientation as shown in Fig. 1(a).
The second fiber shown in Fig. 2 has larger cladding holes and as a result its core is suspended with four glass bridges. The vertical bridges have a wedge shape which concentrates the pressure-induced stress in the core region. This stress yields an extremely high polarimetric sensitivity to pressure, reaching the record high value of 109.5 rad/MPa × m at λ = 1.55 μm. Similarly as for the first fiber, to obtain a positive sign of the modal birefringence, we assumed that the x-axis of the coordinate system is oriented horizontally, i.e., parallel to the longer axis of the elliptical core. As in this fiber the predominant component of the pressure-induced stress is oriented along the short axis of the elliptical core, an increasing pressure enlarges the modal birefringence, which results in a positive sign of Kp. Finally and if we disregard the narrow vertical wings caused by GeO2 diffusion, the shape of the germanium inclusion is almost the same as that of the fiber core. Therefore the birefringence induced by the microstructure and the inclusion are additive in this fiber, which leads to a much higher temperature sensitivity reaching KT = 0.069 rad/K × m at λ = 1.55 μm, Fig. 4.
3. Rocking filter fabrication and characterization
The rocking filters studied in this paper were fabricated using a CO2 laser based system shown in Fig. 5 . The beam from a 30 W CO2 laser was focused by cylindrical lenses and illuminated the microstructured fiber symmetrically from two sides to prevent fiber bending. Every time before making a coupling point, the fiber was twisted with a constant angle. The twist induced a shear stress, which was partially released when the fiber was locally softened by the CO2 beam. By properly adjusting the twist angle, the CO2 beam power and the exposure time, we were able to fabricate – in a repeatable way – a sequence of coupling points in the form of built-in twists without destroying the cladding microstructure. The modal birefringence increases against wavelength in both photonic crystal fibers, which provides a unique opportunity to fabricate the rocking filters with several resonances within a useful wavelength range. For the higher order resonances, the phase matching condition in the rocking filter can be expressed as:Fig. 6(a) , we show the transmission characteristics of the rocking filter fabricated in the first fiber. This filter was composed of 6 segments of length Λ = 27 mm, twisted with respect to each other by about 16 arc degrees. Total length of the filter was 16.2 cm., while the leadings length was about 3 m. One should note that the length of the filter with the first order resonance at Λ = 1.5 μm would be only 5 cm.
The transmission measurements were carried out for the polarizer and analyzer aligned parallel to the same polarization axes and revealed five resonances in the useful spectral range. As the phase modal birefringence changes its sign in the short wavelength range, the resonance of the minus first order was observed at λ = 0.649 μm. The filter fabricated in the second fiber was composed of 5 segments of length Λ = 8 mm, which results in a total length of only 4 cm. The transmission characteristic of this filter shows three resonances with slightly lager FWHM than in the first filter, Fig. 6(b).
The rocking filters were then subjected to pressure changes in the range of 0.1 ÷ 10 MPa (0.1 MPa corresponds to atmospheric pressure). In Fig. 7 we show the shift of the third order resonances observed in response to increasing pressure. According to Eq. (2), in the first filter the pressure-induced resonance shift is clearly towards longer wavelengths, which corresponds to a positive sign of dλ/dp. The pressure-induced displacement of the resonances in the second filter is towards shorter wavelengths, which corresponds to a negative sign of dλ/dp. For both filters the resonance depth and the FWHM of the resonance peaks remain almost unchanged at increased pressure.
In Fig. 8(a) we show the pressure-induced shift of all the resonance wavelengths in the first filter. The substantial nonlinearity of the response observed for low order resonances is related to the greater sensitivity of the rocking filter in the short wavelength range. According to Eq. (2) the sensitivity of the rocking filter is expressed by the ratio of Kp over G, which are both negative and highly dispersive. For longer wavelengths Kp is lower while G is larger and therefore, when the resonance peak shifts towards longer wavelengths, the slope of the pressure characteristics gradually decreases. The same effect is responsible for the decrease of the pressure sensitivity against the resonance order.
In Table 1 we gathered the sensing parameters of both rocking filters determined for all the resonances. As the response to pressure is nonlinear, the sensitivity coefficients dλ/dp were calculated for low and high pressure ranges. The pressure sensitivity of the filter fabricated in the first fiber is very high and ranges from 16.2 to 43.4 nm/MPa, depending on the resonance order.
We also investigated the temperature characteristics of both filters in the temperature range of 20 ÷ 150 °C. As the polymer coating can significantly modify the temperature characteristics of the birefringent fibers  these measurements were conducted for bare filters. For both filters, we observed a gradually decreasing hysteresis in the first three temperature cycles, which disappeared in the following cycles. This effect is most probably related to a partial release of the stress induced birefringence and it caused a permanent shift of the resonance peaks by a few nanometers observed after the first temperature cycles. In Fig. 8(b-c) we present the temperature characteristics of the bare rocking filter fabricated in the first fiber measured after the first three cycles. These results clearly show that the temperature sensitivity coefficient of the rocking filter fabricated in the first fiber is very low for all the resonances and changes sign between the first and the second resonance. This is related to the orientation of the elliptical inclusion with respect to the cladding microstructure, which results in complete compensation of the fiber response to temperature at about 1.3 μm. In Table 1 we also summarize the temperature-pressure cross sensitivity coefficients, which ranges from89 × 103 K/MPa to 28 × 103 K/MPa, depending on the resonance order. This is an extremely high value making the rocking filter fabricated in the first fiber an excellent device for high resolution pressure measurements with no need for temperature compensation.
The sensing characteristics of the rocking filter in the second fiber are shown in Figs. 9 -10 . In this case the resonances move toward shorter wavelengths with increasing pressure and therefore the measurement range for low order resonances is limited by the short wavelength operation limit of our optical spectrum analyzer (0.6 μm). The pressure sensitivity of this filter is larger than that of the filter in the first fiber and increases against pressure. This is in accordance with Eq. (2): the fiber polarimetric sensitivity to pressure Kp increases, while the group modal birefringence G decreases at shorter wavelengths. In the low pressure range, the sensitivity coefficients dλ/dp for this filter range from −72.6 to −97.3 nm/MPa, depending on the resonance order, while at high pressure the sensitivities increase significantly to −110 ÷ −177 nm/MPa. As shown in Fig. 10, a record high sensitivity was observed for the fourth order resonance located at about 2.6 μm at atmospheric pressure. This resonance moves in the useful spectral range at a pressure between 7.4 and 10 MPa and its sensitivity in this pressure range is −178 nm/MPa.
The temperature characteristic for the third order resonance of this filter is shown in Fig. 9(b-c). The additive effect owing to the orientation of the elliptical inclusion with respect to the microstructured cladding yields a relatively high filter sensitivity to temperature dλ/dT ranging from −28.0 to −79 pm/K. These values are almost two orders of magnitude greater than the sensitivity of the first filter and consequently the cross-sensitivity to temperature drops to 1.05 ÷ 3.50 × 103 K/MPa, depending on the resonance order.
We have demonstrated the successful fabrication of higher order rocking filters in two specially designed birefringent fibers with a complex microstructure that yields high polarimetric sensitivity to hydrostatic pressure. The response of the rocking filters to pressure and temperature was measured at different resonances. Our studies reveal that the rocking filter fabricated in the first fiber has a high positive sensitivity to pressure, ranging from 16.2 up to 43.4 nm/MPa at low pressures, and an extremely low sensitivity to temperature of the order of a fraction of pm/K. As shown in Fig. 8(b-c), the rms deviation of the measurement points from the trend line is of the order of 10 pm. This figure can be considered as the resolution with which the position of the resonance wavelength can be determined. Taking into account the measured dλ/dp coefficients, one can estimate the pressure measurement resolution at 3 to 6 mbar, depending on the resonance order. Owing to the extremely low cross-sensitivity to temperature, ranging from 89 × 103 K/MPa to 28 × 103 K/MPa, the filter fabricated in the first fiber can be used for high resolution pressure measurements with no need for temperature compensation.
The pressure sensitivity of the filter fabricated in the second fiber has a negative sign and reaches record high values of −72.6 ÷ −97.3 nm/MPa, depending on the resonance order. An extremely high sensitivity of −178 nm/MPa in the pressure range from 7.4 to 10 MPa was demonstrated for the fourth order resonance at about 2.6 μm at atmospheric pressure. The cross-sensitivity to temperature in this filter is in the range 1.05 ÷ 3.50 × 103 K/MPa and therefore it is better suited for high resolution pressure measurements in less demanding temperature conditions. We expect that the cross-sensitivity to temperature of this filter can be significantly reduced by using a fiber with similar geometry but without germanium doped inclusion.
The work presented in this paper was carried out with support of the Polish Ministry of Science and Education under the grant no. NN 505 560 439 and of the PHOSFOS project funded by the 7th Framework Programme of the European Commission. A. Anuszkiewicz, G. Statkiewicz-Barabach, J. Olszewski and W. Urbanczyk acknowledge the support of the FNP Program “MISTRZ”. A. Anuszkiewicz acknowledges the support of the European Union’s European Social Fund. T. Geernaert is supported by the Research Foundation Flanders (FWO-Vlaanderen). The authors would also like to acknowledge financial support from the Institute for the Promotion of Innovation through Science and Technology, Flanders (IWT-Vlaanderen), the Interuniversity Attraction Poles (IAP) – Belgian Science Policy and the Methusalem and Hercules Foundations Flanders. We also acknowledge the COST TD1001 action.
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