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We report on sensing and transmission characteristics of rocking filters fabricated in a silica side-hole fiber with group birefringence changing its sign at certain wavelength (λG = 0), which corresponds to parabolic-like spectral dependence of beat length. Unusual birefringence dispersion of the side-hole fiber is induced by an elliptical germanium doped core located in a narrow glass bridge between two holes. Rocking filters fabricated in such a fiber have two resonances of the same order located on both sides of λG = 0. The sensitivity of both resonances has an opposite sign, which makes it possible to double the response of the rocking filter by applying the differential interrogation scheme. We demonstrate that in this way a pressure sensitivity of the rocking filter can be enlarged to 132 nm/MPa. We also show that by fabricating the rocking filter with a period close to maximum beat length a coupling between polarization modes can be obtained in a broad band reaching 240 nm.
©2013 Optical Society of America
1. Introduction
Conventional side-hole fibers are well known for their pressure [1–3], temperature [3] and strain [4] sensing capabilities. Especially a polarimetric sensitivity to pressure of the side-hole fibers is very high because of air-holes located in the cladding on both sides of the core. The holes break mechanical symmetry of the fiber and transfer symmetrical load induced by hydrostatic pressure applied to the fiber cladding into nonsymmetrical stress distribution in the core region, which results in the high change of modal birefringence. A similar concept has been recently applied to increase the pressure sensitivity of birefringent photonic crystal fibers [5]. In this case, a pair of side-holes is replaced by an arrangement of holes with large filing factor in the microstructured cladding. Also a combination of the two approaches was theoretically investigated and showed a very high polarimetric sensitivity to pressure of about 100 rad × MPa−1m−1 at λ = 1.55 μm [6].
It has been already demonstrated that fabrication of a Bragg grating or long-period grating (LPG) in highly sensitive side-hole fibers or microstructured fibers facilitates interrogation of birefringence changes and opens new application opportunities, including measurements of pressure, temperature and strain [7] or refractive index changes in gases and liquids [8]. Also rocking filters (RFs), which resonantly couple orthogonally polarized fundamental modes, can be used for interrogation of subtle changes in fiber birefringence, which are transferred into displacement of the resonance wavelength [9,10]. Using this interrogation concept, the record high sensitivity to pressure, exceeding −177 nm/MPa, for the rocking filter fabricated in a specially designed microstructured fiber was reported in [11]. This number is about 100 times greater than the pressure sensitivity of Bragg gratings fabricated in the same fiber [12].
In this paper we demonstrate that the side-hole fiber can be used not only to enhance the polarimetric sensitivity to pressure but also to engineer the chromatic dispersion of modal birefringence. The second feature was achieved by fabricating the fiber with a narrow glass bridge between the holes, which contains a germanium doped elliptical core. In such a fiber, for a short wavelength range, the modal birefringence is induced entirely by the elliptical core. For longer wavelength, the modal field penetrates deeper into the glass bridge and starts to interact with its boundaries, which gives rise to a birefringence increase against wavelength. As a result, the group modal birefringence starts to decrease drastically against wavelength and crosses zero value at λG = 0. A fiber with zero group birefringence at certain wavelength and high phase modal birefringence was already reported in [13]. In this case, a slightly elliptical core was surrounded by a microstructured cladding with no hexagonal symmetry.
In addition to unusual dispersion of modal birefringence, the proposed side hole fiber has very high polarimetric sensitivity to pressure. For a rocking filter fabricated in the fiber with zero group birefringence, two resonances of the same order located on both sides of λG = 0 can be observed. The two resonances have opposite sensitivity to pressure, which allows to double the grating sensitivity by applying a differential interrogation scheme. Moreover, we show that by fabricating the rocking filter with a period close to the maximum value of the beat length, it is possible to obtain a very broad coupling between the polarization modes.
2. Side-hole fiber with zero group birefringence
A SEM image of a cross section of the side-hole fabricated by the Laboratory of Optical Fiber Technology, Maria Curie-Sklodowska University, Lublin, Poland is shown in Fig. 1. The fiber has a highly elliptical core (ex/ey = 4.8) doped with 21 mole% of GeO2. The core is placed in a narrow glass bridge, which separates two large holes assuring high sensitivity to hydrostatic pressure. The thickness of the glass bridge has a fundamental impact on birefringence dispersion. In the proposed fiber, the layer of pure silica glass between the core and the holes’ boundaries is only 1.7 μm thick on average. It causes that in the long wavelength range the evanescent field of the fundamental mode reaches the boundary between the glass bridge and the air holes, which causes a significant increase in the modal birefringence against wavelength. For shorter wavelengths, the modal field is better confined in the core and does not interact with the holes’ boundaries. As a result, for a short wavelength range the modal birefringence is entirely shaped by the elliptical core, which results in reduced dispersion of the phase birefringence. As the phase and the group modal birefringence are related by the following equation:
the increased anomalous dispersion of B in the long wavelength range results in the decrease in the group modal birefringence, which crosses the zero value at λG = 0 = 1.17 μm. Moreover, it can be showed that the fiber beat length given by the following formula:reaches the maximum value at λG = 0 because according to the following relation:only for G(λ) = 0 the condition dLB/dλ = 0 is satisfied.
Fig. 1 SEM image of the side-hole fiber with zero group birefringence (a) and its geometrical parameters (b,c).
In Fig. 2 we show the wavelength dependence of the phase and group modal birefringence measured respectively using the lateral force method [14] and spectral interferometry method [15]. The two parameters have been modeled using the finite element method for the fiber geometry reproduced from the SEM image and show a good agreement with the experimental data. We also measured the polarimetric sensitivity to pressure and temperature in this fiber (Fig. 3), but because of the presence of the higher order mode ( μm) these measurements were limited to the spectral range of 1.0 ÷ 1.7 μm. The sensitivity to temperature has a negative sign, which indicates a decrease in modal birefringence against temperature caused by the release of thermal stress in the core region. A sign of the pressure sensitivity is also negative, which is again connected to the fact that pressure-induced material birefringence in the core region has an opposite sign than the geometrical birefringence related to core ellipticity. The sensitivity to temperature shows almost a linear dependence against the wavelength, while the sensitivity to pressure follows 1/λ dependence in the considered spectral range. The sensitivity to pressure is very high and reaches Kp = −76 rad × MPa−1m−1 at λ = 1.55 μm. The sensitivity to temperature is related to high GeO2 concentration in the core and equals KT = −0.73 rad × K−1m−1 at λ = 1.55 μm. The values of both sensitivities are typical of side-hole fibers [1–3].
Fig. 2 Wavelength dependence of phase and group modal birefringence (a), and beat length (b) measured for the investigated side-hole fiber. Comparison of calculated effective indices for LP01 and LP11 polarization modes with the refractive index of pure silica glass allowing to estimate the cut-off wavelength of the LP11 modes ( μm) (c).
Fig. 3 Wavelength dependence of temperature (a) and pressure (b) sensitivities measured for the investigated side-hole fiber. Dots indicate measurement results.
In Fig. 4(a), we show the results of the measurement of group modal birefringence in the range of 0.9-1.6 μm conducted for different pressure applied to the fiber. Stress birefringence induced by the applied pressure in the core region has an opposite sign compared to the initial fiber birefringence related to the core ellipticity, which results in the linear decrease in G against pressure with a coefficient dG/dp = −2.0 × 10−5 MPa−1 almost independent upon wavelength. We also observed a pressure induced shift of the λG = 0 towards shorter wavelength with a coefficient equal to dλG = 0/dp = −10.9 nm/MPa, Fig. 4(b). The linear dependence of λG = 0 upon the applied pressure confirms a nondispersive character of the pressure-induced birefringence.
Fig. 4 Measured variation of the group modal birefringence (a) and the corresponding shift of λG = 0 (b) induced by pressure changes. Blue arrows indicate the direction of changes in group birefringence for increasing pressure.
3. Rocking filters fabrication and characterization
The rocking filters reported in this paper were fabricated using CO2 based system described in details in [11]. The beam from the CO2 laser was focused by the cylindrical lenses and illuminated the side-hole fiber symmetrically from two sides to prevent fiber bending. Before making a coupling point, the fiber was initially twisted by a constant angle. The initial twist induced a shear stress, which was partially released when the fiber was locally softened by CO2 beams. By properly adjusting the twist angle, the CO2 beam power and the exposition time, we are able to fabricate in a repeatable way a sequence of coupling points in the form of built-in twists without destroying the fiber structure. The phase matching condition for the higher order rocking filters can be expressed as follows:
where LB is the beat length, ΛRF is the filter period and k is the resonance order. In the investigated side-hole fiber, the beat length is a parabolic-like function of wavelength, which provides a unique opportunity to fabricate the rocking filters with the same resonance order on both sides of λG = 0. It was already shown in [11] that the sensitivity to the external parameter understood as the displacement of the resonance wavelength in response to the measurand change can be expressed as follows:As the group modal birefringence changes its sign at λG = 0, the sensitivity of both resonances of the same order arising on both sides of λG = 0 has an opposite sign. It opens the way to increase the sensitivity of the rocking filter fabricated in the proposed side-hole fiber by applying the differential interrogation scheme. To experimentally study this concept, we fabricated the rocking filter (RF1) consisting of 25 segments twisted by about 3.6°. The grating period ΛRF1 = 1.9 mm is slightly lower than the maximum beat length equal to LBmax = 2.044 mm. In Fig. 5 we present the measured and the calculated transmission spectra of the rocking filter with clearly visible first order resonances located at λL = 1.018 μm and λR = 1.327 μm. The left resonance is not as deep as the right one, because of the presence of the first order mode not coupled to the orthogonal polarization.Fig. 5 Measured (a) and calculated (b) transmission characteristics of the first rocking filter (RF1) with period ΛRF1 = 1.9 mm showing two resonances of the first order located on both sides of λG = 0. Dip appearing in the transmission characteristic of the excited mode at 0.9 μm, is the side oscillation of the resonance located at λL = 1.018 μm amplified by noise.
The black curves represent transmission of the excited mode measured for parallel orientation of the polarizer and the analyzer placed respectively at the fiber input and output. The red curve shows the cross coupling between the polarization modes and is measured for the polarizer and the analyzer crossed. In Fig. 5(b) we present the calculated transmission characteristics for the rocking filter with the same geometrical parameters as the fabricated one. For the numerical simulations we used Jones matrix formalism and the birefringence dispersion curve shown in Fig. 2(a). The measured and the calculated transmission characteristics are in a good agreement, which proves that the lengths of the successive segments of the filter and the twist angles are controlled with sufficient precision in the fabrication process.
To measure the sensitivity to pressure, a rocking filter was installed in a specially designed pressure chamber filled with oil and subjected to pressure cycles in the range from 0.1 (atmospheric pressure) to 10 MPa at stabilized temperature. The transmission characteristics of the filter were registered for increasing and decreasing pressure using OSA, Fig. 6(a). As it is shown in Fig. 6(b) the left resonance moved out of the OSA range already at 7 MPa. The response of the right resonance to pressure is slightly nonlinear, therefore, we estimated the differential sensitivity only for the low pressure range (up to 3 MPa), d(λR-λL)/dp0.1-3 = 99 nm/MPa. This value is very high in comparison to the sensitivity of the rocking filter fabricated in a D-shaped fiber, which is only 0.5 nm/MPa for the resonance at 640 nm [12]. Similarly, high sensitivity was reported earlier for the rocking filters fabricated in specially designed photonic crystal fibers with the extreme polarimetric sensitivity to pressure [11].
Fig. 6 Displacement of the transmission characteristics (a) and the resonance wavelengths (b) of the rocking filter RF1 induced by pressure changes. Differential response of the rocking filter RF1 to pressure (c).
The rocking filter was then subjected to temperature changes in the range of 20 ÷ 220 C. The results of measurements presented in Fig. 7(b) show small nonlinearity in the response of the right resonance. The differential sensitivity determined for a low temperature range is equal to d(λR-λL)/dT22-100 = 1.70 nm/K, which is close to the sensitivity of the LPG presented in [16].
Fig. 7 Displacement of the transmission characteristics (a) and the resonance wavelengths (b) of the rocking filter RF1 induced by temperature changes. Differential response of the rocking filter RF1 to temperature (c).
Some nonlinearity of the response to pressure and temperature observed for the right resonance is related to the spectral dependence of KX and G. For longer wavelengths KT and Kp are lower, while G is higher than near λG = 0. According to Eq. (5), it causes that when the right resonance shifts over a wide spectral range, the slope of the pressure and of the temperature sensitivities gradually decreases. Dispersion of KX and G is also responsible for greater sensitivity of the left resonance.
To experimentally study the rocking filter transmission and cross-coupling characteristics for the periods close to the maximum beat length, we exploited the effect of beat length dependence upon pressure. The second fabricated grating RF2 has the period ΛRF2 = 2.2 mm, which is slightly greater than the maximum beat length of the side-hole fiber, Fig. 2(b). For such a long period of the rocking filter, the resonances of the first order do not exist at atmospheric pressure, while the higher order resonances are located outside of the operation range of our optical spectrum analyzer (0.6 ÷ 1.7 μm). As the Kp in the investigated fiber is high and negative, increasing pressure results in an increase in the beat length according to the following relation:
We assume in the above equation that the sensitivity of modal birefringence to pressure given by:is completely nondispersive. This assumption is justified owing to the fact that the principal contribution to the fiber sensitivity to pressure is related to asymmetric stress distribution in the core region. The dependence of the beat length upon pressure calculated from Eq. (6) is shown in Fig. 8. We first investigated the evolution of the transmission and the cross-coupling spectrum for the RF2 in the pressure range of 0.1 ÷ 4 MPa, (Fig. 9).Fig. 9 Evolution of the transmission characteristics for excited (a,b) and unexcited mode (c,d) of the rocking filter RF2 in the range of pressures 1.5 ÷ 4 MPa. Calculated characteristics are shown in (b,d).
The flat dependence of the beat length upon the wavelength near the maximum causes that for LB(p) approaching ΛRF2 the resonance is very broad. As it is shown in Fig. 9, for the RF2 the resonance appears at 1.5 MPa, reaches the maximum width (FWHM) of 240 nm at 3 MPa and splits into two resonances at higher pressure. A similar behavior of the transmission and the cross-coupling characteristics was obtained in the numerical simulations, in which we used experimental data for B(λ) and the dependence of LB upon pressure given by Eq. (6), Fig. 8. For pressure greater than 3.5 MPa there are clearly distinguishable two resonance peaks in the transmission characteristics. Therefore in the range 3.5 ÷ 10 MPa we were able to measure the sensitivity for the rocking filter RF2, Fig. 10. In the linear part of the characteristics (3.5 ÷ 6 MPa) the sensitivity for the left resonance is dλL/dp = −74 nm/MPa, whereas for the right one it equals dλR/dp = 58 nm/MPa. The differential sensitivity of the RF2 is extremely high and reaches d(λR−λL)/dp = 132 nm/MPa in the pressure range (3.5 ÷ 6 MPa) and drops to 95 nm/MPa at 10 MPa.
Fig. 10 Displacement of the transmission characteristics (a) and the resonance wavelengths (b) of the RF2 induced by pressure changes. Differential response of the rocking filter RF2 to pressure (c).
4. Conclusions
We demonstrated a new type of the side hole fiber, in which the group modal birefringence changes its sign at certain wavelength, while the phase modal birefringence is high and positive in the whole spectral range. This feature was obtained by placing the GeO2 doped elliptical core in the center of a narrow glass bridge separating the large holes in the cladding. In such a fiber, the modal field starts to interact with the boundaries of the glass bridge for longer wavelengths, which results in an increase in the phase modal birefringence and pushes the group modal birefringence into negative values. In addition, the proposed fiber has a very high polarimetric sensitivity to hydrostatic pressure reaching Kp = −76 rad × MPa−1m−1 at λ = 1.55 μm. We also studied the transmission and sensing characteristics of the rocking filter fabricated in the developed side-hole fiber. In particular, we demonstrated that the sensitivity of the rocking filter can be doubled by applying differential interrogation of two resonances of the same order located on both sides of λG = 0. This was possible thanks to different signs of the sensitivity of the two resonances related to unusual group birefringence dispersion of the developed side-hole fiber and allowed to achieve an extremely high differential response of the rocking filter to pressure reaching 132 nm/MPa. High sensitivity to hydrostatic pressure −177 nm/MPa was earlier reported for a multiple order rocking filter fabricated in the microstructured fiber [11], but in this case the concept of differential interrogation could not have been applied due to the same sign of the sensitivity for all the resonances.
Finally, we demonstrated that by tuning the maximum beat length close to the period of the rocking filter, it was possible to obtain a very broad coupling between the polarization modes with the FWHM of 240 nm. This effect could be potentially exploited for building a pressure-tunable polarization band-rejection filter.
Acknowledgments
The work presented in this paper was carried out with the support of the National Science Center under the grant no. NN 505 560 439. A. Anuszkiewicz and W. Urbanczyk acknowledge the support of the FNP Program “MISTRZ”.
References and links
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