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We demonstrate that higher order rocking filters coupling energy between polarization modes at several wavelengths can be fabricated in a birefringent photonic crystal fiber using a fusion arc splicer. Three resonant couplings were identified, respectively at 855, 1271, and 1623 nm for the filter with a pitch distance of 8 mm characterized in this work. We also measured the filter response to temperature, elongation and hydrostatic pressure at the first and the second resonance. Our results show that the fabricated filter has very low sensitivity to temperature 1.77 and 1.38 pm/K, moderate sensitivity to elongation 1.35 and 1.12 nm/mstrain, and extremely high sensitivity to hydrostatic pressure 6.14 and 3.30 nm/MPa, respectively at the first and the second resonance.
©2008 Optical Society of America
1. Introduction
Photonic crystal fibers (PCFs) offer unprecedented flexibility in shaping their propagation and sensing characteristics [1-3], which opens new metrological opportunities [4,5]. Among others, the appearance of PCFs stimulated an increasing interest towards fabrication and applications of long period gratings (LPGs) in this new class of fibers. It is already well known that LPGs can be made in PCFs using CO2 laser [6,7], electric arc of a fusion splicer [8,9] or periodic lateral stress [10-12]. With one of these techniques, periodic variations of structural parameters of the PCF are formed, giving rise to resonant coupling of the guided fundamental mode to higher order modes or cladding modes. Applications of LPGs in PCFs to temperature, elongation, and hydrostatic pressure measurements have also been investigated [13-17]. A change in the value of external parameter acting on such grating shifts the resonant wavelength. Therefore, information about the measurand variation can be conveniently retrieved by detecting the position of the resonant peak in the transmission characteristics of the LPG.
It is also known from recent publications [18-20] that LPGs, named rocking filters, can be fabricated in birefringent microstructured fibers. Such gratings couple fundamental modes of orthogonal polarization guided in the core of the birefringent PCFs. The coupling effect has a resonant character and arises at wavelength satisfying the phase matching condition. The rocking filter described in [18] consisted of 25 periodic twists by about 3° made using CO2 laser, which assured an efficient coupling between the polarization modes at 1.5 µm. To our knowledge, however, the sensing characteristics of the rocking filters in HB PCFs have not been studied yet.
In this paper, we demonstrate that the rocking filter can also be fabricated using an arc fusion splicer. Moreover, we show that because of a strong increase of birefringence against wavelength in the PCFs, several resonant couplings can be obtained in the useful spectral range from 0.6 to 1.6 µm for the filters of moderate period. The sensitivity measurements carried out for the first two resonant wavelengths prove that such filters have very promising sensing characteristics.
2. Birefringent fiber used for fabrication of the rocking filter
For fabrication of the rocking filter, we have used a pure silica birefringent PCF produced by Department of Optical Fibre Technology, University of Marie-Curie Sklodowska (UMCS) in Lublin, Poland. The birefringence in this fiber is induced by the enlargement of two holes located symmetrically with respect to the core. Such fiber construction was proposed for the first time in [21]. The SEM image of the fiber cross sections with the indicated reference system is presented in Fig. 1. Its geometrical parameters averaged for first two layers of holes surrounding the core are as follows: pitch distance – 3.75 µm, diameter of cladding holes – 1.7 µm, diameter of large holes – 3.0 µm, and external diameter of the cladding – 127 µm. Direct measurements of the phase modal birefringence B=nx-ny carried out in this fiber using the lateral force method [22] show that this parameter increases against wavelength, which is a characteristic feature of HB PCFs. In consequence, the group modal birefringence
measured using the spectral interferometric method [3] has negative sign and strongly decreases against wavelength, see Fig. 2.
Because the PCFs used for fabrication of the rocking filter is made of silica glass with a uniform composition in the entire cross-section, it has no thermal stress induced by the difference in thermal expansion coefficients between the fiber structural elements. Additionally, as it is shown in [23], residual thermal stress associated to the air-hole microstructure has little impact on temperature properties of such fiber. In consequence, the so-called polarimetric sensitivity to temperature in this fiber:
where φx and φy are phase shifts for the two orthogonally polarized modes, L is fiber length, and α is thermal expansion coefficient, can be a few orders of magnitude lower than in conventional birefringent fibers [23,24].
Using the method described in [3,24], we have measured the spectral dependence of the polarimetric sensitivity to temperature, hydrostatic pressure and elongation in this fiber, Fig. 3. In these measurements, a 1-m long piece of the PCF was exposed to measurand changes. As it was already demonstrated in earlier publications [24], the coating may significantly disturb the fiber response to temperature, therefore the measurements of the temperature sensitivity were carried out for the bare fiber. Sensitivities to all measurands under study have negative sign, which means that increasing the value of measurand results in a decrease in the phase modal birefringence. The sensitivity to temperature shows parabolic like dependence upon wavelength in the analyzed spectral range and reaches minimum value equal to -0.0063 rad/K×m at λ=1.1 µm, which is in agreement with earlier results [23,24]. The sensitivity to hydrostatic pressure is related mostly to asymmetrical distribution of stress induced by applied pressure and equals KP=-18 rad/MPa×m at λ=0.8 µm. This is much greater value than sensitivity to pressure in conventional birefringent fibers ranging from KP=+1.5 rad/MPa×m [25] in the elliptical core fibers up to KP=+8.5 rad/MPa×m in Bow-Tie fibers [26]. The sensitivity to elongation is slightly dispersive, slowly decreases against wavelength from -2.2 at 0.8 µm to -2.0 rad/mstrain×m at 1.55 µm and is lower than sensitivity in conventional elliptical core fibers Kε=-5 rad/mstrain×m [25]. It is worth to mentioned that negative sign of KT, KP, and Kε in the birefringent PCF identified in our experiments is in agreement with earlier theoretical [23,27] and experimental [3,23,24] works.
Fig. 2. Spectral dependence of phase (a) and group (b) modal birefringence measured in the birefringent photonic crystal fiber used for fabrication of the rocking filter.
3. Fabrication of the rocking filter
For fabrication of the rocking filter, we used Ericsson fusion splicer combined with a system of linear and rotational stages allowing to periodically shift and rotate the fiber between electrodes. Every time before making a coupling point, the fiber was initially axially pretwisted by a constant angle of about 20°. The initial twist induced shear stress which was partially released when the fiber was locally softened at high temperature of electric arc. By properly adjusting an angle of fiber pretwist, arc current (~8 mA), and its duration (~0.4 s), we were able to fabricate in a repeatable way periodic coupling points in the form of built-in twist without destroying the cladding microstructure. In Fig. 4 we show a general schema of the fabrication system.
To control the quality of the filter during fabrication process, we excited one polarization mode in the fiber using a broadband Xe-lamp. The transmission azimuth of the analyzer at the fiber output was aligned in parallel to the polarization azimuth of the excited mode. In this way, we were able to register the transmission characteristic for the excited polarization mode after fabrication of each successive coupling point using ANDO AQ6317B optical spectrum analyzer.
The fabrication process was continued until obtaining a satisfactory resonance attenuation. Typically after making 10-15 twists, the resonance attenuation stabilized on the level of 13-25 dB, depending on the resonance order. For higher order resonances, we observed greater resonance attenuation.
Fig. 3. Spectral dependence of the polarimetric sensitivity to temperature (a), hydrostatic pressure (b) and elongation (c).
In Fig. 5, we show the transmission characteristics for the excited and non-excited polarization modes registered for the rocking filter consisting of 13 coupling points, which proves that the energy missing in one mode appears in the other mode of orthogonal polarization. The inset in Fig. 4 shows a microscope image of the coupling area obtained in transverse illumination. From this photograph, we can estimate that the value of the fiber twist at each coupling point is about 5°, while the length of the twisted area is about 30 µm. This photograph also proves that the air channels are not collapsed when the fiber is exposed to electric arc.
Fig. 5. Transmission spectra for the excited (a) and non excited (b) polarization modes measured for the rocking filter with a period Λ=8 mm and 13 coupling points.
For the higher order rocking filters, the phase matching condition can be expressed as:
or equivalently
where Λ is the filter period, LB is the beat length, and i is the resonance order. In Fig. 6, we show the spectral dependence of the beat length in the birefringent PCF used for filter fabrication. In photonic crystal fibers, this parameter decreases against wavelength, thus providing a unique opportunity to fabricate the rocking filters with several resonances within a relatively short wavelength range. In Fig. 6, we show the predicted positions of resonant wavelengths calculated according to Eq. (4) for the filter with a period Λ=8 mm, which are equal to 895, 1400 and 1620 nm, for the first, second, and third resonance, respectively. The estimated values are in relatively good agreement with the measured positions of resonances arising at 855, 1271 and 1623 nm, respectively. The discrepancies between estimated and measured values of resonant wavelengths can be attributed to birefringence variation over fiber length and birefringence changes induced by the fiber twist in the coupling points. The highest discrepancy reaching 10 % is observed for the second resonance wavelength, because in this spectral range the dependence LB(λ) has the lowest slope and therefore small variations in LB result in relatively high changes of resonant wavelength.
Fig. 6. Spectral dependence of the beat length in the fiber used for fabrication of the rocking filter with predicted location of resonances for a filter period Λ=8mm.
4. Sensing characteristics of the rocking filter
We have measured the sensitivity of the resonance wavelengths dλ/dX to temperature, elongation and hydrostatic pressure in the fabricated rocking filter. To achieve a better signal to noise ratio in the transmission characteristics, and in consequence better resolution in determining resonant wavelengths, we used as light sources broadband superluminescent diodes with higher spectral density than Xe-lamp. Because of lack of the diode matching the third resonance, the sensitivity measurements were carried out only for the first two resonances. To further increase the measurement resolution, we fitted the most symmetrical part of the dips in the transmission characteristic with a parabolic function. A location of the symmetry axis of this parabola determined the resonant wavelength with a resolution of about 2 pm. The results of measurement of the filter sensitivity dλ/dX to temperature, elongation, and hydrostatic pressure for the second resonance are shown in Figs. 7-9, while in Table 1 we present the sensitivity coefficients for both resonances as well as the polarimetric sensitivities of the fiber. The sensitivity measurements were carried out for the filter without polymer cover. As it is shown in Figs. 7-9, the response of the filter is linear in the investigated range of measurands changes, 10-100 °C for temperature, 0-1 mstrain for elongation, and 0.01-10 MPa for hydrostatic pressure, with no trace of hysteresis. The average deviation of experimental data from liner trend ranges from 4 pm in case of temperature up to 90 pm in case of hydrostatic pressure characteristics. It should be stress out that in the latter case, the oscillations around linear characteristic have systematic character and are repeatable. This is most probably related to residual changes of the coupling efficiency at successive twists induced by hydrostatic pressure and elongation.
The variation of resonant wavelength very much depends on the type of applied measurand. The sensitivity of the filter to temperature is very low and equals 1.77 and 1.38 pm/K, respectively for the first and the second resonance. These values are close to the sensitivity of the LPGs in endlessly single mode PCFs ranging from 2.0 pm/K up to 6.0 pm/K [8,9,15,17]. The sensitivity of the rocking filter to elongation equals 1.35 and 1.12 nm/mstrain, respectively for the first and the second resonance, and is slightly lower than the sensitivity of the LPGs in endlessly single mode PCFs, 2.04÷2.50 nm/mstrain [9, 15, 17]. Our measurements also show that the sensitivity of the rocking filter to hydrostatic pressure is extremely high and equals 6.14 and 3.30 nm/MPa, respectively for the first and the second resonance. These values are far greater than the sensitivity of the LPG in endlessly single mode PCF equal 0.1 nm/MPa [13] as well as the sensitivity of the rocking filter in conventional elliptical core fibers equal 0.5 nm/MPa [28]. Such sensitivity characteristics make the filter an excellent device for hydrostatic pressure measurements with no need for temperature compensation.
The physical phenomena behind the change of resonance wavelength are related to the variation of phase modal birefringence dB/dX and the filter period dΛ/dX induced by measurand change acting on the fiber. According to Eq. (3), these two effects shift the resonance condition to another wavelength, which can be quantitatively represented by the following relation:
After performing rather straightforward calculations, one can express the terms appearing in the above equation in the following way:
and
Finally, the formula for sensitivity of the rocking filter to measurand X can be represented as:
or more conveniently with relation to the polarimetric sensitivity of the fiber:
The above relations are in agreement with equivalent expressions for sensitivity of the LPGs derived in [29,30]. Equation (9) shows that the filter response to specific measurand dλ/dX can be expressed as a product of the polarimetric sensitivity of the fiber KX and the dispersive proportionality coefficient λ2/2πG(λ). Spectral dependence of the group modal birefringence G(λ) is related to the fiber geometry. It is well known that in fibers with birefringence induced by two large holes, the group modal birefringence can be approximated with the power function G(λ)=a λα [31]. By fitting the experimental results from Fig. 4, we found a=1.44×1012 m-2.62, α=2.62. It means that in the investigated filter, the dispersive multiplicative coefficient between dλ/dX and KX is proportional to 1/λ 0.62.
Relation (9) explains the spectral behavior of the sensitivity dλ/dX to different measurands. The sensitivity to hydrostatic pressure dλ/dp for the first and the second resonance differs by a factor of 1.86. This difference is primarily related to chromatic dispersion of the polarimetric sensitivity KP. As it is shown in Fig. 3, the absolute value of KP decreases from 12.5 rad/MPa×m at 855 nm to 7.9 rad/MPa×m at 1271 nm, which gives the factor of 1.6. The remaining difference is associated with the change of wavelength dependent proportionality coefficient 1/λ 0.62. Moreover, Eq. (9) explains positive sign of dλ/dp. The signs of the group modal birefringence G(λ) and the polarimetric sensitivity to pressure KP are negative, which according to eq. (9) results in a positive sign of dλ/dp. In the same way, positive signs of dλ/dε and dλ/dT can be explained.
The dispersion of the polarimetric sensitivity to temperature KT and elongation Kε in the fiber is relatively small, see Fig. 3. In consequence, the change in the filter sensitivity dλ/dε and dλ/dT is primarily related to the wavelength dependent coefficient 1/λ 0.62. Indeed, this coefficient decreases by about 22% between the first and the second resonant wavelength, which is in relatively good agreement with the change in dλ/dε and dλ/dT.
Finally, in Table 1, we compare the sensitivities of the filter measured and calculated from Eq. (9) at both resonances. For elongation, the differences between the measured and estimated values stay within the measurement error. For hydrostatic pressure, the discrepancies are 20 and 30 %, respectively for the first and the second resonance, while for temperature the measured and calculated sensitivities differ by factor 2.16. High discrepancy in case of temperature is most probably related to possible change of the holes diameters in the twisted areas.
Fig. 7. Transmission characteristic of the rocking filter measured near the second resonance for excited polarization mode at 10° C and 100° C (a) and the displacement of the resonant wavelength against temperature (b).
Fig. 8. Transmission characteristic of the rocking filter measured near the second resonance for excited polarization mode at p=0.01 MPa (atmospheric pressure), 5 MPa, and 10 MPa (a) and the displacement of the resonant wavelength against applied pressure (b).
Fig. 9. Transmission characteristic of the rocking filter measured near the second resonance for excited polarization mode at 0 and 1 mstrain (a) and the displacement of the resonant wavelength against applied elongation (b).
Table 1. Sensing characteristics of the rocking filter measured and calculated from eq. (9) at the first and the second resonance. For convenience, we also present the polarimetric sensitivities of the fiber at the same wavelengths.
4. Conclusions
In this work we demonstrate that the rocking filters can be fabricated in highly birefringent PCFs using easily accessible fusion splicer. We also show that because of a decrease in the beat length against wavelength, which is a unique feature of the HB PCFs, it is possible to fabricate in such fibers the rocking filters with several resonances in the useful spectral range (0.6-1.6 µm). Measurements of the sensing characteristics of the fabricated filter show that its sensitivity to temperature is very low and equals 1.77 and 1.38 pm/K respectively for the first and the second resonance. The sensitivity to elongation is moderate, 1.35 and 1.12 nm/mstrain, while the sensitivity to hydrostatic pressure is very high, 6.14 and 3.30 nm/MPa, respectively. In consequence, the ratio of the pressure sensitivity to the temperature sensitivity is extremely high and equals 3500 and 2400 K/MPa, respectively for the first and the second resonance. This makes the filter an excellent device for hydrostatic pressure measurements with very low cross-sensitivity to temperature.
Acknowledgment
This work was partially supported by the European COST Action 299 – FIDES.
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