Appl Phys B (2009) 94: 635–640 DOI 10.1007/s00340-009-3394-2
Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature T. Martynkien · A. Anuszkiewicz · G. Statkiewicz-Barabach · J. Olszewski · G. Golojuch · M. Szczurowski · W. Urbanczyk · J. Wojcik · P. Mergo · M. Makara · T. Nasilowski · F. Berghmans · H. Thienpont
Received: 14 May 2008 / Revised version: 12 January 2009 / Published online: 21 February 2009 © Springer-Verlag 2009
Abstract We designed, fabricated, and characterized birefringent holey fibers with zero polarimetric sensitivity to temperature. The sensitivity measurements were carried out in a wide spectral range of 0.68–1.55 µm in fibers with different hole and pitch values and with birefringence induced by a pair of large holes adjacent to the core. Our results show that zero sensitivity to temperature can be obtained at certain wavelengths for the bare fibers with properly adjusted geometrical parameters. Moreover, the spectral measurements of the sensitivity to temperature are in good agreement with the modeling results for all the investigated fibers. PACS 42.81.Gs · 42.81.Pa
1 Introduction A crucial factor governing the applicability of a particular optical fiber to a specific sensing task is its sensitivity to temperature changes. For birefringent fibers, this sensitivity
T. Martynkien () · A. Anuszkiewicz · G. Statkiewicz-Barabach · J. Olszewski · G. Golojuch · M. Szczurowski · W. Urbanczyk Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland e-mail:
[email protected] Fax: +48-71-3283696
is often expressed by the polarimetric sensitivity to temperature: 1 d(ϕx − ϕy ) 2π dB = + Bα , (1) KT = L dT λ dT where ϕx and ϕy are phase shifts for the two orthogonally polarized modes propagating through the fiber, L is the fiber length, B is the modal birefringence, and α is the thermal expansion coefficient. In conventional highly birefringent (HB) fibers, the temperature sensitivity is mostly associated with stress induced by the differences in thermal expansion coefficients of the fiber core, the cladding, and the stress applying regions [1]. For this reason, the polarimetric sensitivity to temperature in conventional HB fibers is relatively high and ranges between −5 rad/K m in fibers with stress applying elements to −0.5 rad/K m in elliptical core fibers. The sign of KT in conventional HB fibers is always negative, which means that the birefringence decreases against temperature due to stress release [2]. Birefringent photonic crystal fibers (PCFs) are often made from glass with a uniform composition in the entire cross-section [3–5]. Therefore and in contrast to what occurs in standard fibers, there is no stress in PCFs induced by the difference in thermal expansion coefficients between the different fiber parts. The sensitivity to temperature changes of birefringent PCFs rather stems from:
J. Wojcik · P. Mergo · M. Makara Laboratory of Optical Fiber Technology, Marie Curie-Skłodowska University, Pl. M. Curie-Sklodowskiej 3, 20-031 Lublin, Poland
• Temperature-induced variations of the refractive index (thermo-optic effect) of the glass and of the air filling the holes. • Thermal expansion of the fiber in transverse and longitudinal directions.
T. Nasilowski · F. Berghmans · H. Thienpont Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
The contribution of these effects to the overall temperature sensitivity depends on the guiding mechanism, on the
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fiber geometry, on the wavelength, and on the material used to fabricate the fiber. Low-temperature sensitivity of birefringent PCFs was already confirmed experimentally in several publications [6–18]. The reported results were obtained for different classes of PCFs, including fibers with residual birefringence [6], highly birefringent pure silica fibers [7–16], highly birefringent nonsilica fibers [17], and photonic bandgap fibers [18]. The numerical analysis of the temperature characteristics of HB PCFs, taking into account thermo-optic and expansion effects was carried out in [19]. The results of this analysis show that the temperature sensitivity in birefringent PCFs can vary in a wide range with fiber geometry. One can therefore also obtain PCF with low-temperature sensitivity at a particular design wavelength either by employing proper fiber geometry or by using glass with an adequate ratio of thermo-optic to expansion coefficient. Relying on the theoretical approach proposed in [19], we have designed and fabricated two silica highly birefringent PCFs with two large holes adjacent to the core. Systematic spectral measurements of the polarimetric sensitivity to temperature reported in the following sections prove that KT changes its sign at certain wavelengths and therefore confirm the results of the theoretical predictions. For the purpose of comparison, we also show the temperature characteristic of a commercially available fiber with a comparable geometry (PM 1550-01) that has been studied experimentally in earlier works [9–13]. However, due to the large pitch in this fiber (Λ = 4.3 µm), the polarimetric sensitivity to temperature is negative in the analyzed spectral range. Additionally, we performed numerical simulations of the polarimetric sensitivity to temperature in actual structures employing the model described in [19]. The modeling and measurement results are in very good agreement.
2 Modeling temperature sensitivity For the sake of clarity and completeness, we recall the outline of our theoretical approach for designing temperature insensitive fibers [19]. In the most general case, the phase modal birefringence B in the PCFs fabricated of glass with uniform composition can be represented as a function of five parameters λ/Λ, nglass , nhole , Λ, and dcl /Λ, where λ/Λ is the normalized wavelength, nglass and nhole are the refractive indices of the glass and the material inside the holes (most often air), Λ is the pitch, and dcl /Λ is the filling factor. As derived in [19], the susceptibility of modal birefringence to temperature dB/dT is a function of only three parameters: the temperature-induced changes in the refractive indices nglass
T. Martynkien et al.
and nhole (thermo-optic effects) and the variation of the pitch Λ caused by thermal expansion of the glass: dB(λ) dB dB dB = αglass , γglass + γhole + dT dnglass dnhole dΛ/Λ
(2)
where γglass = dnglass /dT and γhole = dnhole /dT indicate respectively the thermo-optic coefficients of the glass and the material inside the holes, while αglass = dΛ/Λ/dT stands for thermal expansion coefficient of the glass. For silica–air fibers, these coefficients are γSiO2 = 1.1 × 10−5 K−1 [20], αSiO2 = 5.5 × 10−7 K−1 [21], and γair = −9 × 10−7 K−1 [22], respectively. Combining (1) and (2), we obtain an expression for the polarimetric sensitivity of the birefringent fibers: dB 2π dB γglass + γhole KT (λ) = λ dnglass dnhole dB (3) αglass + B(λ)αglass . + dΛ/Λ To determine dB/dT all the terms appearing in (2) were computed using a numerical approach which required multiple calculations of the propagation constants β x,y and the modal birefringence B versus λ/Λ, nglass , and nholes . For calculating the temperature sensitivity of the actual PCFs, we relied on a fully vectorial modal approach based on the finite-element method (FEM). The real geometry of the analyzed fibers was reproduced by processing the SEM images of the fiber cross-sections using the approach described in [23]. In the calculations of the propagation constants β x,y versus wavelength, we applied a mesh composed of about 200k triangular elements.
3 Fibers under test and measurement method All the fibers that we have modeled and characterized are made of pure silica glass. The birefringence in these fibers is induced by enlarging two holes symmetrically located at opposite sides to the core. Such fiber geometry was proposed for the first time in [4]. The SEM images of the fiber cross sections are depicted in Fig. 1. Fibers A (No. 070107P3, Fig. 1(b)) and B (No. 070119P2, Fig. 1(c)) were fabricated at the Marie Curie-Sklodowska University, Poland, while fiber C (PM 1550-01, Fig. 1(d)) is commercially available. The fiber geometrical parameters averaged over the first two hole rings surrounding the core are summarized in Table 1. The temperature sensitivity was measured with the setup shown in Fig. 2. This set-up relied on a spectral interferometric method. To perform the measurements in a wide spectral range, we used a set of broadband superluminescent diodes (SLD) with central wavelengths 680, 822, 935, 1273,
Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature
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Fig. 1 Schematic diagram (a) and SEM images of the fibers: fiber A (b), fiber B (c), fiber C (d)
Fig. 2 Set-up for measuring the polarimetric sensitivity to temperature
Table 1 Average dimensions of the fibers investigated Fiber A
Fiber B
Fiber C
Λ [µm]
2.55
3.55
4.3
d cl [µm]
1
1.36
2.34
dx [µm]
2.4
3.55
4.42
d cl /Λ
0.4
0.38
0.52
and 1391 nm and an amplified spontaneous emission (ASE) source with central wavelength at 1550 nm. The main difficulty in carrying out this experiment stems from the very low temperature response of the fibers. The relatively small phase shifts induced by a temperature change are hidden by a very high phase shift arising between the polarization modes due to the intrinsic birefringence of the fibers under test. To measure the small temperature-induced phase shifts with satisfactory uncertainty, we exposed relatively
long pieces of the bare fiber (LT = 0.65 m) to temperature changes. Moreover, to partially compensate for the phase shift related to the fiber birefringence, we divided the investigated fiber into two parts of lengths L1 (reference fiber) and L2 (tested fiber) (L1 > L2 ), which were aligned in a differential configuration in a fiber optic splicer (the faster mode in the reference fiber becomes the slower mode in the tested fiber). The shorter fiber served only to compensate partially the optical group delay between the polarization modes arising in the thermally cycled fiber. The temperature was changed in the range from 5 to 98°C using water or air heating systems. The light at the input of the reference fiber was polarized linearly at 45° to its polarization axes. Therefore both polarization modes were excited in the reference and in the tested fibers and were made to interfere at the output by passing through the analyzer aligned at 45°. The light from the fiber output was collimated by a lens O2 , then passed through a
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T. Martynkien et al. Fig. 4 Spectral dependence of phase (B) and group (G) modal birefringence measured (dots) and calculated (lines) in the investigated fibers
Fig. 3 Output spectrogram (a) and intensity distributions in output spectrograms registered at different temperatures for fiber A (L1 − L2 = 0.1 m and LT = 0.65 m; the SLD with λ0 = 680 nm) (b)
Soleil–Babinet compensator (SBC) and an analyzer aligned at 45° to the fiber polarization axes, Fig. 2. To observe interference between the polarization modes, we used a diffracting grating followed by a CCD camera. A computer acquired and processed the output spectrograms. The phase shift between the polarization modes accumulated throughout their propagation along the system can be expressed in the following way: φ(T ) =
2π B(λ) L + KT LT (T − T0 ) + φC , λ
(4)
where L = L2 − L1 , LT is the fiber length seeing the temperature changes T − T0 , and φC is the phase shift introduced by the SBC. The phase shift of the compensator at initial temperature T0 was adjusted individually for each light source in such a way that the interference minimum arises at the central wavelength λ0 . From Fig. 3 we see that the phase change caused by a varying temperature results in a small displacement of the interference minimum. The temperatureinduced phase shift was then balanced by the phase shifts of opposite sign introduced by the SBC. The perfect match of these phase shifts, φC = −KT LT (T − T0 ),
(5)
is achieved for an interference minimum set to the central wavelength λ0 . One can therefore immediately obtain the temperature-induced phase shifts from the readings on the SBC.
4 Results Using the lateral force method and the spectral interferometry method described in [24], we first measured the spec-
Fig. 5 Temperature-induced phase shift measured for fiber A at λ0 = 680 nm (a) and λ0 = 1391 nm (b)
tral dependence of the phase (B) and the group (G) modal birefringence in the birefringent fibers fabricated by UMCS, Fig. 4. Additionally and for the sake of comparison, we also show the measured birefringence for the commercially available fibre (PM1550-01) described in earlier work [23]. The results of these measurements show a typical behavior for birefringent PCFs such as the monotonic increase of both parameters against wavelength. Moreover and because of the smaller pitch, the phase and the group modal birefringence in fiber A are larger than in fibers B and C. At λ = 1.55 µm they equal B = 1.3 × 10−3 , G = −1.8 × 10−3 in fiber A, B = 6.4 × 10−4 , G = −9.4 × 10−4 in fiber B, and B = 4.7 × 10−4 , G = −8.3 × 10−4 in fiber C. We measured the sensitivity to temperature in bare fibers manufactured by UMCS. As shown in Fig. 5, we observe a linear response to temperature changes, with no sign of hysteresis, in both uncoated fibers. The measurements were repeated six times for statistical significance. We estimated
Birefringent photonic crystal fibers with zero polarimetric sensitivity to temperature
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liptical core (KT ≈ −0.5 rad/K m). Similarly to the conventional fibers, the sign of KT in a short wavelength range is negative, which means that the birefringence decreases with increasing temperature. As predicted by our numerical analysis, the polarimetric sensitivity to temperature changes its sign at a certain wavelength that depends on the pitch Λ. For both fibers A and B, the zero sensitivity wavelengths arise in the useful spectral range and equal respectively 1150 nm for fiber A (Λ = 2.55 µm) and 1530 nm for fiber B (Λ = 3.55 µm). For longer wavelengths, the sensitivity KT becomes positive and grows with wavelength with increasing slope. This effect is clearly visible for the fiber with shortest pitch, for which the parameter KT reaches a relatively high value of +0.022 rad/K m at 1.55 µm. For the sake of comparison, in Fig. 6(c) we also show the polarimetric sensitivity to temperature vs. wavelength for the commercially available fiber C [13]. However, as predicted by our numerical analysis, the large pitch in this fiber (Λ = 4.3 µm) causes the zero sensitivity to temperature to occur at wavelengths of about 2.2 µm. Hence this could not be detected in earlier measurements [9–13]. The measurements and numerical simulations are all in good agreement. The small deviations are likely related to the limited precision with which the actual geometry of the fibers can be obtained from the SEM images [24]. Additionally, as shown in [25], the geometrical parameters can vary along the fiber length due to fluctuations occurring during the drawing process.
5 Conclusions
Fig. 6 Polarimetric sensitivity to temperature vs. wavelength: (a) fiber A, (b) fiber B, and (c) fiber C. The measurements are indicated with dots, while the solid lines correspond to numerical simulations
that the measurement uncertainty is about 0.0015 rad/K m. In Fig. 6, we compare the measurements and the numerical simulations of the polarimetric sensitivity to temperature vs. wavelength. In both fibers A and B, the spectral dependence of the polarimetric sensitivity to temperature KT is very similar. In a short wavelength range, the temperature sensitivity reaches a minimum, which is about −0.007 rad/K m. This value is about two orders of magnitude lower than the sensitivity in conventional highly birefringent fibers with el-
We measured the spectral dependence of the polarimetric sensitivity to temperature in two specially fabricated highly birefringent PCFs with birefringence induced by two large holes adjacent to the core. The measurements were carried out in a wide spectral range 0.68–1.55 µm for bare. Our results show that the temperature characteristics significantly depend on the geometrical parameters of the fiber. Moreover we demonstrate for the first time a zero polarimetric sensitivity to temperature at certain wavelengths. For the sake of comparison, we also show the temperature characteristic of a commercially available HB PCF (PM 1550-01). However, because of the larger pitch distance (Λ = 4.3 µm) in the commercial fiber, measured temperature sensitivity has negative sign in the analyzed spectral range. Numerical simulations carried out for this fiber reveal that the zero sensitivity to temperature arises at wavelengths of about 2.2 µm, which explains why this zero sensitivity was not detected in earlier experiments. The two other fibers with shorter pitch were specially designed and manufactured to achieve zero temperature sensitivity at useful wavelengths, respectively at 1150 nm for
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the fiber A (Λ = 2.55 µm) and at 1530 nm for the fiber B (Λ = 3.55 µm). The results of the sensitivity measurements are in good agreement with the results of the theoretical analysis based on the model presented in [19]. Acknowledgements The work described in this paper was partially carried out with the support of the PHOSFOS-project (“Photonic Skins for Optical Sensing”), a Small/Medium-Scale Focused Project funded by the European Commission through the 7th ICT-Framework Programme, the EC 6th FP Network of Excellence on Micro-Optics “NEMO” and by the COST 299 action. The SEM photograph was taken by the department META of the Vrije Universiteit Brussel.
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