The properties of a hollow core photonic bandgap fiber designed for 1.55 um transmission are investigated with special emphasis on polarization issues. Large and strongly wavelength dependent phase and group delays are found. At the same time the principle states of polarization move strongly and erratically as a function of wavelength, leading to strong mode coupling. Wavelength regions with high polarization dependent loss coincide with depolarization due to a polarization dependent coupling to surface modes at these wavelengths.
©2005 Optical Society of America
The feasibility of optical fibers based on photonic bandgap guidance has opened the door for a completely new class of fibers  with even more interesting properties than the (effective) index guiding photonic crystal fibers (PCF). Most intriguing, it is no longer necessary for the core to be denser than the cladding material, and therefore light guidance in an air-core can be achieved . One obvious application for such hollow-core photonic bandgap fibers (HC-PBGF) is in high power pulse delivery and shaping [3–5] due to their low nonlinearity and tailorable dispersion. For transmission, in addition to the two previous properties, it is the potentially very low loss of HC-PBGF that is of interest as well.
By optimizing the cladding design and better mastering technological issues allowing for more regular and homogeneous fiber structures, the losses of HC-PBGF was dramatically lowered from ~1000 dB/km to 13 dB/km [6,7], to 1.7 dB/km , to the actual record number of 1.2 dB/km  in just 3 years. At the same time, practical fiber lengths have increased to the km range [8,10]. Although the losses are still large compared to standard SMF and therefore continue to be an important research topic [11–13], fibers are now sufficiently advanced so that other practical topics such as mode structures, chromatic dispersion, bending loss, fiber splicing, etc, become important.
Whereas the modes and group velocity dispersion have been investigated both theoretically and experimentally in some detail [5,7,8,11,13–16], less effort has been put to investigate the other mentioned parameters of practical interest [10,17,18]. Especially, only a few papers report on the polarization properties of HC-PBGF [18–21], and almost no experimental data are available [18,19,21]. It is therefore timely to expand our previous study  on the subject.
The paper is structured as follows: Section 2 gives a short description of our HC-PBGF and its basic properties. In Section 3, we report on different investigations of polarization issues such as differential phase and group delay and their wavelength and temperature dependence, polarization dependent loss and degree of polarization of the transmitted light, and polarization mode coupling. Section 4 finally summarizes the paper
2. Description of the investigated fiber and basic properties
The HC-PBGF investigated in this paper is Crystal Fibers AIR-10-1550. It is designed to operate, single-mode, in the 1550 nm window. Fig. 1 shows scanning electro-micrographs (SEM) pictures of typical cross-sections of the fiber. From Fig. 1 (right), the diameter of the central air core is determined to 8.6 to 9 um, with a ratio of major to minor axis of ~1.05. The physical length of the fiber sample is 50 m. If not stated otherwise, standard SMF pigtails (G.652, MFD 9.3 um at 1550 nm) of ~1m length, spliced to both the launch and receive end of the HC-PBGF, were employed in the measurements.
The overall transmission loss is shown in Fig. 2. It was obtained using a depolarized LED source and an optical spectrum analyzer. The data was verified with some point measures of the transmission using a tunable laser source and a polarization scrambler at the launch end along with a PDL meter capable of giving the mean transmitted power. As can be seen from comparison to the corresponding data for a 2.2 m sample of the same type of HC-PBGF, the transmission window (FWHM) reduces from 179 nm to 116 nm for the 50 m long sample, indicating that there might be some small inhomogeneity in the micro-structure along the fiber. However, a distributed measurement of the reflectivity along the fiber (Fig. 3) using a coherent optical frequency domain technique  shows no indication of isolated point defects, and the loss is found to be homogeneously distributed along the fiber. It amounts to 88 dB/km (1550 nm).
Another interesting feature is revealed by Fig. 3: after the peak from the end-reflection of the HC-PBGF, the reflectivity does not immediately drop to the Rayleigh level of the following SMF pigtail, indicating the presence of some light traveling along the fiber in slower higher order or surface modes. The fact that there is a continuous drop rather than different separate peaks suggests that there might be a continuous forth- and back coupling of light between these higher order modes and the fundamental mode occurring along the fiber (rather than a coupling into different modes directly at the launch end). For 1550nm, the overall energy of these slower moving modes is very small (~2%) compared to the fundamental mode, so that the HC-PBGF can be considered single-moded at this wavelength. This is however not true for all wavelengths in the transmission window as will be shown in the next section. Finally, Fig. 3 also shows that the backscattering level in the HC-PBGF is larger than the Rayleigh backscattering (RBS) in the preceding SMF fiber. Assuming symmetric splice losses of ~2 dB (8.8 dB overall loss minus 4.5 dB fiber loss, all divided by 2), a ratio of ~3.5 is found. Note that mode-field measurements show that most of the energy (~97 %) evolves in the center air hole, and only a very small fraction of light (<1%) propagates in silica, so that RBS will be virtually absent. Therefore, the backscattered light probably mostly stems from surface scattering or from reflective point defects that are too closely spaced to be resolved by the OFDR (a spatial 2-point resolution of 1 cm was employed for Fig. 3).
3. Polarization properties of the HC-PBGF
3.1 Polarization dependent loss
The polarization dependent loss (PDL) is measured with a commercial PDL meter (EXFO IQ-3400B) capable of measuring extremely low PDL values of ~0.01 dB. The results for the HC-PBGF (including both lead pigtails), as a function of wavelength, are given in Fig. 4. The PDL values are found to fluctuate quite a bit when measurements are repeated at different times of the day - note that fluctuations are found to be negligibly small when measuring PDL calibration artifacts. Despite these fluctuations, two well distinct wavelength regions exhibiting very large PDL values of as much as 4 dB or more can be easily discerned. The one at ~1600 nm corresponds to the band-edge (see Fig. 2 with same wavelength scale), and it is not very astonishing to find large PDL values here. To find a similarly large PDL around 1480 nm came as a surprise however, as this wavelength is in close vicinity to the center of the bandgap.
The explanation for this surprising property is found when looking at the transmitted mode-fields (MF), measured with a near-field scanning device (EXFO NR9000). Of course, the output SMF pigtail had to be removed for these measurements. As Fig. 5 demonstrates, the MF at 1515 and 1535 nm are quite similar and closely resemble the calculated fundamental mode for a similar fiber (Fig. 4(b) in ), whereas at 1595 nm, one clearly has a surface or higher order mode (again resembling the corresponding surface mode calculation, Fig. 5(b) in ). The interesting point now is that the transmitted mode at 1480 nm depends on the launch polarization. Whereas one essentially finds the fundamental mode at the HC-PBGF output when averaging over all launch polarizations with a fast polarization scrambler, a surface mode resembling the one at 1595 nm is found when the launch polarization is adjusted for minimum transmitted power. Note that the dithering in the measured MF is probably due to the strong polarization dependence of the transmitted power and a somewhat insufficient stability of the polarization state launched into the HC-PBGF due to several meters of preceding SMF fiber (laser pigtail, fiber of polarization controller, pigtail spliced to the HC-PBGF).
Consequently, in the 1480 nm wavelength region, one of the two polarizations of the fundamental mode does not seem to fully propagate, and only the lossier surface mode is effectively supported. Propagation of a higher order mode while the fundamental mode is not guided was in fact predicted in the literature . By fitting the measured MF contour lines with an ellipse, one finds an axis ratio of 1.1–1.15 for the low PDL wavelength regions, which is slightly higher than the geometrical ellipticity of the central air hole of ~1.05 as determined from Fig. 1. The mean FWHM of the Gauss-like transmitted MF is relatively constant with wavelength and amounts to ~6.5 um.
The surprising fact that one of the two fundamental polarization modes is virtually absent in the 1480 nm wavelength region is also confirmed when looking at the degree of polarization (DOP) of the transmitted light after the 50 m long HC-PBGF as a function of launch polarization. Again, the exit SMF pigtail is removed for this measurement. Whereas the DOP is about constant and high (0.95–1) for all launch polarizations at 1535 nm, it drops to 0.15–0.4 at 1595 nm, indicating the presence of higher-order modes at all launch polarizations. The decrease in the DOP is less drastic at 1480 nm (0.73–1). However, as Fig. 6 demonstrates, the DOP is quite closely correlated with the transmitted power. A low DOP coincides with larger loss (i.e. smaller transmitted power S0). Consequently, when the launch polarization is adjusted for maximum transmission, only the fundamental mode is exited and the transmitted light stays completely polarized (high DOP, low loss). When more and more power is put into the orthogonal polarization, where the power is essentially propagating in lossy surface modes, the DOP becomes lower as different spatial modes are present at the fiber exit. One also remarks a small reduction of the measured PDL to 4.1 dB (raw data in Fig. 6) compared to the previously found value of ~4.5 dB in the presence of the exit SMF-pigtail. Part of the overall PDL therefore seemed to stem from the difference in coupling efficiency at the exit end of the HC-PBGF rather than a difference in loss between the propagating modes.
3.2 Differential phase and group delay at 1550 nm
The phase delay at 1550 nm is measured using a P-OFDR technique described in . As Fig. 7 demonstrates, there are no clearly distinct frequency components in the backscattered signal as would be the case for a fiber with low polarization mode coupling [23, 24], but rather a distribution up to several hundreds of inverse meters. This is a typical signature for large polarization mode coupling [23, 25], and a corresponding model  can be used to extract the mean beatlength <Lb> characterizing the mean phase birefringence of the 50 m long HC-PBGF. Averaging over different launch polarizations, a value of <Lb>=1.1 cm is found. Note that it is very unusual for a fiber with such high birefringence (compared to a SMF fiber where Lb ~30 m) to exhibit strong mode coupling - we come back to this point in more detail in section 3.5. Analyzing the P-OFDR data for different locations along the HC-PBGF, no significant difference in the beatlength is found, and one can therefore reasonably assume that the birefringence is quite homogeneously distributed along the fiber.
We then investigated the differential group delay at ~1550 nm of the HC-PBGF using the interferometric technique . The employed source was an LED centered at 1542.5 nm with a bandwidth (3dB) of 50.6 nm. The corresponding temporal coherence of the source gives a system response of ~0.07 ps (green curve in Fig. 8). The interferometric trace of the HC-PBGF is shown in Fig. 8 (red trace). Again, the curve is a signature of large polarization mode coupling, and averaging over different measurements, a mean group delay of 38±2.6 ps is found. This is a very large delay for a fiber with a length of just 50 m, and the corresponding PMD assuming a square-root length dependence amounts to 170 ps/√km (PMD<0.2 ps/√km for standard SMF). Note however that the measurement of the group delay for the short (2.2 m) HC-PBGF sample gave 3.3 ps, so that the length scaling of PMD does seem to be located somewhere between a linear and a square-root dependence.
We have seen in the previous section that in the given wavelength interval (1517–1567 nm) of the LED, the HC-PBGF is essentially single-mode, and the (potentially very large) delays between different spatial modes should therefore be of negligible influence. That this is indeed the case was further verified by completely depolarizing the LED source (DOP<0.01). This causes the interferences among polarization states of the same spatial mode to disappear, and consequently only the delays between different spatial modes will show up in the interferogram. As is illustrated by the blue curve in Fig. 8, their contribution is indeed negligibly small.
3.3 Wavelength dependence of differential phase and group delay
As the HC-PBGF exhibits different properties as a function of wavelength (see Section 3.1), it is worthwhile to investigate the wavelength dependence of phase and group delay. Their ratio at different wavelengths can further give some insight on the strength of geometrical and stress contributions to the birefringence as was pointed out in .
In order to get the wavelength dependence of the phase delay [28–30], we measure the relative phase difference as a function of wavelength from the evolution of the output polarization state, and add it to the known absolute phase difference at 1550 nm from the P-OFDR measurements (the sign of the relative phase difference was chosen such that ∂β/∂ω fits best with the corresponding DGD for 1550 nm). The corresponding result (blue curve in Fig. 9), normalized with distance, demonstrates that the phase delay is quite strongly changing as a function of wavelength. The change is not linear with frequency which indicates - according to the explanations in  and the references therein- that form birefringence is contributing in an important way to the overall birefringence of the HC-PBGF.
The wavelength dependence of the differential group delay is measured with the standard Jones Matrix Eigenanalysis (JME) method introduced by Heffner et al. . Figure 9 (red curve) shows the corresponding results from different measurement series (note that different wavelength steps have to be used for different wavelength regions due to the strong delay variations). The result of the JME measurement is in good agreement with the interferometric one (group delay of 38 ps, see above): one gets a value of 35.8 ps when averaging over the corresponding LED spectrum. As could be expected from the measurement of the phase delay, the group delay is also strongly wavelength dependent. It virtually explodes towards the bandedge, and shows a distinctive minimum of 1.7 ps at 1535 nm (see inset of Fig. 9). The large PDL region around 1480 nm does not exhibit a distinct group delay (note that the fact that the fiber is not truly single mode at that wavelength does not perturb the JME measurement as only the polarized part of the light is considered for the delay determination).
Figure 9 also gives the ratio (black curve) between differential group and phase delay, which is seen to strongly vary as a function of wavelength and covers values between 0.35 up to as much as 6. This confirms that form birefringence is important , and that one needs to be more careful than usual (when phase and group birefringence are about equal) in choosing the applicable type of birefringence.
3.4 Temperature dependence of differential phase and group delay
We also investigated the temperature robustness. As for PCF , we found a very small temperature dependence of the birefringence for our 50 m HC-PBGF sample. At 1550nm, the phase change with temperature amounts to KT=-0.007 rad/K/m, and the change in group delay with temperature is about Kτ=-0.1 fs/K/m. The birefringence of HC-PBGF is consequently about 100 times less temperature dependent than in a PANDA fiber [28, 30], and these fibers are therefore advantageous for certain applications such as polarimetric pressure sensors requiring good temperature stability [32, 33].
In the previous subsections, we have seen that both the P-OFDR analysis of the beatlength and the interferometric PMD measurements indicate that the HC-PBGF has a quite strong polarization mode coupling. This finding is a big surprise as usually, fibers possessing a relatively large birefringence have quite different properties of the two polarization modes (this is in fact what leads to large birefringence in the first place). Quite different mode properties on the other hand means that there will be less mode coupling as their overlap is smaller. This principle is illustrated in Fig. 10, showing the output polarization state evolution of a PCF having a similar birefringence as the HC-PBGF. As is typical for fibers with a beatlength in the cm range, the output polarization state evolves on circles because the birefringence axis is roughly constant with wavelength and as there is little mode coupling. The same behavior is in fact found for polarization maintaining fibers such as PANDA or elliptical core fibers . As can be seen, the situation is dramatically different for the HC-PBGF. Despite the small wavelength interval of 0.5 nm over which the launch wavelength has been changed, the output polarization state is found to move erratically due to rapidly changing principle states of polarization (PSP).
A possible explanation of why the HC-PBGF exhibits a large mode coupling despite the presence of large birefringence could be as follows. The HC-PBGF is more prone to ‘point defects’ than standard SMF as the modes crucially depend on the exact structure of the innermost cladding holes (the length of the bridges e.g. is very crucial in determining the existence of surface modes [11,12] and also changes the fundamental mode properties), which will, inevitably, show some variations. Note that such point defects do not necessarily lead to strong, isolated reflective events that could have been detected in the backscattered trace using OFDR (see section 2). At this ‘point defects’, the transverse fiber properties (and consequently the mode properties) change strong enough for the mode overlap to become non-negligible independent of the intrinsic mode difference in front of the defect. In other words, the mode coupling (characterized by the change in PSP direction with wavelength, stronger coupling means stronger PSP change) becomes to first order independent of the mode non-degeneracy (characterized by the DGD, larger difference or non-degeneracy means larger DGD). This would mean that the change in PSP direction becomes independent of the DGD, in contrast to the normal situation (see beginning of this section), where PSP direction change and DGD are ‘anti-correlated’ (the larger the PSP change, the smaller the DGD and vice versa).
We verified this assumption by determining the change in the PSP direction between wavelengths that form an interval over which the output polarization state either performs half or full a turn on the Poincaré sphere (i.e. Δλ=π/<Δφ> or Δλ=2π/<Δφ> where <Δφ> is the mean phase change in rad/m at that wavelength). The corresponding results are shown in Fig. 11, along with the differential group delay for comparison. As can be seen, the change in PSP direction seems indeed to be roughly independent of the DGD (or at least not ‘anti-correlated’ to it), in agreement with the above argumentation.
The optical properties of a 50 m sample of the Air-10-1550 hollow core photonic bandgap fiber has been investigated.
The photonic bandgap is found to extend from 1449 nm to 1565 nm. Large PDL of up to 5 dB is however not only found at the lower band-edge, but also in the region around 1480 nm, thereby decreasing the useful frequency range for transmission to 1520–1565 nm. Analysis of the transmitted mode-fields in the 1480 nm wavelength region revealed that the polarization mode with lowest power transmission corresponds to a surface mode, whereas the mode with largest transmission is the fundamental mode. Consequently, in this particular wavelength region, only one of the two fundamental polarization modes seems to be guided properly. Analysis of the backscatterd signal power at 1550 nm using a high-resolution frequency domain technique revealed not only a homogeneously distributed fiber loss of 88 dB/km, but also the co-existence of some higher order or surface modes moving down the fiber at slower speeds. Their overall power is however sufficiently small that the fiber can be considered as effectively single-moded in this wavelength region.
Measurements of the differential phase and group delays and their wavelength dependence showed that the (accidental) fiber birefringence is large and strongly wavelength dependent. Their ratio can be quite different from 1 and is also strongly wavelength dependent, indicating that form birefringence is important. These measurements also showed clear signatures of a strong polarization mode coupling, a very surprising (even unique) property in view of the large birefringence. A possible explanation could be the presence of large local fiber ‘defaults’ leading to strong mode coupling that is essentially independent of the mode degeneracy, an argument supported by the findings from a measurement of the change in PSP direction as a function of wavelength.
The presented results show that the polarization properties of a HC-PBGF can be rather complex. Although some answers could be given in the present paper, the topic definitely merits some more consideration and investigation of a larger number of different HC-PBGF samples.
We would like to thank Michel Moret (GAP Biomédicale, University of Geneva, Switzerland) for his precious help with the SEM pictures.
We further acknowledge financial support from the Swiss OFES in the framework of the European COST P11 research project, and from EXFO Electro-Optical Engineering Inc., Vanier, Canada.
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