We perform detailed measurements of the higher-order-mode content of a low-loss, hollow-core, photonic-bandgap fiber. Mode content is characterized using Spatially and Spectrally resolved (S2) imaging, revealing a variety of phenomena. Discrete mode scattering to core-guided modes are measured at small relative group-delays. At large group delays a continuum of surface modes and core-guided modes can be observed. The LP11 mode is observed to split into four different group delays with different orientations, with the relative orientations preserved as the mode propagates through the fiber. Cutback measurements allow for quantification of the loss of different individual modes. The behavior of the modes in the low loss region of the fiber is compared to that in a high loss region of the fiber. Finally, a new measurement technique is introduced, the sliding-window Fourier transform of high-resolution transmission spectra of hollow-core fibers, which displays the dependence of HOM content on both wavelength and group delay. This measurement is used to illustrate the HOM content as function of coil diameter.
© 2012 OSA
Hollow core fibers are of great interest because of their remarkable properties such as ultra-low nonlinearity . Low loss hollow-core fibers have been demonstrated , but one significant issue is that low-loss hollow core fibers support many higher-order modes (HOMs) , whereas many applications are sensitive to noise introduced by interference between coherent modes. Therefore, techniques for quantifying the mode content are required to enable the use of bandgap fibers in real-world applications. Higher-order modes of hollow-core fibers have been studied experimentally by using a spatial light modulator to selectively launch individual modes . One approach to characterizing the modes of hollow-core fibers is to perform a modal decomposition on the beam profile using the modes from a mode-solver , but this technique depends on a precise measurement of fiber geometry which can be difficult. Spatially and spectrally resolved (S2) mode imaging is a recently developed technique for quantifying the modal content of light propagating in multi-moded fibers in the case where most of the light propagates in a single mode, with small amounts of residual power in other modes [6,7]. The measurement does not depend on solving for the eigenmodes of the fiber. S2 imaging has been used previously on a 19 cell hollow core fiber, but the loss of that fiber was relatively high (~20 dB/km) . Here we present the first S2 imaging measurements of low-loss hollow fiber. Detailed cut-back measurements are presented, and the mode imaging results to at a low loss wavelength are compered to results at a high loss wavelength.
The paper is organized as follows: in Section 2, a brief discussion of the S2 imaging technique is presented. Section 3 introduces the fabricated, low-loss, 19 cell hollow core fiber. Section 4 discusses the expected impact of a non-ideal structure on the mode content in hollow-core fibers. Section 5 presents results on measurements of the mode content at a low loss wavelength, and Section 6 present results on measurements of the mode content at a high loss wavelength. Section 7 introduces a new measurement technique, the sliding-window Fourier transform of high resolution transmission spectra of hollow-core fibers, and applies the technique to an initial measurement of the dependence of higher-order mode content on fiber coil diameter. Finally, Section 8 presents discussion and conclusions.
2. S2 imaging of hollow-core photonic bandgap fiber
S2 imaging is performed by spatially resolving the spectral interference that occurs between coherent modes propagating with different group delays in the fiber under test. The measurement can quantify the power level and relative group delays of higher order modes with respect to the fundamental mode. Because the relative group delays of modes are obtained, S2 imaging can also distinguish between scattering that occurs between modes at discrete points such as a splice, and distributed scattering that occurs along the length of the fiber under test.
The original S2 measurement setup was implemented using a broadband source that was launched into a fiber under test. The output beam from the test fiber was imaged onto a single mode fiber which was coupled to an optical spectrum analyzer (OSA). Typically the wavelength span of the OSA was between 10 and 50 nm. A polarizer ensured all modes had parallel polarizations at the SMF pigtail pickup. The SMF probe was placed on automated translation stages and rastered in x and y, perpendicular to the direction of beam propagation. At each (x,y) point the optical spectrum was measured. If two different modes overlapped spatially in the image plane an (x,y) point, they generated spectral interference at that point due to group delay differences between the modes in the fiber under test. With appropriate Fourier filtering and data processing of the optical spectra at each (x,y) point, the group delay difference between higher-order mode and fundamental mode, together with the spatial dependence of the spectral interference could be analyzed to obtain images of HOMs and their relative power levels [6,7].
The primary issue in using this setup to measure hollow-core photonic bandgap fibers is the maximum group delay that can be measured is the inverse of the spectral resolution. A typical optical spectrum analyzer with 0.05 nm resolution bandwidth is therefore limited to measuring group delays differences between modes that is less than about 80 ps. However in hollow core fibers many modes of interest can have relative group delays of several hundred picosecond per meter, and a setup based on an OSA is therefore limited to measuring very short lengths of fiber.
An alternative setup for performing S2 imaging uses a tunable laser and CCD camera [7–9]. A schematic of the setup is shown in Fig. 1 . By measuring the beam profile as a function of wavelength, the same three dimensional set of data in (x,y,λ) is obtained as with the original S2 setup. To increase the measureable group delay a tunable laser with ~100 kHz linewidth and 1 pm wavelength step size was used as the optical source. With the wavelength step size of 1 pm, group delay differences as large as 4000 ps can be measured, making the setup ideal for characterizing hollow-core photonic bandgap fibers. In addition, an InGaAs camera was used to measure the beam profile at 1550 nm.
3. Low loss, hollow-core photonic band-gap fiber
A microscope image of the fabricated fiber is shown in Fig. 2 . The fiber was fabricated using a modified stack-and-draw process. The 19-cell core was 25.6 μm in diameter. The pitch was 5.2 μm and the air-fill fraction for the cladding was approximately 96%.
Cutback measurements to measure the loss were performed on a 250m length of fiber. In these measurements, as well as in all the S2 measurements described in this work, SMF was fusion spliced to the PBF to launch light into the hollow core fiber. The fusion splice was made as short and cold as possible to prevent collapse of the air-holes while still maintaining the integrity of the splice and optical launch conditions over the length of the measurement.
A broadband source was launched into the PBF, and an OSA was used to measure the optical spectrum. As mentioned, the light was launched through a fusion splice; the output end was free-space coupled to the OSA which was set to 2nm resolution bandwidth. Approximately 1 m of fiber was left after the cutback was performed. The results of this measurement are shown in Fig. 3 . A low loss window with minimum value of 5.9 dB/km at 1520 nm was obtained.
4. Mode content in a non-ideal fiber
Ideal hollow-core fibers have modes that closely resemble textbook step-index fiber modes, but mode structure in real fibers is much more complicated. A real fiber may have some nearly ideal core modes, but generally includes some strongly coupled mixtures of core modes with surface modes. Surface modes are very sensitive to geometry, and so irregularity plays a crucial role in the mode-content analysis, just as it does for other properties of hollow-core fibers. It is known that tiny geometric distortions tend to make fiber losses much higher and low-loss bandwidths much smaller in real fibers than in ideal designs . Even irregularities beyond the resolution of typical scanning electron microscope images can qualitatively change mode properties, including the position of surface modes . Mode-content measurements will unavoidably differ substantially from calculations, since precise measurement of the fiber geometry is quite difficult.
To illustrate features that we expect to find in the mode content measurement, Fig. 4 shows a simulation of a geometry resembling the measured fiber (hole spacing 5.1 microns, 95% air-fill fraction), including irregularity in core-web thickness comparable to what we estimate for the real fiber. Dark lines show the LP01-like modes (blue), LP11-like modes (red) and group (black) of LP02- and LP21-like modes. Other modes, including surface modes, are shown with thinner black lines. There are clear avoided-crossings between surface and core modes, indicating that the modes mix.
Many of the calculated mode profiles show the expected shapes, with calculated relative group delay (with respect to the LP01) in the 10-60 ps/m range, e.g. LP11 (b-c), LP02 (d), and LP31 (e). Even slight interactions with surface modes, far from the clear avoided crossings, have a dominant impact on relative group delay: for example, although (b) and (c) have similar and nearly ideal fields, (b) has 12ps/m and (c) has quite different 26ps/m delay relative to the fundamental. A comparable SIF mode (assuming Dcore = 21.4μm,ncore = 1, and a fictitious nclad = 0.99) would have relative delay of 4ps/m, essentially constant across this wavelength range. Modes near anti-crossings have highly distorted field profiles and larger relative delays. For example, LP02 and LP21–like modes (f-h) are substantially mixed with each other and with a group of surface modes at around 1480nm. These modes with stronger surface-mode content (f-h) have relative group delay >200 ps/m. Measured S2 images are derived from interference with the fundamental mode, and are thus intrinsically polarized; accordingly, we show polarized calculated field profiles, plotting |Ex|2 (b-c) or |Ey|2 (d-h). The mode images obtained from the simulations are typical of what are observed in the experiments. In particular, the three lobed pattern in Fig. 4(h), the asymmetric LP02–like mode in Fig. 4(d), 4(g), and 4(f), and the 6 lobed LP31 mode in Fig. 4(e) were all observed in experimental measurements, examples of which are shown in Fig. 5 . Further details of the measurements will be given in the following sections.
5. S2 imaging results at 1500 nm
A 20 m length of PBF was fusion spliced to the SMF launch pigtail in the S2 setup shown in Fig. 1, and the output end was cleaved. S2 measurements were made with a measurement range 1500 nm to 1505 nm, the center of the low loss window, and at 1560 nm to 1565 nm, where the loss was approximately 60 dB/km. The fusion splice and launch conditions were held fixed as the PBF length was cut back and S2 measurements performed at each length. This section and the following report the detailed results of these measurements.
Figure 6 shows the beat amplitude vs. group delay difference between HOMs and fundamental mode measured at 1500 nm for a 50 cm length of fiber. The group delay axis has been normalized to fiber length to obtain group delay per unit length in ps/m. The images associated with the HOMs, obtained through the analyzing the spatial dependence of the beat note at different group delays are shown in Fig. 6(a) through Fig. 6(h).
At small relative group delays a number of sharp peaks are observed. Many of the images of the HOMs at these group delays correspond to expected shapes for the (a) LP11, (b) LP12, and (c) LP02, for example. At larger group delays (Fig. 6(d),6(e)), the mode images did not necessarily correspond to precisely expected LPmn, modes, but it should be emphasized that these mode images were repeatedly observed in multiple measurements
At larger group delay differences, the distinct peaks disappear and are replaced by long flat plateaus. By integrating over the range of group delay from 100 ps/m to 270 ps/m, the mode image in Fig. 6(f) is obtained, which appears to contain a strong component of surface modes. This mode shape is obtained when any region within the range label ‘f’ is examined. It should be emphasized that the mode in Fig. 6(f) could extend to shorter group delays as well, but the signal at short group delays is dominated by the strong discrete scattering signal from the core guided modes. The mode labeled ‘h’ also shows a similar appearance over a broad range of group delays.
By integrating over the entire range of group delays in the measurement, the total HOM mode content launched into the PBF at the splice is obtained. The HOM content is found to be approximately −8.4 dB with respect to the fundamental mode, of which the LP02 mode, at −13.4 dB with respect to the fundamental mode, is the strongest component.
The beat amplitude for a 15 m length of fiber at 1500 nm is shown in Fig. 7 . It can be seen that the discrete peaks at lower group delays are still clearly visible. The nature of the mode content of these peaks is discussed in sections 5.1 and 5.2. Here we simply note that the continuum of modes at large group delays for long lengths of fiber appears to be a mixture of the LP12 and surface modes Fig. 7(a) through 7(d), with this mixture appearing over a broad range of group delays. The modes corresponding to the sharp peaks at short group delay consist of multiple split LP11 modes, as discussed in the next Section, 5.1.
5.1 Splitting of the LP11 mode
For short fiber lengths of 0.5 m, a single LP11 peak was measured. However, at longer fiber lengths, this peak was observed to split into multiple LP11 peaks. This result is shown in Fig. 8 , where the measurement for 0.5 m fiber length is shown as a blue line, and the measurement for 15 m is plotted as a red line. For a 15 m length of fiber the peaks labeled (a) through (d) all correspond to the LP11 mode with different geometric orientations. For 0.5 m of fiber, peaks (b), (c), and (d) cannot be resolved at short lengths of fiber.
All four LP11 peaks could be fully resolved when the fiber was longer than 5 m. In fact, the relative geometric orientation of the four split LP11 peaks was preserved over ten meter of fiber, as illustrated in Fig. 9 . Splitting in group delay of different geometric orientations of the LP11 mode in large mode area fiber has been previously reported . In that experiment, coiling of the fiber caused bend-induced distortions to the index profile and generated a preferential axis along which the splitting occurred. Here small geometric imperfections in the structure are sufficient to cause the splitting in group delay and maintain the geometric orientation of the modes.
5.2 Relative loss of higher-order modes
In principle, by tracking the relative strength for the different HOMs as a function of fiber length, the loss of the HOMs relative to the fundamental mode can be measured. Previous measurements of HOMs in PBF fibers  however found that the discrete scattering peaks quickly disappeared, and only a continuum of unidentifiable HOMs was left after a meter or so of fiber.
The HOMs in the low loss region of this PBF showed very different behavior. In fact the discrete peaks were found to be observable over lengths of fiber as long as 20 m. The beat amplitude vs. group delay for three different lengths of fiber is shown in Fig. 10 . The number of discrete peaks increases for longer length of fiber because of the geometric splitting of the modes, as discussed in the previous section. Therefore, for each length of fiber measured, the relative power in all the discrete modes was tabulated. For a given mode order all the various split peaks were summed to find the total power contained in a given HOM. The result of this measurement for some of the lower order modes is shown in Fig. 10(b).
The LP11 and LP02 modes are well guided and the loss was too low to measure in a 20 m length of fiber. By comparison, the loss of the LP12 was 0.48 dB/m (obtained via linear fit to the data in Fig. 10(b)). It has recently been shown that cross-mode beating between higher-order modes can lead to spurious peaks in S2 imaging data . For this reason we restricted the analysis in this section to low order HOMs.
6. S2 imaging results at 1560 nm
Up to this point the measurement results have focused on the low loss region of the fiber. It is instructive to compare the mode properties at low loss wavelengths to those at high loss wavelengths.
Figure 11 shows the mode beat vs. group delay in a 20m length of fiber at 1500 nm compared to that at 1560 nm. As discussed in Section 4, the discrete scattering beat notes of core guided modes remain clearly visible, whereas they cannot be distinguished at 1560 nm in the high loss region of the fiber. Second, the level of total mode content at 1500 nm is −8.9 dB, and is not dramatically different from that 1560 nm, which is −8.1 dB. However, the group delays at which modes are observed and most of their power resides (discrete, core guided light, compared to a broad continuum) is very different.
The mode beats and images at 1560 nm for 15 cm and 10 m of fiber are shown in Fig. 12 . The curves for the mode beats in Fig. 12 have been offset vertically for clarity; the level of the mode beat at group delays greater than 100 ps/m is similar for both lengths of fiber.
For the 15 cm length of fiber, only two core guided modes, the LP02, and LP12, can be distinguished. The image in Fig. 12(c) was obtained by integrating over the entire continuum from 10 ps/m to 400 ps/m. It can be seen to consist of a mixture of surface modes and other modes which are indiscernible.
For long lengths of fiber, the discrete mode scattering events of the core modes completely disappear. What is left is a continuum over broad group delays which appears to be a mixture of surface modes and the LP02 mode. This can be contrasted to the appearance of the modes in the continuum at 1500nm, which appears to be a mixture of surface modes and the LP12 mode.
7. The sliding-window Fourier transform and coiling properties of hollow-core fibers
The previous sections detailed the complex nature of the mode structure of hollow core fibers and compared the modes in a low loss region to those in a high loss region of the fiber. However, in general, a photonic bandgap fiber is expected to show complex wavelength dependence to the mode structure. To examine the wavelength dependence of the mode structure, we utilized a new tool, a sliding-window Fourier transform of the transmission spectrum of hollow core fiber.
This measurement is based on the same coherent interference of modes with different differential group delays as is utilized in S2 imaging. However, in this measurement an SMF fiber is spliced to the output end of the fiber under test, and the power transmission measured as shown in Fig. 13(a) . A narrow linewidth tunable laser is used to obtain the transmission spectrum; a typical transmission spectrum is shown in Fig. 13(b), illustrating the coherent interference between modes that is observed. In principal, the same information can be obtained by integrating the intensity from the beam profile from the CCD camera, however, the simple transmission measurement with a power meter can be much faster, and a swept wavelength system can measure many tens of thousands of data points in a few minutes time. Note that because the modes of the fiber are orthogonal, some form of aperture at the output of the hollow-core fiber, either in the form of pixels on a CCD camera, or an output SMF fiber, is required to obtain the interference spectrum shown in Fig. 13(b).
Once the transmission spectrum is obtained, the Fourier transform of the spectrum is again performed, as in the S2 imaging data analysis. However, because of the large number of data points the transmission spectrum can be windowed, and the Fourier transform is applied to only a small (few nm) subset of the full transmission data. The HOM content as a function of group delay of this window is obtained by applying the data analysis calculation of Ref 6 on the resulting Fourier transform. Next, the window selecting the subset of data is moved (i.e. slid) through the full transmission data set and the Fourier transform calculation repeated to obtain a measure of the HOM content as a function of both wavelength and group delay.
The results of this measurement and sliding-window Fourier transform calculation are shown in Fig. 14 . A 5 m length of fiber was used. The transmission spectrum was measured using the same tunable laser as used in the S2 imaging setup. This measurement was performed with a wavelength step size 0.003 nm and a measurement range from 1500 nm to 1570 nm, representing 23,000 data points. The size of the sliding window used in the Fourier transform calculation was approximately 3 nm. The color scale represents the HOM content in decibels.
The wavelength dependence of the various HOMs can clearly be seen in Fig. 14. As discussed in Sections 5 and 6, in the low loss region of the fiber, discrete scattering peaks were clearly observed, however, in the high loss region of the fiber the narrow discrete peaks disappeared into a broad plateau. This behavior is clearly illustrated in the sliding-window calculation results. The discrete scattering peaks appear as narrow tracks in the low loss region of the fiber, but as the fiber transitions into the high loss region, the nature of the mode scattering changes dramatically into a broad plateau.
The utility of this measurement can be increased significantly by pairing it with an independent S2 measurement to identify which modes are responsible for which tracks in the sliding-window Fourier calculation. A few of the modes obtained from an S2 measurement at 1500 nm, are also given in Fig. 14(a) and arrows indicate which of the tracks these mode images correspond to.
Once the modes are identified, the power of the sliding-window Fourier transform calculation is that it provides a rapid means for studying behavior HOM behavior in a length of fiber over a broad wavelength range. As an example, we used the measurement as an initial study of the impact of coiling on HOMs. Figure 14(a) shows the result of the measurement when the fiber was coiled to 15 cm diameter, and Fig. 14(b) shows the measurement for a coil diameter of 5 cm. There is little change in the HOM content with coiling. This is expected: it is known that the fundamental mode of hollow-core fibers is typically quite robust to macrobending, and that higher-order modes of a 19-cell core are well-confined modes with calculated losses only a few times that of the fundamental . Our calculations have shown that such modes cannot be suppressed by moderate bends.
8. Discussion and conclusions
In this work we have presented the first S2 mode imaging measurements in a low-loss, hollow core, photonic bandgap fiber. Detailed measurements of the modes at a low loss wavelength of the fiber were compared to measurements at a higher loss wavelength. By fusion splicing the SMF launch pigtail to the PBF fiber consistent launch conditions were obtained at different wavelengths ranges and over the course of the cutback measurement. With a fusion splice to launch from the SMF to PBF fiber, the total HOM content launched into the fiber was −8.4 dB at the low loss wavelength of 1500 nm, which means 86% of the light launched into the fiber was in the fundamental mode. Furthermore, the sliding-window Fourier transform of high-resolution transmission spectrum was introduced, providing a rich picture of the complex behavior of modes in group-delay and wavelength.
One of the most striking features of the S2 measurement of hollow core fiber is the observation of discrete scattering peaks at small group delay differences, together with the continuum of modes at longer group delays that appears as a mixture of core guided modes and surface modes. This continuum of modes seems to be unique to hollow-core fibers and has not been observed in S2 measurements of conventional large-mode area and multi-mode fibers. In general, the measured mode beating spectrum showed strong wavelength dependence. The specifics of the mode mixtures in the continuum, the number of measured discrete modes, their mode orders, and the length over which the discrete peaks depended on whether the fiber was being measured at a wavelength with low loss or high loss. The rapid disappearance of the discrete peaks at the high loss wavelength was similar to previous reported S2 measurements in high loss hollow core fiber. In contrast the discrete peaks were maintained over long lengths of fiber in the low loss region.
By tracking the strength of the discrete mode scattering events as a function of length the loss of various mode orders compared to the fundamental mode loss could be measured. However, the existence of the continuum placed limitations on the ability to make this measurement. Modes that had high loss compared to the fundamental disappeared quickly into the continuum of modes. Such was the case of the modes measured at the high loss wavelength range, as the discrete scattering modes were not maintained over significant lengths of fiber. In contrast, the LP11 and LP02 loss relative to the fundamental mode was too low to measure in 15 m of fiber at 1500 nm, the low loss wavelength. The loss of the LP12 was 0.48 dB/m.
Another phenomenon observed for the first time was the splitting in group delay of different geometric orientations of the LP11 mode. In fact the splitting was enough that the relative orientations of the split modes were observed to be strongly preserved over 10 m of fiber.
Finally, we have introduced the sliding-window Fourier transform of high-resolution transmission spectra of hollow-core fibers as an additional tool for visualizing the complex wavelength and group delay dependence of the mode content in hollow-core fibers.
In conclusion, S2 imaging of the higher modes of hollow-core photonic bandgap fiber reveals a rich picture of the modal properties. S2 imaging, coupled with the sliding-window Fourier transform of high resolution transmission spectra, is a powerful tool which can be used to understand modal properties of the hollow core fiber. These measurements are expected to be instrumental in the optimization of many aspects of hollow core-fibers, such as the design of fibers that aid in reducing the mode content of hollow-core fibers, understanding fundamental mode properties such as macro-and micro-bending loss, modal group delay and dispersion, and in optimization of fiber splicing.
Distribution Statement “A” (Approved for Public Release, Distribution Unlimited). The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.
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