Supplementary information to Nature article: Wavelength-scalable hollow optical fibres with large photonic band gaps for CO 2 laser transmission

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Roberta Holt
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1 Supplementary information to Nature article: Wavelength-scalable hollow optical fibres with large photonic band gaps for CO 2 laser transmission I. Modal characteristics of CO 2 laser guiding fibres Due to their large core size, these fibres are expected to support many modes of propagation. The core radius is ~30 times the operating wavelength, and the boundary conditions can be approximated by those of a hollow metallic waveguide 1 ; based on these assumptions we estimate the number of modes supported by our fibre to be greater than 10,000. However, imaging of the output patterns reveals that in practice these fibres operate in a fewmode regime. This can be explained by the efficient coupling of the laser source to the low order modes and the strong mode discrimination due to the combination of radiative and absorptive loss mechanisms that exist in such fibres 1. Thus only those modes that are excited and propagate most efficiently are found in the fibre output field patterns. Similar behavior has been observed in hollow metallic waveguides of comparable core diameters 2. Various modal output patterns were achieved by varying the input coupling conditions of the CO 2 laser light in ~ 4 meter long fibres with core diameters of ~700 microns that were held nominally straight (supplementary figure 1). Beam images were recorded using a Spiricon Pyrocam III. Figure 1 (supplementary). Output field patterns of CO 2 laser light from hollow photonic band gap fibre held nominally straight. The three panels represent the range of different behaviors observed with varying input coupling conditions. The fibre was ~4 meters long and had a core diameter of 700 microns. One of the mechanisms that causes additional bending losses in these fibres is inter-mode coupling (coupling can occur to more lossy or potentially to radiative modes). Imaging the output field pattern from the same fibre bent near the output at an angle of 90 degrees with a bending radius of 10.5 cm (supp. fig. 2) shows that similar modes dominate the output of the bent fibre as those found in the straight case. However, there is a degradation in the modal purity compared to the straight fibre, though this behavior is still in the few-mode regime (less than 10 modes). In general, the modal output is quite sensitive to the specific bending conditions.

2 Figure 2 (supplementary). Output field patterns of CO 2 laser light from hollow photonic band gap fibre bent at the fibre output at an angle of 90 degrees with a bending radius of 10.5 cm. The three panels represent the range of different behaviors observed with varying input coupling conditions. The fibre is the same used in supp. fig. 1. II. Bending losses of CO 2 laser guiding fibres We have performed bend loss measurements using a broad band FTIR source as well as a CO 2 laser operating at 10.6 microns. During all bending measurements, the fibres were bent at an angle of 90 degrees around metal cylinders of varying radii. A straight length of fibre after the bend was held constant at ~15 cm. Supplementary figure 3 shows the relative transmitted intensities as measured using an FTIR spectrometer for a straight ~50 cm long fibre and the same fibre bent with different bending radii. Transmission (arb. u.) straight bent r=10.5 cm bent r=8.3 cm bent r=6.5 cm bent r=4.3 cm Wavelength (microns) Figure 3 (supplementary). Transmitted intensity vs. wavelength for a ~50 cm long hollow fibre measured using an FTIR spectrometer. Transmission for the straight fibre is compared to transmission for fibres bent at 90 degrees with different bending radii r, denoted on the chart.

3 The FTIR bending measurements shown in figure 3 give a total bending loss value below 1 db for the bend with the largest radius; this loss increases by a few tenths of a db with decreasing bend radius. In order to corroborate this behavior with CO 2 laser measurements, similar tests were performed using a ~2.5 meter long fibre and our CO 2 laser measurement setup. Supplementary figure 4 depicts the average bending loss in db for 90 degree bends like those described above, referenced to the straight fibre case. 1.3 Bending Loss (db) Bend curvature (1/m) Figure 4 (supplementary). Measured bend loss vs. bend curvature for CO 2 laser transmission through 90 degree fibre bends. The fibre was ~2.5 meters long with a core diameter of 700 microns and was bent 15 cm from the output. Loss values are obtained by comparing the total transmitted power through the bent fibre to the same fibre when held straight. These CO 2 laser bending loss results represent an average of multiple trials; the variability in observed losses is on the order of 0.2 db. This variability can be attributed to the multi-mode operation regime. These results have the same qualitative characteristics as those obtained using the FTIR. It should be noted that the two light sources used have different coherency, numerical aperture and polarization state and it is thus expected that they would couple to modes having different loss characteristics. It is of interest to analyze the effects of fibre core size on the bending losses and modal characteristics. Reducing the core size will reduce the number of propagating modes and thus may also reduce the bending losses since the inter-mode coupling coefficient depends on ( β) -1, i.e. the difference in the propagation constant between modes 3. However, decreasing the core size should also increase total propagation losses due to material interaction, increased radiation, and perturbation by the inner seam of the fibre. These competing effects are reserved for future study.

4 III. CO 2 laser measurement apparatus and further description of cutback measurements The CO 2 laser (10.6 microns) apparatus assembled and utilized for both fibre cutback and bending loss measurements described in this work is shown below in supplementary figure 5, with the HeNe laser (633 nm) alignment beam. HeNe guide laser mirror Dual-position locking mirror ZnSe beamsplitter ZnSe focusing lens assembly CO 2 laser Dualchannel powermeter High-power detector Reflected beam absorber Pinhole aperture assembly Fibre mount Hollow PBG fibre Figure 5 (supplementary). CO 2 laser measurement apparatus. The apparatus consists of a 25 watt CO 2 laser (Coherent) that is precisely aligned with a HeNe laser. The path of the HeNe laser traces the path of the CO 2 laser when the locking mirror is in the down position, as shown. The HeNe can be readily transmitted through the hollow fibre by glancing specular reflections when the fibre is nominally straight. A ZnSe beamsplitter is placed in the beam path and the reflected beam is recorded as a reference. The transmitted beam then passes through a ZnSe focusing lens assembly as well as a pinhole aperture assembly and finally is coupled into the fibre. Data is collected simultaneously from the beamsplitter reference beam and the fibre output using a Newport dual-channel powermeter with a GPIB/LabView computer interface. In the cutback measurements, the fibres could not be fractured or cleaved by conventional cutting methods due to the toughness of the polymer. It was found that a swift razor-cutting action produced fairly reproducible cuts. In order to account for any residual variability in

5 cutting, many short cuts (1-2 mm) were performed around each data point recorded in the cutback measurement data shown in the main body of this work (figure 5 inset of main paper). Power levels were found not to vary greatly due to cuts (while data from obviously poor cuts were discarded). The resulting many similar power levels around each data point shown in the main paper, figure 5 inset, were averaged (while taking a length average within the few mm of change from the short cuts) to smooth out any cut variability. Thus, each data point shown in the main paper, figure 5 inset, is in fact an average of many highly similar data points that are separated by only a few mm. In addition, the power ratio between the transmitted and reference beams measured after each cut was time-averaged over several minutes, which was found to be more than adequate to smooth out any random detector fluctuations. As mentioned, the fibre was held fixed at multiple points (with a constant number of fastening points for each measurement) throughout the entire cutback experiment to minimize modal and input coupling variations. These meticulous techniques resulted in straight fibre attenuation data with very satisfactory statistical correlation, as shown by the quality of the curve fit in the inset of figure 5 shown in the main body of this work. IV. Description of movie In the movie included as supplementary information to this work, a CO 2 laser transmission experiment through our fibre is shown. The video traces the path of a 2.5 meter long fibre (which appears dark) from the input and through multiple bends to the output where a target is placed. The target consists of a PES film, which is the majority component of the fibre, backed by a piece of ordinary yellow paper. When the laser is switched on, the invisible infrared beam emerging from the bent fibre melts the PES film and burns through the paper backing. The fiber is easily manipulated by hand to form a burn pattern on the PES target using the output laser beam. Up to 0.4 W of power was transmitted in this trial through a fibre with a core diameter of 700 microns. This video demonstrates a key theme of this paper, namely the enormous reduction in fibre transmission-loss relative to the intrinsic materials-loss of the constituents. References 1. Ibanescu, M., Johnson, S.G., Soljacic, M., Joannopoulos, J.D., Fink, Y., Weisberg, O., Engeness, T., Jacobs, S.A., & Skorobogatiy, M. Analysis of Mode Structure in OmniGuide Fibers. Submitted for publication. 2. Matsuura, Y., Abel, T., Hirsch, J. & Harrington, J. A. Small-bore hollow waveguide for delivery of near singlemode IR laser radiation. Electronics Letters 30, (1994). 3. Johnson, S. G. et al. Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers. Optics Express 9, (2001).

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