Open Access
Add to BibSonomyAbstract
Hollow silica capillaries are examined as optical waveguides evaluating the antiresonant reflecting optical waveguide (ARROW) effect by sequentially reducing the wall thickness through etching and measuring the optical transmission. It is found that the periodicity of the transmission bands is proportional to the wall thickness and that the propagation loss is of the order of a few dB/m.
© 2013 Optical Society of America
1. Introduction
Antiresonant reflecting optical waveguiding [1] has been identified to play an important role in electromagnetic wave transmission in different systems, such as planar structures [2–6], THz waveguides [7–9] and in infrared radiation fibers [10–12]. The importance of antiresonance has also been reported in the context of Bragg fibers [13–17] and photonic crystal fibers (PCFs) [18,19], including Kagome fibers [20,21] and fibers with a “negative curvature” arrangement [22–24]. Due to its simplicity, capillary designs have been the basis of numerical studies [25–27] of the optical loss and spectral dependence in more complex waveguides such as PCFs with many holes, to understand the role of antiresonance. A capillary tube is a very simple glass structure that can in principle make use of the antiresonance interference from the inner and outer walls to allow for light propagation in the air-hole, otherwise forbidden in total internal reflection fibers. Although visible light guidance in the air-hole of a capillary has been reported [28,29], the role of antiresonance waveguiding was not detailed. The possibility of guiding visible light in a simple capillary over considerable distances has potential importance in optofluidic applications [30,31]. Here, we study visible and near-infrared light propagation in thin-walled silica capillaries and the effect of varying the capillary wall thickness. The light guidance at particular wavelengths is consistent with the ARROW mechanism. Cutback measurements and analytical calculations are used to estimate the propagation loss of the capillaries.
2. Measurements
Two different silica capillaries are used in the present study and their cross-sections are shown in Fig. 1. Both capillaries have outer diameter ~125 µm and the wall thicknesses are approximately 9.5 µm and 18.5 µm, respectively. The capillaries are drawn protected by a conventional acrylate layer of thickness ~125 µm, not shown in Fig. 1. The results discussed below are taken with the capillaries chemically stripped from the acrylate protection with H2SO4 at 120 °C.
Fig. 1 Cross section of capillary with 125 µm outer diameter and (a) 9.5 µm and (b) 18.5 µm wall thickness.
When light from an NKT Photonics SuperK COMPACT white light source is launched through a 6 cm focal length lens into the hollow center of the capillaries, a relatively round symmetrical mode is observed through capillary sections tens of centimeters long, as seen in Fig. 2 (taken for 70 cm). The capillaries are held relatively straight during the measurement.
Fig. 2 (upper) Near-field output image from the 9.5-µm thick capillary. (lower) Near-field output image from the 18.5-µm thick capillary. White light is launched (a,b) into the glass wall, (c,d) partly into the glass wall and partly into the center of the capillary, and (e,f) into the center of the capillary.
A 20x microscope objective and an imaging camera allow for viewing the near-field distribution at the capillary end-face. Light is led by total internal reflection when the input beam is coupled into the glass walls as seen in Figs. 2(a) and 2(b). When the parallel beam is coupled into the hollow center, most of the guided light propagates in the air hole, as seen in Figs. 2(c) and 2(d). When focusing is optimized, all measurable guided light is in the hollow-core as seen in Figs. 2(e) and 2(f). The central spot is white when the alignment is optimized, gaining different colored stains for slight misalignment. Similar modal distributions are observed when a monochromatic light source is used (e.g. HeNe laser).
In order to evaluate the spectral content of the light transmitted in the center of the capillaries, an 1800 LP/mm grating is used to disperse the spectrum. Rather than a continuum distribution of colors as provided by the light source and displayed in Fig. 3(a), the transmission through the capillary is strongly modulated, as seen in Fig. 3(b).
Fig. 3 (a) input spectrum launched into the capillary fibers. (b) output spectrum transmitted through a 9.5-µm walled capillary.
The propagating light interacts with the capillary walls and undergoes a resonant reflection. Since the interaction with the glass walls takes place at grazing incidence as illustrated in Fig. 4, the antiresonant condition for the maximum reflection back into the core and the free spectral range (Δν) are given by [18]:
where h is the wall thickness, ν is the optical frequency, c is the speed of light, n1 = 1 and n2 = 1.444 are the refractive indices of the air core and the glass wall respectively, and N is an integer number.Fig. 4 Schematic setup of Fabry-Perot reflection off of the walls of the capillary assuming grazing incidence.
The antiresonant condition expressed by Eq. (1) has two features worth noting. It predicts that constructive interference is satisfied at specific values of optical frequency [18] and that the periodicity observed depends on the capillary wall thickness. In order to verify the validity of Eq. (1) in describing light guidance in a silica capillary, the glass wall thickness is varied in small steps by etching the capillaries in 40% hydrofluoric acid (HF). The optical input and output are kept relatively unaltered by splicing an input and an output fiber to a ~14 cm long piece of the capillary to be thinned down. The input fiber has a small core (Corning SMF28, 8 µm core diameter) and the output fiber a large core (50 µm core diameter for light collection). All fibers (for delivery, transmission, and collection) are etched simultaneously. After every etching period (15 or 30 s) the fibers are removed from the acid and a spectrum is recorded, using an Ocean Optics QE65000 spectrometer, shown in Fig. 5 for the 9.5-µm thick capillary. Care is taken to keep the capillary at constant tension throughout the characterization. As can be noted from Fig. 5(a), the separation between the transmission peaks increases for subsequent etchings.
Fig. 5 (a) Sequence of normalized measured spectra from a capillary with initial wall thickness of 9.5 µm, (b) Initial spectrum as a function of frequency showing periodic peak separation and (c) Fourier transform of frequency spectrum and calculated wall thickness (top axis).
When the spectra are plotted in the frequency domain as seen in Fig. 5(b), the separation between transmission peaks is relatively constant [18,26]. The fast Fourier transform (FFT) illustrated in Fig. 5(c) shows various peaks each situated at an integer multiple of the first peak. These harmonics arise from repeated reflections on the glass walls to result in constructive interference. The Q-factor for the Fabry-Perot reflections in the ARROW waveguide at 1.55 µm wavelength is estimated using Q = ν0/δνFWHM to be 25 for the 9.5-µm thick capillary and 95 for the 18.5-µm thick capillary.
Equation (1)(b) predicts a linear dependence between the thickness (h) and the reciprocal of the free spectral range (1/Δν). This is illustrated in Fig. 6 for both capillary thicknesses studied. The etch rate is measured to 1.22 µm/min and 0.91 µm/min for the 9.5-µm and the 18.5-µm thick capillary, respectively, the difference in etching rate is attributed to a difference in acid concentration. The interference patterns of the 18.5-µm thick capillary were only discernible down to ~6 µm thickness, after which the noise level grew too large, possibly due to the roughening of the fiber surface.
Fig. 6 Reciprocal of frequency peak separation versus wall thickness in capillaries with initial thickness 9.5 µm (black) and 18.5 µm (red) measured after etching during ~30 s periods.
To estimate the propagation loss, cutback measurements are performed. The output from a tunable laser source (ANDO TLS AQ4321A) is collimated and focused into the hollow core of the chemically stripped capillary using a 5x lens. The TLS is tuned to 1580 nm and 1510 nm to match the transmission maxima of the 9.5-µm and the 18.5-µm thick capillary in the tuning range of the TLS (1480 nm-1580 nm). The output power is measured using a broadband Ge photodetector as the capillary is cut to shorter lengths. The propagation losses, shown as the slopes in Fig. 7, are 6.0 dB/m and 9.7 dB/m for the 9.5-µm and the 18.5-µm thick capillary respectively.
Fig. 7 Normalized cutback measurement of transmission through 9.5-µm and 18.5-µm thick capillary. The loss (slope) is 6.0 dB/m for the former and 9.7 dB/m for the latter.
3. Numerical analysis
To estimate the theoretical propagation loss in the fiber, it is useful to calculate the angle with which different modes impinge on the inner walls of the capillary. In the schematic illustration of Fig. 4 it is seen that the propagation direction is nearly perpendicular to the normal of the surface (grazing incidence). The angles are calculated using the effective refractive index neff with the equation θ1 = sin−1(neff/n1). The effective refractive index is approximated using the dispersion relation [32]:
where uμν = [2.4048, 3.8317] are the two first roots to the eigenvalue equation Jμ-1(uμν) = 0 and r is the air core radius. The incidence angles are for both capillaries approximately 89.3° and 88.9° at 1.5 µm for the fundamental mode and the first high-order mode, respectively. Knowing the angles, the propagation loss can be estimated [7] by calculating the Fresnel reflections for the TE and TM modes and assuming a radial Fabry-Perot etalon, as shown for the first few modes in Fig. 8. The HEμν modes (μ≠1) are calculated as the arithmetic average of the TEµ-2ν and TMµ-2ν modes [25]. The periodicity of the calculated spectra closely matches the periodicity of the measured spectra, recorded with an ANDO AQ6317B optical spectrum analyzer for 1 m long capillaries without acrylic coating. The minimum propagation loss for the 9.5-µm thick capillary, found at 1.58 µm, is calculated to be 0.60 dB/m for the fundamental mode and 0.91, 2.45, and 3.82 dB/m for the TE01, HE21, and TM01 mode respectively. For the 18.5-µm thick capillary, the minimum propagation loss at 1.51 µm is found to be 1.11 dB/m for the fundamental mode and 1.68, 4.49, and 7.30 dB/m for the TE01, HE21, and TM01 mode respectively.. This can be compared to the propagation loss shown in Fig. 7 of 6.0 dB/m for the 9.5-µm thick capillary at 1.58 µm wavelength and 9.7 dB/m for the 18.5-µm thick capillary at 1.51 µm wavelength. The difference in loss between the two capillaries come from the difference in air-core radii This order-of-magnitude difference suggests that the light in the capillary measured by cut-back does not propagate solely in the fundamental mode, and implies that even lower propagation loss could be achieved if proper mode discrimination were employed.Fig. 8 Simulated propagation loss for the fundamental mode and the first higher order modes for (a) 9.5-µm and (b) 18.5-µm thick capillary.
4. Conclusion
The periodic frequency spectrum favoring wavelengths which satisfy constructive interference shown in Fig. 5(b) and the reduction of the capillary wall thickness which is linearly related to the reciprocal of the free-spectral range seen in Fig. 6 indicate that the visible and near IR light guidance discussed here is accurately described by the ARROW mechanism. The propagation loss for low-order modes is relatively low (few dB/m) considering that only two glass-air surfaces contribute to guidance. If multiple surfaces were to be employed in a Bragg fiber geometry, the propagation losses would be significantly reduced [27]. In a practical implementation of the capillary as a waveguide, any perturbation to the two reflecting surfaces can destroy the antiresonant reflection condition and significantly increase the loss. This includes coating residue along the outer surface and the mounting system for mechanical support. The mechanical support could be elaborated to act favorably in suppressing high-order modes and make the capillary more single-mode, a strategy used in PCF design.
Acknowledgments
All fibers used in this paper were fabricated by Acreo Fiberlab. Financial support from ADOPT Linnaeus Center in Advanced Optics and Photonics and the Swedish Research Council (VR) are gratefully acknowledged.
References and links
1. M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986). [CrossRef]
2. Y. Kokubun, T. Baba, T. Sakaki, and K. Iga, “Low-loss antiresonant reflecting optical waveguide on Si substrate in visible-wavelength region,” Electron. Lett. 22(17), 892–893 (1986). [CrossRef]
3. F. Prieto, A. Llobera, D. Jiménez, C. Doménguez, A. Calle, and L. M. Lechuga, “Design and analysis of silicon antiresonant reflecting optical waveguides for evanescent field sensor,” J. Lightwave Technol. 18(7), 966–972 (2000). [CrossRef]
4. T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, “Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration,” J. Lightwave Technol. 6(9), 1440–1445 (1988). [CrossRef]
5. J. M. Kubica, J. Gazecki, and G. K. Reeves, “Multimode operation of ARROW waveguides,” Opt. Commun. 102(3,4), 217–220 (1993).
6. D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, “Waveguide loss optimization in hollow-core ARROW waveguides,” Opt. Express 13(23), 9331–9336 (2005). [CrossRef] [PubMed]
7. C. H. Lai, B. You, J. Y. Lu, T. A. Liu, J. L. Peng, C. K. Sun, and H. C. Chang, “Modal characteristics of antiresonant reflecting pipe waveguides for terahertz waveguiding,” Opt. Express 18(1), 309–322 (2010). [CrossRef] [PubMed]
8. L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010). [CrossRef] [PubMed]
9. E. Nguema, D. Férachou, G. Humbert, J.-L. Auguste, and J.-M. Blondy, “Broadband terahertz transmission within the air channel of thin-wall pipe,” Opt. Lett. 36(10), 1782–1784 (2011). [CrossRef] [PubMed]
10. T. Hikada, T. Morikawa, and J. Shimada, “Hollow-core oxide-glass cladding optical fibers for middle infrared region,” J. Appl. Phys. 52(7), 4467–4471 (1981). [CrossRef]
11. Y. Matsuura, R. Kasahara, T. Katagiri, and M. Miyagi, “Hollow infrared fibers fabricated by glass-drawing technique,” Opt. Express 10(12), 488–492 (2002). [CrossRef] [PubMed]
12. A. Mazhorova, A. Markov, B. Ung, M. Rozé, S. Gorgutsa, and M. Skorobogatiy, “Thin chalcogenide capillaries as efficient waveguides from mid-IR to terahertz,” J. Opt. Soc. Am. B 29(8), 2116–2123 (2012). [CrossRef]
13. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68(9), 1196–1201 (1978). [CrossRef]
14. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core Omniguide fibers,” Opt. Express 9(13), 748–779 (2001). [CrossRef] [PubMed]
15. G. Vienne, Y. Xu, C. Jakobsen, H. J. Deyerl, J. B. Jensen, T. Sorensen, T. P. Hansen, Y. Huang, M. Terrel, R. K. Lee, N. A. Mortensen, J. Broeng, H. Simonsen, A. Bjarklev, and A. Yariv, “Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports,” Opt. Express 12(15), 3500–3508 (2004). [CrossRef] [PubMed]
16. C. Baskiotis, Y. Quiquempois, M. Douay, and P. Sillard, “Leakage loss analytical formulas for large-core-low-refractive-index-contrast Bragg fibers,” J. Opt. Soc. Am. B 30(7), 1945–1953 (2013). [CrossRef]
17. A. Baz, G. Bouwmans, L. Bigot, and Y. Quiquempois, “Pixelated high-index ring Bragg fibers,” Opt. Express 20(17), 18795–18802 (2012). [CrossRef] [PubMed]
18. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27(18), 1592–1594 (2002). [CrossRef] [PubMed]
19. P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, W. J. Wadsworth, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Realizing low loss air core photonic crystal fibers by exploiting an antiresonant core surround,” Opt. Express 13(20), 8277–8285 (2005). [CrossRef] [PubMed]
20. F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006). [CrossRef] [PubMed]
21. G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St J Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express 15(20), 12680–12685 (2007). [CrossRef] [PubMed]
22. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010). [CrossRef] [PubMed]
23. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow-core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011). [CrossRef] [PubMed]
24. W. Belardi and J. C. Knight, “Effect of core boundary curvature on the confinement losses of hollow antiresonant fibers,” Opt. Express 21(19), 21912–21917 (2013). [CrossRef] [PubMed]
25. M. Miyagi and S. Nishida, “Transmission characteristics of dielectric tube leaky waveguide,” IEEE. Trans. Microw. Theory and Technol. 28(6), 536–541 (1980). [CrossRef]
26. J.-L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. 11(3), 416–423 (1993). [CrossRef]
27. F. Poletti, J. R. Hayes, and D. J. Richardson, “Optimising the performances of hollow antiresonant fibres,” ECOC 2011, paper Mo.2.LeCervin.2 (2011).
28. R. Romaniuk, “Capillary optical fiber – design, fabrication, characterization and application,” Bulletin of Polish Academy of Science, Technical Sciences 56(2), 87–102 (2008).
29. M. Borecki, M. Korwin-Pawłowski, and M. Beblowska, “Light transmission characteristics of silica capillaries,” Proc. SPIE 6347, 634715 (2006). [CrossRef]
30. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1(2), 106–114 (2007). [CrossRef]
31. M. Borecki, M. L. K. Pawlowski, M. Beblowska, and A. Jakubowski, “Short capillary tubing as fiber optic sensor of viscosity of liquids,” Proc. SPIE 6585, 65851G (2007). [CrossRef]
32. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964). [CrossRef]
