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Bending-Induced Mode Coupling in Chalcogenide Negative Curvature Fibers Chengli Wei1, Jonathan Hu1, and Curtis Menyuk2,* 1
Baylor University, One Bear Place #97356, Waco, TX 76798 USA 2 University of Maryland Baltimore County, TRC 205A, 5200 Westland Blvd., Baltimore, MD 21227 USA *Email:
[email protected]
Abstract: We study the bending-induced mode coupling between the core and tube modes in chalcogenide negative curvature fibers. The fibers with a larger tube wall thickness can sustain a smaller bend radius. OCIS codes: OCIS codes: (060.2280) Fiber design and fabrication; (060.2390) Fiber optics, infrared
Negative curvature hollow-core fibers have drawn much attention in recent years due to their attractive properties such as low transmission loss, low nonlinearity, and large transmission bandwidth [1–3]. In negative curvature fibers, the surface normal to the core boundary is oppositely directed from the core. The guiding mechanism uses antiresonant reflection [4]. The delivery of CO2-laser radiation has been demonstrated in the chalcogenide negative curvature fibers [3]. It has been shown that bending of negative curvature fibers can lead to an increase of the leakage loss, which is caused by coupling between the core and cladding tube modes [2]. In this paper, we use numerical simulations to study the bending-induced leakage loss in chalcogenide negative curvature fibers with different tube wall thicknesses. We find that negative curvature fibers with a larger tube wall thickness, corresponding to a higherorder transmission band, can sustain a smaller bend radius than fibers with a smaller tube wall thickness, corresponding to a lower-order transmission band. Figure 1(a) shows the full negative curvature fiber geometry. The gray regions represent glass, and the white regions represent air. We model a negative curvature fiber with eight cladding tubes. We assume that the bend is along the x-axis, and we take advantage of the reflection symmetry with respect to the y = 0 plane to only keep values for which y > 0 in the simulation [5]. The inner tube diameter, dtube, and the inner core diameter, Dcore, are related by: Dcore = (dtube+2t)/sin(π/8) ̶ (dtube+2t). The parameter t denotes the thickness of the tube wall. We use a core diameter, Dcore, of 60 µm and a wavelength, λ, of 2 µm. The measured refractive index of the As2S3 chalcogenide glass is used in our simulation [6]. We calculate the fiber modes and their propagation constants using Comsol Multiphysics, a commercial full-vector mode solver based on the finite-element method. A conformal transformation is used to replace the bent fiber with a straight fiber that has an equivalent index distribution: 𝑛𝑛′(𝑥𝑥, 𝑦𝑦) = 𝑛𝑛(𝑥𝑥, 𝑦𝑦) ∙ exp(𝑥𝑥/𝑅𝑅), where R is the bend radius [2,7]. Figure 1(b) shows a contour plot of the bend loss as a function of bend radius and tube wall thickness. We observe that the losses are consistently high for the tube wall thicknesses t = 0.46, 0.92 and 1.38 µm that satisfy the resonance condition, 𝑡𝑡 = 𝑚𝑚𝑚𝑚/2/(𝑛𝑛12 − 𝑛𝑛02 )1/2 [4], where m is equal to a positive integer, while n1 = 2.4 and n0 = 1.0 are the real parts of the refractive indices of chalcogenide glass and air [6], respectively. We observe three transmission bands, I, II, and III, that are separated by the three high loss regions in Fig. 1(b). There are additional high loss regions that are
Fig. 1 (a) Negative curvature fiber geometry. (b) Bend loss of the fundamental mode with respect to the tube wall thickness and the bend radius.
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Advanced Photonics © 2015 OSA
Fig. 2 (a) Bend loss for the negative curvature fibers with the tube wall thicknesses of 0.30 µm, 0.75 µm and 1.20 µm. Mode fields at the bend radii of (b) 6.5, (c) 8.0 and (c) 10.0 cm, corresponding to the three crosses in Fig. 2(a). (e) Minimum bend radius as a function of tube wall thickness for given bend losses of 1, 2 and 3 dB/m.
marked by plus signs. In order to analyze these high loss regions, we plot the bend loss with fixed tube wall thicknesses of 0.30, 0.75 and 1.20 µm in Fig. 2(a). The high loss peaks in Fig. 2(a) correspond to the high loss regions in Fig. 1(b) that are marked by the plus signs. The mode fields for the tube wall thickness of 0.3 µm at the bend radii of 6.5, 8.0 and 10.0 cm, corresponding to the three crosses in Fig. 2(a), are shown in Fig. 2(b), (c) and (d), respectively. Coupling between the core and tube modes at the bend radius of 8.0 cm is visible, while there is no apparent coupling at the bend radii of 6.5 and 10.0 cm. Hence, the bend loss peaks in Fig. 2(a) are induced by the mode coupling between the core and tube modes in the negative curvature fiber [2]. We also observe that the peak in the bend loss for fibers with a larger tube wall thickness happens at a smaller bend radius. Mode coupling occurs when the effective indices of the core and tube modes are close. When there is no bending, our simulations show that the effective indices of the tube modes in the fibers with a larger tube wall thickness are smaller than those with a smaller tube wall thickness. The effective indices of the core modes are almost the same for the different tube wall thicknesses we consider here. Hence, the effective indices of the core and tube modes have a larger difference for the fiber with a larger tube wall thickness. Since bending effectively increases the effective index of the tube modes, the mode coupling in the fiber with a larger tube wall thickness happens at a smaller bend radius as shown in Fig. 2(a). Figure 1(b) also shows the minimum bend radius for a given loss. We then plot the minimum bend radius with respect to the tube wall thickness for given bend losses of 1, 2, and 3 dB/m in Fig. 2(e). We observe three transmission bands. As expected, a smaller loss requires a larger bend radius. We can also see that the minimum bend radius for any given bend loss shown in Fig. 2(e) decreases as the transmission-band order increases in the parameter range we study here. Hence, a negative curvature fiber with a larger tube wall thickness has a smaller minimum bend radius. The reason is that the mode coupling in the fiber with a larger tube wall thickness occurs at a smaller bend radius, as we explained earlier. The loss is 1 dB/m with a bend radius of 8.6 cm in the transmission band III, corresponding to a loss value of 0.54 dB/turn. In conclusion, we study the bending-induced mode coupling between the core and tube modes in chalcogenide negative curvature fibers. A fiber with a larger tube wall thickness can sustain a smaller bend radius due to the mode coupling between the core and tube modes. The reason is that the effective indices of the core and tube modes have a larger difference for a fiber with a larger tube wall thickness. [1] F. Yu and J. C. Knight, “Spectral attenuation limits of silica hollow core negative curvature fiber,” Opt. Express 21, 21466–21471 (2013). [2] W. Belardi and J. C. Knight, “Hollow antiresonant fibers with low bending loss,” Opt. Express 22, 10091–10096 (2014). [3] A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express 19, 25723–25728 (2011). [4] N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002). [5] T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [6] J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Computational study of a 3–5 μm source that is created by using supercontinuum generation in As2S3 chalcogenide fibers with a pump at 2 μm,” Opt. Lett. 35, 2907–2909 (2010). [7] M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
