Chalcogenide negative curvature hollow-core photonic crystal fibers with low loss and low power ratio in the glass Chengli Wei1, Robinson Kuis2, Francois Chenard2, Jonathan Hu1,* 1
Baylor University, One Bear Place #97356, Waco, TX 76798 IRflex Corporation, 300 Ringgold Industrial Parkway, Danville, VA 24540 *Email:
[email protected]
2
Abstract: We study the chalcogenide negative curvature hollow-core PCFs. The leakage loss and power ratio in the glass decrease as the number of tubes increases or the ratio of tube wall thickness to diameter decreases. OCIS codes: (060.2280) Fiber design and fabrication; (060.2390) Fiber optics, infrared
Hollow-core photonic crystal fibers (PCFs) confine the light inside a hollow air core surrounded by a photonic crystal glass cladding, which can provide low loss and high power transmission [1–3]. Negative curvature hollow core fibers made by silica shows near to mid-infrared (IR) transmission [4]. Negative curvature means the surface normal to the core boundary is oppositely directed from the core [4,5]. The guiding mechanism is that the tube walls satisfy the condition of the antiresonance, which confines the light into the center core [4–7]. The guidance of the СО2-laser radiation at a wavelength of 10.6 μm in the chalcogenide negative curvature PCF was also demonstrated [5]. However, there is no detailed study on the optimal geometry to lower the leakage loss and power ratio in the glass in the chalcogenide negative curvature PCFs. In this paper, we will study the As2S3 chalcogenide negative curvature PCFs. We show that leakage loss and power ratio in the glass decrease as the number of tubes increases or the ratio of tube thickness to diameter decreases. Figure 1(a) shows the fiber core geometry for negative curvature PCFs. Note that the grey regions represent glass and the white regions represent air. Only a quarter of the geometry, as shown in Fig. 1(b), is used in modeling negative curvature PCFs because of the symmetry of the fundamental core mode. Note that tube diameter, dtube, and core diameter, Dcore, have the following relationship, Dcore = dtube/sin(π/Ntube)−dtube. The parameter, t, represents the thickness of the tube wall. We calculate the fiber modes using Comsol Multiphysics, a commercial full-vector mode solver based on the finite-element method. The measured refractive index and loss of the As2S3 chalcogenide glass are used in our simulation [8]. We search for the modes, which have majority of the power in the hollow core at a wavelength of 2 μm, as we vary the core diameter. One can obtain results for different wavelengths by scaling the wavelength and fiber geometry within the glass transmission region, since Maxwell’s equations are scale invariant [9]. Figure 1(c) shows the leakage loss and effective index of the mode as a function of core diameter. The number of tubes, Ntube, is 8 and the ratio of tube thickness to the tube diameter, t/dtube, is 0.06. Hollow-core PCFs have been fabricated with tube wall thickness to diameter ratios, t/dtube, between 0.02 and 0.12 [4−7]. Note that the first three resonant tube wall thicknesses are 0.45 μm, 0.9 μm, and 1.35 μm according to the resonant condition, t = mλ/2/(n2glass−n2air)1/2, where m is the resonance order [6]. The corresponding core diameters are 12 μm, 24 μm, and 36 μm. We can see the antiresonance transmission bands in the middle of two resonances. Note that the Band I is located below the first resonance at a core diameter of 12 μm. The minimum losses are around 2 dB/m at the core diameters of 22 μm and 35 μm, which are located in the transmission Band II and Band III. Since the fiber structures in Band I might give very small core size, we will focus on the fiber geometries in transmission band II in the rest of the analysis.
Fig. 1 (a) Full negative curvature PCF geometry. (b) A quarter of the fiber geometry used in simulation. (c) Loss and effective index of the mode for the negative curvature PCFs with 8 tubes and t/dtube = 0.06.
Fig. 2 (a) Minimum loss and (b) power ratio in the glass as a function of number of tubes.
Fig. 3 (a) Minimum loss and power ratio in the glass as a function of t/dtube in the fiber with 8 lattice tubes. (b) Minimum loss and the corresponding core diameter as a function of t/dtube in the fiber with 8 lattice tubes.
Then, we carry out the same analysis for fibers with different tube wall thickness to diameter ratios, t/dtube and different number of tubes, Ntube, of 8, 10, 12, and 14. Note that more tubes may increase some experimental complexity in the fiber drawing. Figure 2(a) and (b) show the minimum loss and power ratio in the glass for the modes in the negative curvature PCFs with different numbers of tubes. We can see that when the number of tubes increases from 8 to 14, both the loss and power ratio in the glass decrease. Figure 3(a) shows the minimum loss and power ratio in the glass as a function of tube wall thickness to diameter ratios, t/dtube, in the negative curvature PCFs with 8 lattice tubes. Figure 3(b) shows minimum loss and the corresponding core diameter as a function of t/dtube. Note that the red solid curves for the loss in both Fig. 3(a) and (b) are the same for the comparison. With the fixed tube thickness, t, to satisfy the antiresonance condition, PCFs with lower t/dtube have larger tube diameter, dtube, and core diameter, Dcore, which leads to lower loss and lower power ratio in the glass. We can see that one can achieve a leakage loss of 0.1 dB/km and a power ratio in the glass of 10−4 by using negative curvature PCFs with t/dtube = 0.02. In conclusion, we study the loss and power ratio in the glass with different fiber parameters in the chalcogenide negative curvature PCFs. We find that leakage loss and power ratio in the glass decrease as the number of tubes increases or tube wall thickness to diameter ratio decreases. [1] C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan & K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [2] P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). [3] J. Hu, and C. R. Menyuk, “Optimization of the operational bandwidth in air-core photonic bandgap fibers for IR transmission,” Opt. Commun. 282, 18–21 (2009). [4] 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, 1441–1148 (2011). [5] 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). [6] F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and Photonic Guidance of Multi-Octave OpticalFrequency Combs,” Science 318, 1118–1121 (2007). [7] W. Belardi and J. C. Knight, “Effect of core boundary curvature on the confinement losses of hollow antiresonant fibers,” Opt. Express 21, 21912–21917 (2013). [8] 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). [9] J. D. Joannopoulos, et. al., Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton U. Press, 2008).
