Photonics Research, 2017, 5 (2): 02000088, Published Online: Sep. 26, 2018
Analytical formulation for the bend loss in single-ring hollow-core photonic crystal fibers Download: 963次
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Fig. 1. (a) Sketch of the geometry of a single-ring HC-PCF, showing the local coordinate system. The inner diameter of the six capillaries is d , and the core diameter (the minimum distance between two diametrically opposite capillaries) is D . (b) Index difference Δ n 01 01 between LP 01 -like core and capillary modes, plotted against R / D for d / D = 0.696 at four different values of λ / D .
Fig. 2. Numerically calculated axial Poynting vector distributions and loss α of a single-ring PCF with d = 55 μm , D = 79 μm , λ = 2.8 μm and capillary wall thickness t = 1.15 μm , for (a) bend radius slightly greater than R cr 01 = 17.2 cm , (b) close to R cr 01 , and (c) and (d) close to the radius of curvature that phase-matches the LP 01 core mode to capillaries placed at θ = ± 60 ° . The arrows indicate the polarization of the electric field.
Fig. 3. Numerically calculated bend loss for the fibers for θ = 0 ° , plotted against normalized bend radius R / D . A : ( d , D , λ ) = ( 55,79 , 2.8 ) μm , i.e., d / D = 0.70 and λ / D = 0.035 . B : ( d , D , λ ) = ( 22,36 , 1.2 ) μm , i.e., d / D = 0.61 , λ / D = 0.033 . The dashed vertical lines mark the corresponding analytical solutions for the critical bend radius using Eq. (4 ) with θ = 0 ° . The dotted vertical line shows the bend radius for phase-matching to the capillaries at θ = ± 60 ° . In each case the loss is calculated for modes polarized normal to the bend, i.e., in the y direction in Fig. 1(a) .
Fig. 4. Experimentally measured bend loss in two fibers with the same shape parameters as in Fig. (3 ). (a) d / D = 0.70 and (b) d / D = 0.61 . The bend radii were changed in steps of 1.25 cm, and between these steps the colors are interpolated. The measured loss versus wavelength in (b) was smoothed with a moving average filter. The gray rectangle in (a) marks the region where the core mode phase-matches to a resonance in the walls of the capillaries, causing high attenuation. In each case, the white solid and dashed lines are solutions of Eq. (4 ) for θ = 0 ° and θ = 30 ° , respectively.
Michael H. Frosz, Paul Roth, Mehmet C. Günendi, Philip St.J. Russell. Analytical formulation for the bend loss in single-ring hollow-core photonic crystal fibers[J]. Photonics Research, 2017, 5(2): 02000088.