We also investigated the influence of rotating the antiresonant tubes on the con- finement loss. Close up examples of the antiresonant tube rotations are given in Fig. 2.8: (a) for several different rotation angles θ; and (b) for two different values ofηsuperimposed, whenθis fixed. The rotation may occur unintentionally during the fabrication process, and hence this study gives an indication of the fiber fabrication tolerance. When the tubes are rotated, the symmetry is broken, and we cannot calculate the confinement loss only with the quarter structure. Therefore, here we must use the full structure in the calculation domain. Figure2.8(c) shows the confinement loss as a function of the antiresonant tube rotation angleθfor several different values ofηatλ =1.06µm. It clearly indicates that the confinement loss depends strongly onθ. The loss increases dramatically above a critical angle. One can see from Fig.2.8(a), that when the antiresonant element rotates, the extra resonator formed at the node between the antiresonant tube and its nested element moves closer to the core. This enhances coupling between the core and the clad- ding modes, and thus the overall loss increases. Figure2.8(c) also shows that the critical angleθcrit, which is the angle where the confinement loss is doubled from
Figure 2.8 Schematic diagram of one antiresonant tube in the fiber showing (a) the rotation of
the nested element at several different rotation angles, and (b) the rotated nested element for two differentη, whenθis fixed. ER denotes the extra resonator formed at the node between the antiresonant tube and the nested element. NCnis the negative curvature of the nested element. The
confinement loss as a function of the rotation angleθis presented in (c) for several different values ofη. The solid dots indicate the critical angleθcrit. (d) (left) The confinement loss as a function of
four different cases of random rotation angleθof ellipticity of the nested tubes forη=0.55. The
selected four different cases are shown at the right-hand side of panel (d).
tolerance. We can explain this by noting the relative position between the negative curvature in the nested element and the extra resonator shown in Fig.2.8(b). It shows that whenηis small, the extra resonator is more easily exposed to the LP01
mode than whenηis large. Hence, whenηis small, LP01 mode is significantly
affected by the extra resonator at a smallerθ, leading to a smallθcrit. The effect
2.8 Summary 35 antiresonant fiber, i.c. NANF[23]. Comparing the two results shows that the fiber structure proposed in this work is more susceptible to the rotation due to extra resonator approaching closer to the core with the rotation. Figure2.8(d) shows the results of additional analysis of the fabrication tolerance. Here, we consider random angle distribution of randomly chosen nested elliptical tube. It shows better loss performance compared to Fig.2.8(c) as the deviations in the value of loss are much smaller. This is due to the fact that if any of the elliptical tubes is rotated randomly then the smaller number of extra resonators will be approaching the core. Therefore, the fiber structure will be less sensitive to the rotation of the tubes.
2.8.
Summary
In this chapter, we propose a new type of negative curvature fiber. It has antireson- ant tubes nested by an elliptical element that provides active negative and positive curvatures. Our numerical results show that despite using only a single nested tube, ultra-low loss is achievable overλ =0.9µmto1.8µm. We also studied the single-modeness of the fiber, which can be effectively controlled by changing the ellipticity or circularity of the nested element. Therefore, the fiber is highly suitable for low-loss, single-mode delivery of ultrashort pulses in the near-infrared region, which makes it an excellent candidate for applications in ultrafast nonlinear optics and high-speed data transmissions.
CHAPTER 3
Empirical representation of
hollow-core antiresonant fibers
In recent years, there has been a remarkable improvement in the guiding proper- ties ofHC-ARFs because researchers have been paying much more attention on improving the guiding properties. Simultaneously, they are also taking a signi- ficant care to obtain the guiding properties easily as possible. One way to obtain the guiding properties of HC-ARFs accurately is to use numerical approaches. However, the geometrical complexity ofHC-ARFs often leads to large computer resource requirements. On the other hand, a capillary approximation can be used conveniently to get the guiding properties. In this case, a careful formulation of the approximations is crucial for obtaining accurate results. Marcatili and Schmeltzer derived analytical formulae for dispersion and confinement loss of hollow dielectric waveguides, which work well for simple capillary fibers [8]. Travers et al. utilized this model and employed a different core approximation for use in the dispersion of kagome-lattice photonic crystal fibers [38]. Later, Finger et al. proposed an empirical formula for obtaining more accurateGVDof kagome-lattice photonic crystal fibers [78]. Vincetti presented an empirical formula for the confinement loss of single-element negative-curvature fibers [79]. More recently, Tani et al. in- corporated the anti-crossing dispersion for the resonances into the capillary model and demonstrated the important role of the resonance term in ultrafast nonlinear
3.1 Fiber structure 37 applications [80].
In this work, we present empirical formulae describing the guiding properties of
HC-ARFs. Namely, our model introduces a GVDformula that is accurate over a wider spectral range. Additionally, we introduce a formula for obtaining the effective mode area ofHC-ARFs.
3.1.
Fiber structure
Figure3.1presents idealized cross sections of negative-curvatureHC-ARFs that are considered in this work. Each structure consists of different number of antiresonant
Figure 3.1 Idealized cross-sectional structures of negative-curvatureHC-ARFs with (a)n=6, (b) n=8and (c)n=10.Randtgdenote the core radius and the glass-web thickness, respectively. The
antiresonant tubes have the outer diameterd, andgis the perimeter gap.
tubesn, i.e. (a)n= 6, (b)n =8and (c)n= 10. TheHC-ARFs have core radiusR, the glass-web thicknesstgand the perimeter gap between the antiresonant tubes g.
Then, the outer diameter of the antiresonant tubedis given by:
d= 2Rsin (π /n)−g
1−sin (π /n) . (3.1)
In order to numerically calculate the guiding properties of these structures, we employ theFEM. For accurate numerical simulations, we use mesh resolution of up toλ/8and apply an optimized perfectly-matched layer on the boundary. By carefully analyzing the numerical results, we were able to obtain empirical formulae for characterizing the guiding properties of a large variety ofHC-ARFs over a wide spectral range. Note that in this study, we consider only the fundamental mode.