Abstract
An error was made in converting the units of bend radius within the computer program used to obtain the reported results. This caused the calculated values of the bending induced stress to be significantly smaller than their true value. Corrected results for stress within the fiber and bend losses are reported. Since bending-induced stresses cause a relatively small correction to the refractive index profile, these corrections result in no changes in the main conclusions of this work.
©2012 Optical Society of America
In evaluating Eq. (2) of the original manuscript [1], the coiling radii rx and ry were expressed in units of cm and the positions x and y were expressed in units of µm requiring an additional factor of 10−4 in the numerator of this expression. In the in-house computer program used to calculate the mechanical and optical properties of the fiber this factor was incorrectly entered as 10−6 as would be the case if converting from µm to m. This error caused the bending-induced stress to be effectively neglected. This error affected all of the reported results therefore all of the calculations were repeated.
Since the publication of the original manuscript, several improvements in the computational method have been made including a higher resolution mesh enabled by increases in available computational power, perfectly matched layer boundary conditions with element-wise arbitrary orientation, hybrid linear tangential quadratic nodal elements [2], and transverse variation of the modal propagation constant [3]. The corrected results reflect these improvements. Furthermore the overall stress field was normalized with respect to that of a pure fused silica fiber which maintains some residual stress. All of the figures and tables in the original paper have been revised to reflect the corrected results (see Figs. 1 –13 and Table 1 below). The original discussion regarding the numerical results remains valid with the revised loss values given here in the corrected figures. The main conclusion that a particular photonic crystal fiber design exhibits bend loss mode discrimination slightly superior to a comparable step index fiber stands. The author sincerely regrets this error.
References and links
1. B. G. Ward, “Bend performance-enhanced photonic crystal fibers with anisotropic numerical aperture,” Opt. Express 16(12), 8532–8548 (2008). [CrossRef] [PubMed]
2. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]
3. B. G. Ward, “Solid-core photonic bandgap fibers for cladding-pumped Raman amplification,” Opt. Express 19(12), 11852–11866 (2011). [CrossRef] [PubMed]