There is one particular hollow-core fiber cladding design, however, formed by the periodic arrangement of the David’s star, also known as the Kagomé lattice, which displays notoriously wideband guidance. It was not until 2007 that a better theoretical understanding of Kagomé fibers guidance was developed, and it was shown that although this special lattice did not exhibit photonic bandgaps it could guide light with reasonably low loss (~dB/m). Among the reasons for such a delayed understanding of the guiding principles is the high-frequencies involved in the numerical modeling, as measured by the normalized wavevector k0Λ, where k0 is the vacuum wavevector and Λ is the cladding unit-cell pitch. Such high frequencies usually lead to computationally expensive simulations. Despite the rich and complex photonic density of states in such fibers, simple capillary-waveguide based toy models were able to predict its basic guidance properties.
In this letter, Martin A. Finger and collaborators take these analytical models one step further and extend the early Marcatili and Schmeltzer model (MSM) to predict the group-velocity dispersion of Kagomé fibers using simple analytical formulas. As GVD is a fundamental parameter when dealing with phase matching in nonlinear interactions, the present work provides an effective design tool towards understanding and designing Kagomé fibers for both extreme and attosecond-fast nonlinear optics.
The authors also show that the naïve deployment of Marcatili’s model to calculate the effective refractive index may lead to large errors beyond a critical wavelength. This critical wavelength is approximately given by the geometric mean between the core radius and its glass wall thickness; in typical kagomé fibers such critical wavelength is as short as 800 nm, limiting the predictive power of the MSM. To overcome this limitation the authors provide a single parameter empirical relation that redefines the equivalent core area, extending the model’s predictive power well into the near infrared. Since the MSM deals with a circular fiber, one must define an effective core radius for the hexagon-shaped kagomé fiber core. One common choice is the area-preserving radius, which maps the Kagomé core to a circular fiber with equivalent core area. To overcome this limitation the authors provide a single-parameter empirical relation that redefines the equivalent core area, extending the model’s predictive power well into the near infrared.
All in all, this work provides a simple design guideline to predict the dispersive properties of Kagomé fibers. This is of great value given the computational cost involved in the full numerical simulation of such fibers. Further usage of the proposed guidelines may confirm its robustness and validity within different cladding designs that do not rely on photonic bandgaps.
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