Effective index numerical modelling of microstructured chalcogenide-glass fiber for frequency conversion to the mid-infrared band

Chalcogenide glass fibers offer broad transparency range up to the mid-infrared and high nonlinear coefficients making them excellent candidates for four wave mixing frequency conversion. However, the use of microstructured air-chalcogenide fibers is mandatory to achieve phase-matching in such a fiber. Numerical modelling of the phase matching condition can be done using the simplified effective index model, initially developed and extensively used to design air-silica fibers. In this paper, we investigate the use of the effective index model in the case of microstructured As2S3 and As2Se3 fibers. One essential step in the method is to evaluate the core radius of a step-index fiber equivalent to the microstructured fiber. Using accurate reference results provided by finite-element computation, we compare the different formulae of the effective core radius proposed in the literature and validated for air-silica fibers. As expected, some discrepancies are observed, especially for the highest wavelengths. We propose new coefficients for these formulae so that the effective index method can be used for numerical modelling of propagation in air-chalcogenide fibers up to 5 mu m wavelength. We derive a new formula providing both high accuracy of the effective core radius estimate whatever the microstucture geometry and wavelength, as well as uniqueness of its set of coefficients. This analysis reveals that the value of the effective core radius in the effective index model is only dependent on the microstructure geometry, not on the fiber material. Thus, it can be used for air-silica or air-chalcogenide fibers indifferently.