Improved fully vectorial effective index method for photonic crystal fibers: evaluation and enhancement

In the effective index method, which models photonic crystal fibers by means of a step-index waveguide analogy, two critical parameters are the effective index of the cladding and the effective core radius. It has been shown that the use of an effective core radius as a function of the relative air hole diameter, or also of the relative wavelength, can improve the accuracy of this method. We show, by comparison with a rigorous finite-difference frequency-domain method, that the reported improved fully vectorial effective index methods have commonly adopted a radius of the equivalent circular unit cell, which does not give the best accurate effective cladding index as compared with the use of an equivalent circular unit cell having the same area as the hexagonal unit cell. Furthermore, by defining both the radius of the equivalent circular unit cell and the effective core radius as a function of the relative air hole diameter, and the relative wavelength, we believe that the fully vectorial effective index method can be further enhanced in terms of accuracy of both the effective cladding index and the modal index.