Structural dependence of effective area and mode field diameter for holey fibers

A rigorous full-vector finite element method is effectively applied to evaluating the effective area Aeff and the mode field diameter (MFD) of holey fibers (HFs) with finite cross sections. The effective modal spot size (a half of MFD), weff, is defined with the help of the second moment of the optical intensity distribution. The influence of hole diameter, hole pitch, operating wavelength, and number of rings of air holes on Aeff and weff is investigated in detail. As a result, it is shown that Aeff and weff are almost independent of the number of hole rings and that the relation Aeff = piweff 2, which is frequently utilized in the conventional optical fibers, does not always hold, especially in smaller air-filling fraction and/or longer wavelength regions. In addition, we find that for HFs with large air holes operating at longer wavelengths, the mode profiles of the two linearly polarized fundamental modes are significantly different from each other, even though they are degenerate. Using the values of Aeff and weff obtained here, the beam divergence and the nonlinear phase shift are calculated and are compared with the earlier experimental results.