Gaussian and sech approximations of mode field profiles in photonic crystal fibers

We propose using the least square method for approximating the electrical field distribution of the fundamental mode in photonic crystal fibers (PCFs) by using a Gaussian and a hyperbolic-secant (sech) function. It is shown that the mode field can be fitted closely to a Gaussian for large d/Λ values (i.e., for strongly guiding structures). For small d/Λ values (for weakly guiding structures), a sech function fits the mode field well because the field gradually extends into the cladding region, implying that the analogy of PCFs with step index fibers is not applicable in this regime.