Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches

摘要

The accuracy of the solution of the fundamental space-filling mode of photonic crystal fibers by scalar and vec-torial analytical approaches and its effect on the effective index models are investigated. Using a plane wave method as a benchmark, we show that the optimal choice of the radius of the equivalent circular unit cell used in the approximations is different for the two approaches and this value has a great effect on the accuracy of the solution of the fundamental space-filling mode. We also show that the vectorial approach with a properly defined value of the radius is highly accurate over a wide parameter range, whereas the scalar approach causes the main error in the scalar effective index model. We also confirm that a fully vectorial effective index model is accurate and efficient in the case of photonic crystal fibers with large air filling fractions.