Performance of the effective index method in the modeling of nanoscale rectangular apertures in a real metal

We examine the performance of the widely used effective index method (EIM) in the modeling of a sub-wavelength rectangular hole in a real metal. Two different ways of applying the EIM, depending on the dimension (shorter or longer) considered first, are found to give very much different results for the modal characteristics of the modes guided by such structures. It is shown that the EIM gives accurate results only if one starts with the surface plasmon polariton (SPP) mode irrespective of shorter or longer dimension. The present findings should be useful in applying the EIM to analyze apertures of other shapes also.