what does divergence in the reflectivity mean?

Dale

Recently I was reading some paper on design surface plasmon polaritons(so called "SPPs") on corrugated surfaces, mainly these two papers listed below:

1.Pendry, J. B., et al. (2004). "Mimicking surface plasmons with structured surfaces." Science 305(5685): 847-848.

2.Garcia-Vidal, F. J., et al. (2005). "Surfaces with holes in them: new plasmonic metamaterials." Journal of Optics a-Pure and Applied Optics 7(2): S97-S101.

It shows that bound electromagnetic surface waves mimicking SPPs can be sustained even by a perfect conductor.

in these two papers, they just take corrugated surfaces as an effective medium dielectric, and calculate the dispersion relation formula from the divergence of the reflectivity between air and effecective medium.

It is comment by "Maier, S. A. (2007). Plasmonics: fundamentals and applications, Springer Verlag." that: the reasoning behind this technique is that the surface mode resonance corresponds to a divergence in the reflectivity - the mode can exist for a vanishingly small excitation.

As I know, the max value of reflectivity is 1, so as these 2 papers treat denominator of reflectivity as zero and make it infinite. I am puzzled here.

Could any one help me? thanks for any reply!