Long-range surface modes supported by thin films

A detailed analysis of the surface modes of a thin slab of material of dielectric constant ${\mathrm{\epsilon }}_2$ (=${\mathrm{\epsilon }}_{\mathit{r}2}$-i${\mathrm{\epsilon }}_{\mathit{i}2}$) surrounded symmetrically by dielectric media is presented. Results show that in the thin-film limit, as well as the well-known long-range surface plasmon for a thin metal layer and the TM guided mode for a thin dielectric, a long-range surface mode exists for almost any value of ${\mathrm{\epsilon }}_2$. This is even true if the imaginary part of ${\mathrm{\epsilon }}_2$, ${\mathrm{\epsilon }}_{\mathit{i}2}$, is much larger than the real part ${\mathrm{\epsilon }}_{\mathit{r}2}$. We also find that a long-range surface mode may arise from the coupling between two surfaces which individually cannot support a surface mode. These are a pair of special coupled-surface modes which may exist below a certain critical film thickness and which have two separate propagation vectors each with the same field symmetry. It is also found that the inverse situation may pertain, that is for certain relative values of dielectric constants even though ordinary surface modes may exist, below a critical thickness the resulting coupled long-range mode no longer exists. The analysis has also been extended to practical situations with weakly absorbing surrounding media and to circumstances where the dielectric constants of the surrounding media are slightly different. Both of these effects modify the dispersion relations obtained for the simple case and introduce further limit thicknesses into the problem. Analytic formulas in the thin-film limit are presented for all the above situations and field distributions and energy flow (Poynting vector) profiles presented to illustrate as necessary the nature of the modes supported by these systems. Finally experimental results are presented which illustrate the rather sweeping conclusion that a long-range surface mode may exist on a thin film for almost all values of ${\mathrm{\epsilon }}_{\mathit{r}2}$ and ${\mathrm{\epsilon }}_{\mathit{i}2}$. This result paves the way for a range of optics experiments on absorbing structures.