Thermodynamic limit to light trapping in thin planar structures

Thermodynamic limit to photonic-plasmonic light-trapping in thin films on metals

“…7 However, Stuart and Hall wrote r m ¼ C m av m g u m (their Equation (15)); v m g is the group velocity of mode m, not the group velocity for a radiative mode. 3 As a consequence, their expression (18b) for f m (the fractional absorption) contains v m g =v 0 g , which is the ratio of the group velocity of the waveguide mode to the ordinary speed of light in a material of index n. With our interpretation, the ratio is v 0 g =v 0 g , which of course simplifies their expression to the one we've used (Eq. (4) above).…”

“…In this paper we shall use the basic formalism developed by Stuart and Hall for their calculations of the thermodynamic limit for the absorptance of a thin semiconductor film 3 ; they note that their approach is an application of the extended radiance theorem proven by Bassett. 14 In this section we briefly reprise some of their results that we use subsequently when surface plasmon polaritons are incorporated.…”

“…(18b) of Stuart and Hall's paper, 3 but is simpler because of a somewhat different interpretation of absorption coefficients a. This issue is treated in the Appendix.…”

“…For a sample this thin classical expression (4n 2 ) needs some adjustment for waveguide mode cutoff effects. 3,7 In Fig. 7 we present our calculations for the full absorptance spectra A 0 scl for a series of values of c p ; we chose the plasma frequency to obtain a surface plasmon resonance at k sp ¼ 853 nm, corresponding to the enhancement maximum in Fig.…”

“…For simplicity, he used the volume density-of-states of an infinite dielectric to obtain the 4n 2 result. The ergodic approach has been extended to accommodate more general forms for the photonic density of states, including exact treatments of waveguide modes, 3 and of multiplelayer dielectric structures. 4,5 Non-ergodic treatments of periodic gratings imposed on the metal and the thin-film layers have indicated light-trapping larger than inferred from the 4n 2 limit.…”