Plasmonic gain in long-range surface plasmon polariton
waveguides bounded symmetrically by dye-doped polymer
Choloong Hahn,1 Seok Ho Song,1 Cha Hwan Oh,1 and Pierre Berini2,3,4
1Department
2School
of Physics, Hanyang University, Seoul, 133-791, Korea
of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Ontario K1N 6N5,
Canada
3Department
4Centre
of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
for Research in Photonics at the University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
Supplementary Information:
Position-dependent lifetime near metal surface
The lifetime of a dipole becomes a function of position when a dipole is placed near a metal surface. The
position dependence comes from several decay channels created due to the presence of the metal. p(y) can be
written as:1–3


 p (d )    nr    P(u, d )du
0

1
,
(S1)
where nr = 1   is the non-radiative decay rate,  is the quantum yield of the dipole,  is the positionindependent lifetime, d is the distance of dipole from metal surface, u is the dipole’s field wave-vector parallel
to the metal surface normalized to the far-field wave-vector, and P(u,d) is the averaged power dissipation
density over all possible dipole orientations normalized by the power dissipation far from the metal surface.
P(u,d) can be computed as function of u for a dipole placed at a certain distance from metal surface. In the
computations, we assume that IR140-doped PMMA is deposited onto a 25-nm-thick Ag thin film and we take 
= 0.167 for IR140.4 The computed P(u,d) for two cases are plotted in Figs. S1(a) and S1(b), for several distances
between the dipole and the Ag film surfaces. Fig. S1(a) represents P(u) at d = 0.1, 1, 10, 100 nm when the
IR140-doped PMMA layer is optically semi-infinite. The IR140 dye in PMMA layers have several decay
channels including decay into radiative modes (RAD), decay into the LRSPP and the short-range SPP (SRSPP),5
and direct decay to the metal through the creation of electron-hole (EH) pairs therein. As shown, at small d (the
dipole placed close to the metal surface), the decay to EH pairs becomes dominant and eventually the optical
gain efficiency decreases (i.e., quenched). P(u) at finite PMMA thickness (950 nm was assumed in this
computation) is plotted in Fig. S1(b). It shows same decay channels with the semi-infinite case, but it has
additional decay channels due to guided modes (GM). Since the thickness of PMMA layer is finite, guided
modes within the PMMA are supported. This produces a different behavior for the position-dependent lifetime.
FIG. S1. Normalized power dissipation density P(u) of IR140 at labeled distances from the corresponding Ag surface in: (a)
semi-infinite-thick PMMA layer, and (b) finite-thick PMMA layer.
References:
1
I. De Leon and P. Berini, Opt. Express 17, 20191 (2009).
2
W. L. Barnes, J. Mod. Opt. 45, 661 (1998).
3
G. W. Ford and A. Arbor, Phys. Rep. 113, 195 (1984).
4
K. Rurack and M. Spieles, Anal. Chem. 83, 1232 (2011).
5
M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, Nat. Photonics 4, 457 (2010).