15 Cooperative Effects in Plasmonics
547
(a)
(b)
Fig. 15.11 RET versus distance for R = 30 nm Ag NP is shown at θ = π/3 with (a) d a = d d = d
and (b) d a = 20 nm, d d = d using the full Eq. (15.61), the nonradiative (NR) channel only, Förster’s
transfer Eq. (15.45), and the Gersten–Nitzan (GN) model [62, 63]
be enhanced or reduced as compared to Förster’s transfer, consistent with experiment
[52–60].
We consider a donor and an acceptor near the surface of a metal NP (see inset
in Fig. 15.11) which are represented by pointlike dipoles located at r j with induced
moments p j (ω) = p j (ω)e j oriented along e j ( j = a, d). The dipoles are driven by
the common electric field,
p j (ω) = α j (ω)E(r j , ω) + δ jd p
0
d (ω),
(15.46)
where α j (ω) = α √
j (ω) + iα √√
j (ω) is complex polarizability assumed here isotropic,
p 0
d (ω) = α d (ω)e d E 0 is the donor’s initial dipole moment with some constant E 0
depending on excitation, and δ jk is Kroniker’s symbol. The electric field E is, in
turn, the solution of Maxwell’s equation with dipole sources [33]:
547
(a)
(b)
Fig. 15.11 RET versus distance for R = 30 nm Ag NP is shown at θ = π/3 with (a) d a = d d = d
and (b) d a = 20 nm, d d = d using the full Eq. (15.61), the nonradiative (NR) channel only, Förster’s
transfer Eq. (15.45), and the Gersten–Nitzan (GN) model [62, 63]
be enhanced or reduced as compared to Förster’s transfer, consistent with experiment
[52–60].
We consider a donor and an acceptor near the surface of a metal NP (see inset
in Fig. 15.11) which are represented by pointlike dipoles located at r j with induced
moments p j (ω) = p j (ω)e j oriented along e j ( j = a, d). The dipoles are driven by
the common electric field,
p j (ω) = α j (ω)E(r j , ω) + δ jd p
0
d (ω),
(15.46)
where α j (ω) = α √
j (ω) + iα √√
j (ω) is complex polarizability assumed here isotropic,
p 0
d (ω) = α d (ω)e d E 0 is the donor’s initial dipole moment with some constant E 0
depending on excitation, and δ jk is Kroniker’s symbol. The electric field E is, in
turn, the solution of Maxwell’s equation with dipole sources [33]: