Biomedical Engineering Reference
In-Depth Information
5.2 From Hyper Rayleigh Scattering to SHG
In the description of the interaction between light and matter, the optical properties of a molecule are
determined by its dipole moment (
µ
that can be described as
)
µ
=
µ
+
α
E
+
1
2
β
EE
+
(5.1)
0
where
E
is the driving electro-magnetic field,
µ
0
is the permanent molecular dipole, α is the molecular
polarizability that describes linear absorption and scattering of light, and β is a tensor describing the
first hyperpolarizability term, responsible for nonlinear scattering processes known as hyper-Rayleigh
scattering (HRS). The condition for a nonzero value of first hyperpolarizability (β) in a molecule is the
presence of an asymmetry of charge distribution, due to an electron donor and electron acceptor moi-
eties. Such asymmetry perturbs the electron oscillations in the dipole, introducing frequencies different
from that of the driving field. Figure 5.1 provides a simplified illustration of these principles.
Owing to the lack of energy absorption in scattering processes, HRS is characterized by phase and
energy conservation, leading to the possibility of coherent summation of the scattered waves from all the
irradiated molecules. To describe such coherent summation, we start from the behavior of a pair of HRS
emitters and illustrate the strong dependence of detectable HRS on the relative orientation of the emitters.
Figure 5.2a shows two parallel emitters located within a distance smaller than the optical wavelength.
When the molecules are irradiated with an electro-magnetic field, due to the alignment of their donor−
acceptor moieties, they emit in-phase HRS photons that will constructively interfere. If, on the other hand,
the two molecules are oriented antiparallel, as in Figure 5.2b, the opposition of their donor−acceptor moi-
eties produces out-of-phase HRS photons that will destructively interfere. Based on this simple example, it
(a)
ω
ω
(b)
A
ω
ω
D
2
ω
FIgurE 5.1
Basic principle of hyper-Rayleigh scattering. (a) The figure shows a symmetric dipole interacting
with an incoming electric field oscillating at a frequency ω. The induced electron oscillation (shown below the
dipole) follows the frequency and phase of the incident field, producing Rayleigh scattering at the same frequency
ω. (b) The asymmetric nature of the dipole, highlighted by its donor (D) and acceptor (A) moieties, produces an
asymmetry in the induced electron oscillation, introducing a component at frequency 2ω in the scattered light. This
component is termed hyper-Rayleigh scattering (HRS). (Inspired from Mertz, J. P.S.B.R. Masters, ed. Applications
of second-harmonic generation microsocpy. In
Handbook of Biomedical Nonlinear Optical Microscopy
, 2008.
Oxford: Oxford University Press. By permission of Oxford University Press.)
