b2815 Tissue Engineering and Nanotheranostics “9.61x6.69”

154 Tissue Engineering and Nanotheranostics

ext 2 () ()

1

2

2 1 Re LL,

L

L ab

k

p ∞

σ

=

=++∑ 

(2)

σσσabs=−ext sca, (3)

where k is the incoming wave vector and L are integers representing

the dipole, quadrupole, and higher multipoles of the scattering. The

scattering coefficient can be simplified somewhat by introducing the

Riccati–Bessel functions:

()()()

ψρρρξρρρ==, .()^1 ()

jhnn nn (4)

Then, aL and bL are the following parameters:

()()()()

()()()()

L LL LL,

L L LL

m mx x mx x

a

m mx x mx x

ψψψψ

ψξψξ

′′−

=

′′−

(5)

()()()()

()()()()

L L L LL.

L L LL

mx x m mx x

b

mx x m mx x

ψψψψ

ψξψξ

′′−

=

′′−

(6)

Here, n is the complex refractive index of the metal, and nm is the

refractive index of the surrounding medium. Also, r is the radius of

the particle, and km = 2 p/λm is defined as the wave number in the

medium rather than the vacuum.

If the nanoparticle is assumed to be very small as compared to the

wavelength, the Riccati–Bessel function can be approximate by power

series. Following Bohren and Huffman, if one and keeps only terms

to order, and switches the refractive index to dielectric function, then

Equations (1) and (2) simplify to

()

()()

3

(^22)
ext (^22)
12
(^18) ,

2

m

m

pεV ελ

σ

λ ελεελ

=

++

(7)