114
6 Light Scattering by Dielectric Bodies of Irregular …
for domain S 2 , where k is the wavenumber, ε is the permittivity of the medium, μ
is the permeability of the medium, ε 1 is the permittivity of the cell core, ε 2 is the
permittivity of the plasma membrane, E s is the scattered field, E I is the incident field,
E 1 is the internal field, and E 2 will be defined below.
Let us write the following integral equations [14]:
E I (r 1 ) + ∇ ×
s 2
n 1 × E 1 (r
1 )G(r 1 , r
1 )ds(r
1 ) +
i
kε
∇ × ∇ ×
s 2
n 1 × H 1 (r
1 )×
× G(r 1 , r
1 )ds(r
1 ) = 0,
(6.33)
−∇ ×
s 2
[n 2 × E 2 (r
1 )]G(r 1 , r
1 )ds(r
1 )−
−
i
kε 2
∇ × ∇ ×
s 2
[n 2 × H 2 (r
1 )]G(r 1 , r
1 )ds(r
1 )+
+∇ ×
s 1
[n 1 × E 1 (r
1 )]G(r 1 , r
1 )ds(r
1 ) +
i
kε 1
∇ × ∇ ×
s 1
[n 1 × H 1 (r
1 )]×
×G(r 1 , r
1 )ds(r
1 ) = 0,
where G(r, r
) and G(r, r
) are the Green functions.
The expression for the field scattered by the jth particle has the form
E s ( j) =
∞
n=1
n
m=−n
i E mn [a
j
mn N
3
mn + b
j
mn M
3
mn ],
(6.34)
Let us write the expansion of the wave incident on the surface of the jth particle
in vector spherical harmonics
E I ( j) = −
∞
n=1
n
m=−n
i E mn [ p
j
mn N
1
mn + q
j
mn M
1
mn ].
(6.35)
In view of the finiteness of the field at the center, the internal field of the particle in
the region 0 ≤ r ≤ r 1 (i.e., in the vicinity of the center of the particle) can be written
in the form
E 1 ( j) = −
∞
n=1
n
m=−n
i E mn [d
j
mn N
1
mn + c
j
mn M
1
mn ],
(6.36)