108
6 Light Scattering by Dielectric Bodies of Irregular …
Denoting matrices by Q
11
01 and Q
31
01 we can write expression (6.15) in the form
a
j
b
j
= T
j
1
p
j
q
j
, T
j
1 = −Q
11
01 (k, k 1 ) · [Q
31
01 (k, k 1 )]
−1
.
(6.16)
The elements of matrix T
j
1 can be expressed in the form of surface integrals:
I
11
1mnm n = α(−1)
m
s
[M
3
(−mn) (kr) × M
1
(m n ) (k 1 r )]ndS,
(6.17)
I
12
1mnm n = α(−1)
m
s
[M
3
(−mn) (kr) × N
1
(m n ) (k 1 r )]ndS,
(6.18)
I
21
1mnm n = α(−1)
m
s
[N
3
(−mn) (kr) × M
1 (m n ) (k 1 r )]ndS,
(6.19)
I
22
1mnm n = α(−1)
m
s
[N
3
(−mn) (kr) × N
1 (m n ) (k 1 r )]ndS,
(6.20)
I
11
1mnm n = α(−1)
m
s
[M
1
(−mn) (kr) × M
1
(m n ) (k 1 r )]ndS,
(6.21)
I
12
1mnm n = α(−1)
m
s
[M
1
(−mn) (kr) × N
1
(m n ) (k 1 r )]ndS,
(6.22)
I
21
1mnm n = α(−1)
m
s
[N
1
(−mn) (kr) × M
1
(m n ) (k 1 r )]ndS,
(6.23)
I
22
1mnm n = α(−1)
m
s
[N
1
(−mn) (kr) × N
1
(m n ) (k 1 r )]ndS,
(6.24)
where α = k
2
/π .
6.3 Explicit Expressions for the Integrals with Vector
Products of Vector Spherical Functions
Let us write the expression for the normal of the object in the Cartesian system of
coordinates:
n = n x i + n y j + n z k,