MATLAB Functions for Mie Scattering and Absorption

7
n
1
= ((
n
( zj ( z)
)'
2
2
!'
j
! $
n(
z)
n
+ n* + n+
) d(cos
) = 2n(2n
+ 1) &(
n + 1) + # (7)
!%
z z !"
n r
*
) 1
Now, the absorption cross section follows from integration over the radial distance r
inside the sphere up to the sphere radius a:
# a
2
2
!"( mn
cn
+ nn
dn
) $
2
' = k &"%
r dr
(8)
abs
n=
1 0
The integrand contains the radial dependence of the absolute-square electric field
2
E
averaged over spherical shells (all θ and φ, constant r):
! "
n=
1
2
2
( mn
cn
+ nn
dn
)
2 1
E =
(9)
4
and in terms of this quantity, the absorption efficiency becomes
Q
abs
=
x
4"
" 2 2
! E x'
dx'
2
x
0
(10)
where x’=rk=z/m. Note that (9) is dimensionless because of the unit-amplitude
incident field; In case of Rayleigh scattering (x1, the
maximum size parameter is strongly diminished.
3.1.2 Computation of Bessel Functions
The ordinary Bessel Functions J ν (z) and Y ν (z) are standard functions in MATLAB.
The spherical Bessel Functions used here follow from (4.9-10) of BH.
3.1.3 Computation of angular functions
The angular functions, π n and τ n, are computed from the recurrence relations (4.47)
of BH with the initial functions given for n=1 and 2.