Biomedical Engineering Reference
In-Depth Information
1.3.3 influence of tight Focusing on the Local Polarization: Beyond the
Paraxial Approximation
Under conditions of tight focusing, the local fields experienced within the confocal volume are gener-
ally distinct from those introduced in the far field. The reasons for this effect are depicted qualitatively
in Figure 1.4. In brief, the high angles of incidence arising when using high NA objectives introduce
field components in all three directions even if starting with linearly polarized light. The most com-
mon strategies developed for modeling the local fields generally consider the focusing of a Gaussian
spatial profile for the far-field beam. In this limit, the local electric fields are given by integrals over
Bessel functions.
E
E
E
−
i I
(
+
I
cos(
2
φ
))
−
iI
sin(
2
φ
)
x
0
2
2
e
e
=
e
e
H
H
=
−
iI
sin(
2
φ
)
i I
(
+
I
cos(
2
φ
))
G r
( ,
φ
, )
z
(1.18a)
y
2
0
2
0
V
V
−
2
I
cos( )
φ
−
2
I
cos( )
φ
L
L
z
1
1
l
,
0
where
α
1
2
I
( , )
r z
=
cos
θ
sin
θ
(
1
+
cos
θ
)
J kr
(
sin exp
θ
)
(
i
kz
cos d
θ
)
θ
(1.18b)
0
0
0
FIgurE 1.4
Graphical depiction of the origin of
z
-polarized incident field from beam polarized in the
x
direc-
tion. Upon focusing, the path of the beam is bent, converting some of polarization component in the plane of bend-
ing into the
z
direction. (left) Rays in the plane perpendicular to the polarization will not have this effect (right) and
rays between these two extremes will produce some
y
- and
z
-polarization (not pictured).
