
108
Second Harmonic Generation Imaging
e second-order susceptibility tensor, therefore, can be written as
χ
χ
χ χ χ
χ
( )
( )
( ) ( ) ( )
( )
2
2
2 2 2
2
0 0 0 0 0
0 0 0
0 0 0 0 0
=
xxy
yxx yyy yzz
zyz
(5.9)
Considering an electric eld propagating along the z-axis and linearly polarized at an angle
ψ
with
respect to the y-axis (axis of cylindrical symmetry of the sample):
E E e E e
x y
= sin cosψ ψ+
(5.10)
substituting Equation 5.9 into Equation 5.5, the second-order polarization can be written as
P E e E E
( )
( ) ( ) (
sin (
2
2 2 2 2 2 2 2 2
2= + +ψ ψ χ ψχ ψχcos sin cos
yxx x yxx yyy
))
)
e
y
(5.11)
e intensity of SHG (I
SHG
) is proportional to the squa ...