plate is defined by the pressing direction; namely, the y-axis from top to bottom.
Figure 15.3c is the retardance plot against the position of the quartz plate. A uniform
retardance of 2 Â 10
À2 rad was realized in the central position of the plate; thus, we
can use that value for the elliptically polarized light in this experiment.
The matrices of the absorption of left and right circular-polarized light (β and γ)
by the chiral sample are described as
β ¼
1
2
k
0
þ 1
i k
0
À 1
ð
Þ
Ài k
0
À 1
ð
Þ
k
0
þ 1
!
,
ð15:4Þ
and
γ ¼
1
2
k þ 1
Ài k À 1
ð
Þ
i k À 1
ð
Þ
k þ 1
!
,
ð15:5Þ
where the transmittance of left- and right-handed circular-polarized light is k
2 and
k
02 , respectively. Note that β and γ commute; thus, the Jones matrix for circular
dichroism (M CD ) can be written as their sum [7], as follows:
M CD ¼
1
2
k þ k
0
Ài k À k
0
ð
Þ
i k À k
0
ð
Þ
k þ k
0
!
:
ð15:6Þ
The second linear polarizer is described by
LP y ¼
0 0
0 1
!
ð15:7Þ
Finally, the transmitted light (J(θ, δ)) in Fig. 15.1 after the second linear polarizer
is calculated by the sequential multiplication of Eqs. 15.6 and 15.7:
J θ,δ
ð Þ¼LP y ÁM CD Áα θ,δ
ð ÞÁζ x ÁJ init
¼
1
2
0
E x ρcos
δ
2
þ 2kÀρ
ð
Þsin2θsinδ
þiρcos2θsin
δ
2
n
o
e
i φ x þ
π
2 þ2πνt
ð
Þ
"
#
: ð15:8Þ
The observed light intensity as a function of θ and δ (I(θ, δ)) is the square of J(θ,
δ):
I θ,δ
ð Þ¼ J θ,δ
ð Þ
j
j
2
¼
1
4
I 0
2
ρ
2 cos
2 δ
2
þρ 2kÀρ
ð
Þsin2θsinδþ 2kÀρ
ð
Þ
2 sin
2 2θsin
2 δ
2
þρ
2 cos2θsin
2 δ
2
n
o
ð15:9Þ
where we defined the parameter ρ as
332
Y. Araki