for right-handed polarized light. Passing through chiral media, which exhibit molar
circular dichroism (Δε), the ellipse undergoes some variation, namely, light intensity
in the vertical and/or horizontal axis of the ellipse. To estimate such a change, the
second glan-laser prism, which is in crossed Nicol directions with respect to the first
glan-laser prism, is placed to detect the horizontal intensity of the elliptically
polarized light. Finally, the light is collected by a diode array, equipped with an
image-intensifier to obtain horizontal intensity as a function of θ.
Such an experimental situation is best formulated by the Jones vector approach.
First, we show the relationship between elliptically polarized light and molar circular
dichroism (Δε), described by the Jones calculus shown below [9].
Polarized light J init is generally expressed by the two-component vector
J init ¼
E x e
i φ x þ2π ν t
ð
Þ
E y e
i φ y þ2π ν t
ð
Þ
"
#
,
ð15:1Þ
where E x and E y denote the complex magnitudes of electric vectors of the observation light along the x- and y-axis in right-handed coordinate system, respectively, z is
the direction of light propagation, φ x and φ y are the phases of those vectors, and ν is
the light frequency. This apolarized light from the light source is converted to
linearly polarized light through the first linear polarizer (LP x ) in Fig. 15.1. The
linearly polarized light is generated by the first linear polarizer, followed by the
conversion to an elliptically polarized light by the retarder (α(θ, δ)), which has two
variables—retardance (δ) and azimuth (θ). The Jones matrices of the first linear
polarizer and α(θ, δ) are represented as
LP x ¼
1 0
0 0
!
ð15:2Þ
and
α θ, δ
ð Þ ¼
cos
2
θ ∙ e
i
δ
2 þ sin
2
θ ∙ e
Ài
δ
2
2i cos θ sin θ sin
δ
2
2i cos θ sin θ sin
δ
2
cos
2
θ ∙ e
Ài
δ
2 þ sin
2
θ ∙ e
i
δ
2
2
6
4
3
7
5:
ð15:3Þ
Retardance is defined as the difference in phase shift of its slow axis against its
fast axis. Now, the fast axis is defined from top to bottom in the home-built retarder
(the pressing direction of the quartz plate by the screw, which is the Ày direction in
Fig. 15.1), and the azimuth is also defined as depicted in Fig. 15.2.
The performance of the retarder is shown in Fig. 15.3. Figure 15.3a is the front
view of our home-built retarder. In the home-built retarder, the 2-mm thick quartz
plate was mounted on the θ-stage and pressed slightly from the top of the plate.
Owing to the pressure, the quartz plate possesses birefringence. Figure 15.3b
shows the two-dimensional map of the quartz plate birefringence. The fast axis of the
330
Y. Araki
circular dichroism (Δε), the ellipse undergoes some variation, namely, light intensity
in the vertical and/or horizontal axis of the ellipse. To estimate such a change, the
second glan-laser prism, which is in crossed Nicol directions with respect to the first
glan-laser prism, is placed to detect the horizontal intensity of the elliptically
polarized light. Finally, the light is collected by a diode array, equipped with an
image-intensifier to obtain horizontal intensity as a function of θ.
Such an experimental situation is best formulated by the Jones vector approach.
First, we show the relationship between elliptically polarized light and molar circular
dichroism (Δε), described by the Jones calculus shown below [9].
Polarized light J init is generally expressed by the two-component vector
J init ¼
E x e
i φ x þ2π ν t
ð
Þ
E y e
i φ y þ2π ν t
ð
Þ
"
#
,
ð15:1Þ
where E x and E y denote the complex magnitudes of electric vectors of the observation light along the x- and y-axis in right-handed coordinate system, respectively, z is
the direction of light propagation, φ x and φ y are the phases of those vectors, and ν is
the light frequency. This apolarized light from the light source is converted to
linearly polarized light through the first linear polarizer (LP x ) in Fig. 15.1. The
linearly polarized light is generated by the first linear polarizer, followed by the
conversion to an elliptically polarized light by the retarder (α(θ, δ)), which has two
variables—retardance (δ) and azimuth (θ). The Jones matrices of the first linear
polarizer and α(θ, δ) are represented as
LP x ¼
1 0
0 0
!
ð15:2Þ
and
α θ, δ
ð Þ ¼
cos
2
θ ∙ e
i
δ
2 þ sin
2
θ ∙ e
Ài
δ
2
2i cos θ sin θ sin
δ
2
2i cos θ sin θ sin
δ
2
cos
2
θ ∙ e
Ài
δ
2 þ sin
2
θ ∙ e
i
δ
2
2
6
4
3
7
5:
ð15:3Þ
Retardance is defined as the difference in phase shift of its slow axis against its
fast axis. Now, the fast axis is defined from top to bottom in the home-built retarder
(the pressing direction of the quartz plate by the screw, which is the Ày direction in
Fig. 15.1), and the azimuth is also defined as depicted in Fig. 15.2.
The performance of the retarder is shown in Fig. 15.3. Figure 15.3a is the front
view of our home-built retarder. In the home-built retarder, the 2-mm thick quartz
plate was mounted on the θ-stage and pressed slightly from the top of the plate.
Owing to the pressure, the quartz plate possesses birefringence. Figure 15.3b
shows the two-dimensional map of the quartz plate birefringence. The fast axis of the
330
Y. Araki