A method for measuring the rotatory power of a chiral medium

A method for measuring the rotatory power of a chiral medium

Der-Chin Su *a

Chen-ChihHsu a

_,Jiun-You

Lin a and

Ju-Yi Lee *b

a

_Institute

of Electro-Optical Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road,

Hsin-Chu, Taiwan, R.O.C.

b Center for Measurement

_{Standars, Industrial Technology Research Institute, Bldg. 16, 321 Kuang}

Fu Road, Sec 2, Hsin-Chu, Taiwan, R.O.C.

ABSTRACT

A light beam coming from a circularly polarized heterodyne light source passes through a chiral medium, its rotation angle is just half of the phase difference between p- and s- polarization components. And this phase difference can be measured accurately with heterodyne interferometric technique. The rotatory power is obtained by dividing

the estimated rotation angle with its path length. This method has many advantages, such as, high stability, high

resolution, easy operation, and real-time measurement.

Keywords: chiral medium, rotatory power, optical rotation angle, heterodyne interferometry.

1. INTRODUCTION

Rotatory power or specific rotation is an important characteristic constant of a chiral medium[1]. Although there are some techniques that have been proposed for measuring rotatory power, almost all of them are related to the light intensity variations[2-4]. However, the stability of light source, the scattering light, the internal reflection, and other

factors influence the accuracy of measurements and decrease the resolution of results. In order to overcome these

drawbacks, some improved methods using heterodyne interferometry are proposed[5-8]. Their heterodyne light sources are achieved by either introducing an acoustic-optic modulator to each arm of Mach-Zehnder interferometer or rotating polarization optical elements. Owing to their uncommon path configurations or the mechanical vibration, they are easily influenced by the surrounding vibration and air turbulence.

Further author

information-*

D.C.S._{(correspondence): Email: [email protected]; Telephone: 886-3-5731951; Fax: 886-3-5716631}

*

In this paper, an improved method for measuring the rotatory power of a chiral medium is presented. A

circularly polarized heterodyne light source consisting of a linearly polarized laser source, an electro-optic modulator driven by a voltage signal generator, and a quarter-wave plate is used. The light beam coming from this light source passes through the tested chiral medium, its phase difference between p- and s- polarization components is twice of the rotation angle. And it can be measured accurately with heterodyne interferometric technique. Then, the rotatory power can be estimated by dividing the estimated rotation angle with the concentration and the the path length of the tested

chiral solution[9]. Because of its common-path heterodyne interferometric configuration, this method has many

advantages, such as, high stability, easy operation, and real-time measurement. And its feasibility is demonstrated and it has 0.015 degree resolution

2. PRINCIPLE

Circularly polarized

heterodyne light source

__

Fig.1: Schematic diagram for measuring the phase difference. EO: electro-optic modulator; FG: function generator; Q: quarter-wave plate; BS: beam splitter; CM: chiral medium; AN: analyzer; D: photodetector; PM: phasemeter.

The schematic diagram of this method is shown in Fig. 1. For convenience, the +z axis is chosen along the

propagation direction and the y-axis is along the vertical direction. If the light beam coming from a laser source is linearly polarized at 45°withrespective to the x-axis, then its Jones vector can be written as

E ==(J,

(1)

And it passes through an electro-optic modulator EO and a quarter-wave plate Q with the fast axis being at 45° with

respective to the x-axis. If the fast axis of EO is along the x-axis, and an external sawtooth voltage signal from a

function generator FG with angular frequency wandamplitude V,2, the half-wave voltage of EO, is applied to EO, then the retardation produced by EO can be expressed as cot,andthe Jones vector of the light can be written as

E' =

_Q(45)EO(ot)E

1(1 i")e2

0

₁₍₁

7\i

11)

0 e2

71

1(1"\ .O)t

1"

•wt.it

= —f-I _{Ie'T +}

1e22

. ₍₂₎

2Li)

2L—i)

From Eq.(2), it is obvious that left- and right-circular polarizations have an angular frequency difference w. The

complete set-up for performing the operation Eq. (2) consists of a laser, an electro-optic modulator EO which is driven

by a function generator FG and a quarter-wave plate Q. This set-up acts as a circularly polarized heterodyne light

source. Then, the light is incident on the beam-splitter BS and is divided into two parts by BS : the reflected light and the transmitted light. The reflected light passes through an analyzer ANr with the transmission axis being at 45° with respective to the x-axis and enters into a photodetector Dr. Consequently, the Jones vector of the light becomes

Er=ANr(45°) E'

• (Ot — 1(1

l')l(l

i') e'j

0

l(1

—

2l

i)jTi i)

0 e

_.2! iT'

₂ 1

_.

= _(l+l)cos(__)J

(3) Hence the intensity measured by Dr is

Here, 'r

Sthe reference signal. On the other hand, the transmitted light enters the solution of a chiral medium

contained in a cylindrical glass tube. Then, it passes through an analyzer ANt with the transmission axis being at 45° with respective to the x-axis and is detected by another photodetector Dt. And the Jones vector ofthe light becomes

Et=ANt(45°)CM(O

) E'

—

ill

1( cosO _{sinO") 1 (1}

i"1 e' 0

1 (1

—

21

1A—sin9 cosO)

i)

_e2

1 (Dt

= _(1+i)cos(_+9)1)

, (5)

whereCM(G) is the Jones matrices of the chiral medium[6I and 9 is the optical rotation angle. Therefore, the intensity

measured by Dt is

1=IEt

2

=i[1+cos(wt+26)]

.

(6)

Here, I is the test signal. From Eq.(4) and Eq.(6), it is obvious that both the reference signal and the test signal are

sinusoidal with angular frequency co.Thesetwo sinusoidal signals are sent to the phase meter PM as shown in Fig. 1. The phase difference between the reference signal and test signal

çb=20

, (7)

can be obtained. From Eq. (7), it is seen that the phase difference q5 is just twice of the rotation angle 9 .From the relation O=q5/2,the rotation angle 9 can beestimated.Finally, the rotatory power or the specific rotation

T

0

[a]Ph

=

_CL

(8)

can be calculated under the measurements of the rotation angle 9, the concentration C of the solution of the chiral medium, and the path length L of the cylindrical glass tube. [a]Phis_{expressed in degree/(dm gil) or degreel(dm}

glg)[9I. C and L are expressed in gil or gig and decimeters (dm), respectively. The symbols ?, pH and T means that the rotatory power a depends on the wavelength X, pH and the temperature of the solution of the chiral medium.

3. EXPERIMENTS AND RESULTS

A He-Ne laser with a 632.8 nm wavelength and an electro-optic modulator (Model PC200/2, manufactured by England Electro-Optics Developments Ltd.) with a half-wave voltage of 170 V were used[1O]. The frequency of the sawtooth signal applied to the electro-optic modulator was 2kHz. At first, to show the validity of this technique, a half-wave plate was introduced to replace the solution of the chiral medium. Fig. 2 shows the relation curve of the measured

phase difference q5 versus the optical rotation angle 0 introducedby the half-wave plate. This relation curve is a

straight line with a slope of 2. Hence, it is clear that our derivation shows good validity.

0) a)

0

-e-a) (I) Co

-0

Fig. 2 : The relation curve of the phase difference versus the optical rotation angle 0fora half-wave plate.

Secondly, several sucrose solutions with different concentrations were measured. A cylindrical glass tube with a 2 decimeter length and 20 ml volume was used to contain the sucrose solution. The theoretical and experimental curves

of the rotation angle 0 versus the concentration C (in g/lOOg) are shown in Fig. 3. In this figure, the solid curve

represent the theoretical values which are obtained by introducing the reference rotatory power[9] into Eq. (8). It is

10 15 20 25

clear that this curve shows good correspondence except at high concentration. From the experimental results, the

rotatory power of the sucrose solution is 56.25(g/lOOg )

(dm)

at 632.8nm and the reference value is

56.51(g/lOOg)1 (dm)1 at 636.2 nm.[9] ci

2

a) C)

0

Fig. 3 .Thetheorectical and experimental curves of the optical rotation angle 8 versusthe concentration C for sucrose solution.

4. DISCUSSION

Because a circularly polarized heterodyne light source is used in this method, the intensities of the signals are

independent on the azimuth angles of the transmission axes of analyzers. But, when the transmission axis of the

analyzer fixed at 45 ,thephase difference error coming from the extinction ratio of analyzer will be minimum. The

resolution depends on the resolution of the phasemeter and the optical configuration. From Eq. (7), we can estimate the error in optical rotation angle 0. Itcan be written as

L,/Y

°

:

°

I Co 5 10 15 20 25

Concentration

C (gil OOg)

2

(9)

where

A9

isthe error in the phase difference. Angular resolution, second harmonic errors and polarization-mixing

error may influence the errors in the phase difference in this method[1O]. So the total phase difference error can

decrease to 0.03° inour experiments. Substituting this data into Eq. (9), we have 0.015

Eq. (8) is valid only for the chiral liquid and the solution of the chiral medium. As for a crystal, this method is still valid. But the rotatory power is defined as the measured rotation angle divided by its thickness (in mm unit).

This method is not related to the measurement of light intensity variations, it is free from the stability of a light source. In addition, because of its common-path interferometric structure, it is very stable and has a high resolution.

5.CONCLUSION

A light beam coming from a circularly polarized heterodyne light source passes through a chiral medium, its rotation angle is just half of the phase difference between p- and s- polarization components. And this phase difference can be measured accurately with heterodyne interferometric technique. Based on these facts, an improved method for measuring the rotatory power of a chiral medium is presented in this paper. It is very stable and has a high resolution. And its feasibility is demonstrated and its resolution is 0.015 degree.

ACKNOWLEDGMENTS

This study was supported in part by the National Science Council, Taiwan, under contract N5C89-2215-E009-083.

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