Applied Mechanics and Materials
ISSN: 1662-7482, Vols. 300-301, pp 1267-1270
doi:10.4028/www.scientific.net/AMM.300-301.1267
© 2013 Trans Tech Publications, Switzerland
Online: 2013-02-13
The Analysis Of The Experiment Of Polarized Light In Uniaxial
Dichroism Crystal
Ye Nanyang1,a, Han Dahai1,a
1
School of Information and Communication Engineering
Beijing University of Posts and Telecommunications, Beijing University of Posts and
Telecommunications, Beijing 100876, China
a
[email protected]
Keywords: polarized light; error analysis; least square method
Abstract. In the experiment of the polarization of light, circularly polarized light can’t be got
though all instruments are carefully adjusted and the polarized light we get is generally regarded as
elliptically polarized light. We analyzed the process and find the light we get isn’t circularly
polarized light or elliptically polarized light as usually thought and deduced the light intensity
distribution function and it can fit the experimental results with small errors.
INTRODUCTION
Theoretically, when the angle between the polarizer and the optical axes of the quarter wave
plate ψis 45 degrees, we can get circular polarized light. However, the circularly polarized light is
never observed on this occasion. Instead, we usually have the dumb-bell like intensity distribution,
which corresponds to a elliptically polarized light, as shown in Fig. 3.This phenomenon is usually
attributed to the reason thatψ is not accurately 45 degrees.[1] However, circularly polarized light
can’t be got even after we adjusted ψ with the step of 0.1 degrees.
We got the light intensity polar diagram when ψ is 45 degrees, as shown in Fig 2. Obviously it
can be concluded that the curve isn’t a circle or eclipse.
Fig.1 Experimental instruments
Fig. 2 Schematic of the experiment of polarization of light
of the polarization of light.
Fig.3 Normalized experimental light intensity in rectangular coordinates, in which ψ is 45 degree.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.ttp.net. (#69713749, Pennsylvania State University, University Park, USA-13/09/16,04:22:23)
1268
Mechatronics and Applied Mechanics II
2. THERORETICAL ANALYSIS
In the following analysis, we suppose that:
1. The geometrical centers of all devices are in the line of the spindle.
2. The rotating angleψ of the quarter wave plate is accurate.
1. Polarizer
Non idea polarizer can’t polarize all incident natural light and polarization direction of the
polarizer doesn’t perpendicular to the spindle. So the emergent light is a mix of natural light and
ordinary ray and extraordinary ray. The polarization direction of the polarizer’s nonperpendicularity to the spindle can results in the emergent light’s non-perpendicularity to the
quarter wave plate. Here we set the incident angle of the light when arrived at the quarter wave
plate as φ.
2. Quarter wave plate
Fig.4 Geometrical relationships of light on the surface of the wave
plate
To get the accurate phase difference between ordinary light and extraordinary light, we must
consider the walk-off angle αof extraordinary light.[2]
(n 2 − no 2 ) tan φ
tan α = e2
(1)
ne + no 2 tan 2 φ
The incident angle φ is usually small and we leave out total reflection from consideration.
According to the geometric relationships:
The distance of ordinary light and extraordinary light is:
t = d cos ϕ (tan(α + ϕ ' ) − tan(ϕ ' ))
The phase difference of ordinary light and extraordinary light is :
2π d
1
1
∆ϕ =
(ne − no )(
−
)
'
λ
cos(ϕ ) cos(ϕ ' + α )
'
(2)
(3)
Where ϕ is the refraction angle of ordinary light in the plate.
In the experiment, to get circle polarized light, we need to adjust ∆ϕ to 45°,through careful
adjustment, when the curve level symmetry axis is parallel to the level direction , we can that ∆ϕ is
45°,note that the reading of the rotating angle is not necessarily 45°.
Because the thickness of the plate is small, we ignore the optical attenuation in the plate.
3.Polarization analyzer
When light transmit to the analyzer, from the analysis above, we can conclude that:
1. Ordinary light direction and extraordinary light direction are not necessarily orthogonal.
2. Ordinary light intensity and extraordinary light intensity are different.
3. Ordinary light and extraordinary light are not coincident.
To check our conclusion, we took the photo of the laser facula when the light transmits out from
the quarter wave plate. (Fig 5)
Applied Mechanics and Materials Vols. 300-301
Fig.5 Experimental intensity distribution of
light emergent from the quarter wave plate
1269
Fig.6 Geometrical relation of the edge of
light emerge from the quarter wave plate.
When light transmit to the polarization analyzer, the laser facular can be divided to three areas as is
showed in Fig 6.
Set the ordinary light transmitting to the analyzer’s light intensity as Ioin ，the ordinary light
transmitting out of the analyzer’s light intensity as Io, the extraordinary light transmitting to the
analyzer’s light intensity as Iein, the extraordinary light transmitting out of the analyzer’s light
intensity as Ie ,the combination light intensity(the light intensity detector get) as Isum .
we can conclude that the total light intensity (light intensity detector get) is:
I = 2π r 2 (Ioin sin2 ψ + Iein cos2 ψ )
+ Ioin Iein 2sin(2ψ ) cos ∆ϕ(r2ar cos
t
t2
− 2t r 2 − )
2r
4
(4)
We get the measured data of I- ψ , when ∆ϕ = 45° used the least squares method to find the
value of Ioin , Iein , r, t, ∆ϕ :
The least-squares function:
f ( Ioin, Iein, r , t , ∆ϕ ) = ∑ ( I theory (i ) − I exp (i ))2
(5)
To find the find the value of Ioin , Iein , r, t that can make :
f ( Ioin, Iein, r , t , ∆ϕ ) = f min
We used genetic algorithm [4] to find the minimum value of the f and get the results:
Io
= 1.17934 r = 0.215mm t = 0.41m
Ie
(6)
3.CONCLUSION
We have deduced a theoretical model by considering the prosperities of the polarization plate.
We explained the reason why we can’t get circularly polarized light in the experiment.
The methods this article used can be applied to the accurate direction detection of the optic
axis’s direction of the uniaxial dichroism crystal in the manufacturing of precision optic
instruments.
4. ACKNOWLEDGMENT
Our research is funded by the Research Innovation Fund for College Students of Beijing
University of Posts and Telecommunication
1270
Mechatronics and Applied Mechanics II
REFERENCES
[1] Jerry D.Wilson, Cecilia A.Hernández, Physics Laboratory Experiments. Brooks Cole, Pacific
Grove:2009.
[2] Zhang Xiao-yu, Zhang Fan,”Analysis of the abnorrmal phenomena of extraordinary light in
birefringence by using the Huygens construction,” in College Physics, vol. 31, 2012, pp. 54-55.
[3] Hugh D. Young, Roger A. Freedman, Lewis Ford, University Physics with Modern Physics
(12th Edition). Addison-Wesley, Boston: 2007.
[4] David E.Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning.
Addison-Welsley, Boston: 1989.
[5] Xiaoyi Jiang, Horst Bunke, “EdgeDetection in Range Images Based on Scan Line
Approximation,” Computer Vision and Image Understanding, vol. 73, Feb. 1999, pp 183-199.