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Frank L. H. Wolfs, EditorDepartment of Physics and Astronomy, University of Rochester, Rochester, New York 14627

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Balanced polarimeter: A cost-effective approach for measuringthe polarization of light

Luke H. C. Patterson and Kenneth E. KihlstromDepartment of Physics, Westmont College, Santa Barbara, California 93108

Michael A. Everesta)

Department of Chemistry, Westmont College, Santa Barbara, California 93108

(Received 21 July 2013; accepted 18 September 2014)

We have designed and built a fast and precise balanced polarimeter from components commonly

found in undergraduate physics laboratories. Balanced polarimetry measures the orientation of

linearly polarized light by splitting the beam into orthogonal polarization components and detecting

each separately. Our polarimeter is capable of measuring the orientation of linearly polarized light

with a precision of approximately 0:001�=ffiffiffiffiffiffiHzp

. The apparatus cost less than $1000. Measurements

of the specific rotation of sucrose and of the Faraday effect were performed, both of which produced

results that were comparable to previously reported values. VC 2015 American Association of Physics Teachers.

[http://dx.doi.org/10.1119/1.4896747]

I. INTRODUCTION

Ever since Huygens first used polarization to explain thephenomena of the double image produced by the Iceland sparin 1678, the polarization of light has been an important topicin physics.1 In addition to elucidating an important aspect ofthe fundamental nature of light, polarimetry (the measure-ment of the polarization of light) is also used to explore thephysical properties of matter from macroscopic to atomicsamples. Polarimetry has been used to validate the Fresnelequations in the instructional laboratory2 and to investigatethe Faraday effect.3–7 The rotation of polarized light by atomshas even been used to probe atomic parity violation.8

Despite the importance of polarization, we are unaware ofa readily available, inexpensive, high-precision (�0.1�)instrument. Hopgood has reported a simple design whichuses sheet polarizers and a protractor,9 a design which isinexpensive but lacks speed and precision. Over 70 yearsago, Underwood presented a device in this journal whichwas more sophisticated, but only accurate to a tenth of adegree.10 Recently, Lisboa et al. designed a solution polar-imeter that uses the near-extinction method.11 The precisionrotation mount used in this approach may yield polarizationangles as precise as 0.08�, but it will also be limited in itstime resolution to the speed at which the operator can findand record the null angle. Each of these designs has its par-ticular advantages, but none of them is inexpensive, simple,

fast, and precise. Therefore, we have designed and built a po-larimeter that meets all of these criteria.

Unlike null or near-extinction polarimetry, balanced polar-imetry does not diminish the intensity of the incident light butrather analyzes its components. Polarized light is separated bya polarizing beamsplitter into two orthogonal polarizationcomponents. If the polarization of the incident light is orientedat 45� to the principal axis of the beamsplitter, the intensitiesof the transmitted and reflected components are equal. If anadditional optical element is introduced that rotates the polar-ization, the intensities of the two beams become unequal. Thedegree of rotation can be determined by measuring the inten-sities of the two individual components. The advantages ofbalanced polarimetry are discussed by Bouchiat et al.12

Balanced polarimetry has been applied in fundamentaland applied physics. For example, the nuclear weak force isknown to cause optical activity in atoms,13–15 which hasbeen directly measured with balanced polarimetry byBouchiat and coworkers.8,12 Other applications of balancedpolarimetry include laser frequency stabilization,16 detectionof radio-frequency magnetic fields,17 and optical NMRdetection.18 Therefore, in addition to providing a concretedemonstration of the nature of light and providing an appara-tus that can be used to demonstrate other physical phenom-ena, such as the Faraday effect, this particular approach topolarimetry can provide students a window into theadvanced physics research laboratory.

91 Am. J. Phys. 83 (1), January 2015 http://aapt.org/ajp VC 2015 American Association of Physics Teachers 91

In this paper, we present the polarimeter design and thetheory of its operation. The performance of the polarimeter isevaluated with two experiments, the optical rotation of sucrosesolutions and the Faraday effect in fused silica, that demon-strate the precision, speed, and versatility of our apparatus.

II. EXPERIMENTAL

A. Apparatus

A schematic diagram of our balanced polarimeter isshown in Fig. 1. Light from a diode laser L (OS-8525A,PASCO, nominally 650 nm 6 10 nm) passes through a polar-izing filter P (OS-8473, PASCO). An optional multi-orderhalf-wave plate HWP (WPMH05M-633, Thorlabs) placed ina precision rotation mount between the polarizer and thesample area facilitates small adjustments in the polarizationof the incident beam without affecting the intensity of trans-mitted light. After traversing the sample area, the beam issplit into its polarization components by a polarizing beams-plitter cube PBS (PBS101, Thorlabs). The p component istransmitted by the cube to photodiode detector D2 and the scomponent is reflected by 90� to detector D1 (both detectorsCI-6504A, PASCO). The photodiode signals are digitizedand transferred to a personal computer for further analysis(750 Interface and DataStudio Software, PASCO). Allexperiments were carried out in ambient air with ambientroom lighting. The total cost of the system is approximately$750, excluding the half-wave plate, the mounting surface,and the computer interface and software.

B. Theory

Assuming an ideal polarizer and ideal proportional detec-tors with equal sensitivity, the signals at detectors D1 andD2 will be Ss ¼ Itot cos2/ and Sp ¼ Itot sin2/, where Itot isthe total intensity of the beam and / is the angle of the polar-ization of the light incident on the beamsplitter measured rel-ative to an axis that is perpendicular to the plane ofincidence. The angle / can be determined from the ratio ofthe two signals according to

Ss

Sp¼ cos2/

sin2/

/ ¼ arctan

ffiffiffiffiffiSp

Ss

r:

(1)

The amount by which a material or perturbation (such as amagnetic field) in the sample area rotates the angle of polar-ization is easily determined by measuring /blank in the ab-sence of the material or perturbation and /sample in the

presence of the material or perturbation. The rotation owingto the material or perturbation is

h ¼ /blank � /sample: (2)

III. RESULTS

A. Performance

Figure 2 displays the smoothed signal from the two detec-tors with an acquisition rate of 1000 Hz over a period ofapproximately 45 s with only ambient air in the sample com-partment. The data in this and all subsequent figures havebeen smoothed with a 50-point moving average algorithm.All numerical results reported are calculated usingunsmoothed data. The raw data from Fig. 2 have been con-verted to polarization angles with Eq. (1) and are shown inFig. 3. The slight difference in voltage between the twochannels, apparent in Fig. 2, leads to an angle of polarizationmeasurably different from 45� in Fig. 3. The standard devia-tion of the data shown in Fig. 3, before smoothing, is 0.019�.

To determine the effect of the sampling rate on noise, datawere acquired with a 100-Hz sampling frequency. The calcu-lated polarization angles at this frequency are shown inFig. 4. The standard deviation of the polarization angle isapproximately 0.005� and the angle is increasing at a rate of4.13� 10�5/s. On occasion, the polarization angle fluctuatedmeasurably (Fig. 4 inset). We attribute these large

Fig. 1. Schematic of the experimental setup: L is a laser, P is a polarizer,

HWP is a half-wave plate (optional), PBS is a polarizing beamsplitter cube,

and D1, D2 are light sensors.

Fig. 2. The smoothed signals from detectors D1 and D2 measured at

1000 Hz during an interval of approximately 45 s with ambient air in the

sample compartment.

Fig. 3. The smoothed polarization angle, calculated from the data in Fig. 2.

92 Am. J. Phys., Vol. 83, No. 1, January 2015 Apparatus and Demonstration Notes 92

fluctuations to the temperature dependence of the half-waveplate or other optics elements under the influence of theroom air conditioning. Comparing the standard deviation ofthe measurements with 100-Hz and 1000-Hz acquisitionrates indicates that the precision of our apparatus, defined asthe standard deviation of many measurements divided by thesquare root of the sampling rate, is approximately0:001�=

ffiffiffiffiffiffiHzp

. Therefore, our polarimeter can measure rota-tions with a precision of 0.01� in approximately 10 ms.

B. Sample experiments

In order to demonstrate the capabilities of the polarimeter,we performed two experiments that can be adopted in theundergraduate laboratory.

1. Optical rotation of sucrose

Chiral molecules, including many biological molecules,display optical rotation. For small molecules in solution, op-tical rotation is quantified by the specific rotation a, definedas the optical rotation induced in light traversing through onedecimeter of a one-gram-per-milliliter solution.

We determined the specific rotation of sucrose at a wave-length of approximately 654 nm, measured by diffraction offa grating. Several solutions of granulated sugar from a localgrocery store in deionized water were made by serial dilu-tions and placed in a 0.1000-m cell (Rudolph ResearchAnalytical) in the sample compartment of our polarimeter.The optical rotation of deionized water and each solutionwas measured at ambient temperature. The measured values,five at each concentration, are shown in Fig. 5.

The data are well fit by the equation h ¼ ½54:7ð3Þ�=ðg=mLÞ� � cþ 0:081ð4Þ �, where c is the concentration ofsucrose in g/ml and the uncertainties are standard deviations.This expression gives a value of 54.7 6 0.3� for the specificrotation of sucrose at room temperature. This value is within3% of the expected value of 53.3� obtained from the Drudeexpression:

a½ �Tk¼A

k2 � k20

(3)

using A and k0 from Lowry et al.19 The small discrepancybetween the expected and measured values may be due totemperature variation of the optics or the specific rotation,

impurities in the sugar sample, uncertainty in the laser wave-length, or unequal gains in the two detectors. The latter couldbe eliminated with a double-subtraction procedure.12

2. The Faraday effect

Many materials display the Faraday effect: optical rotationinduced by a magnetic field.20 The magnitude of the rotationh depends on the Verdet constant V of the material, the mag-netic flux density B in the direction of propagation, and thedistance d light travels through the material according to thefollowing equation:

h ¼ VBd: (4)

There are several reports of undergraduate activities relatedto the Faraday effect.3–7 Experimental measurements typi-cally employ lock-in amplification.3,6 With our balanced po-larimeter, however, it was possible to measure the Faradayeffect using both DC and AC magnetic fields of only hun-dreds of gauss without lock-in amplification.

We measured the optical rotation of light passing througha 6.35-mm thick fused silica optical window (CVI,PW1-1025-UV) in a magnetic field. The window was housedin a 1 in. diameter lens tube (Thorlabs, SM1L20) whichformed the scaffold for a solenoid which was approximately2 00 long with 840 turns of 24 AWG copper wire. Weapplied currents ranging from 0.5–1.75 amperes. The mag-netic field strength was estimated using the long-solenoid

Fig. 5. The optical rotation of various concentrations of sucrose solutions.

There are five overlapping markers at each concentration.

Fig. 4. The polarization angle acquired with a 100-Hz sampling rate. The

inset shows a temporary large fluctuation, attributed to changes in

temperature.

Fig. 6. The Faraday rotation angle h as function of the estimated magnetic

field strength.

93 Am. J. Phys., Vol. 83, No. 1, January 2015 Apparatus and Demonstration Notes 93

approximation B¼l0NI/L, where N is the number of turns, Iis the current, and L is the length of the solenoid.

Figure 6 shows the optical rotation by fused silica as afunction of the estimated magnetic field strength. These dataare fit by the line h ¼ ½1:01ð6Þ � 10�4 �=gauss� � B�4ð2Þ � 10�3 � (uncertainties are standard deviations). Theslope of this line yields a Verdet constant of 159�/T �m.Fujioka et al. provide an expression for VðkÞ which predictsa value of approximately 197�/T �m at 654 nm, approxi-mately 25% larger than our measured value.21 This discrep-ancy is possibly due to variations from one sample of fusedsilica to the next or to our estimates of the magnetic fieldstrength. There may also be significant error in the valuesestimated from the literature; two methods of estimating V inRef. 21 differ by approximately 8%.

IV. CONCLUSION

We have constructed a fast and accurate polarimeter forless than $1000 using readily available parts. The design per-mits direct observations of the polarization components oflight and can be used to demonstrate physically importantphenomena such as the optical rotation by a biological mole-cule in solution and the Faraday effect.

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