STOKES POLARIMETRY STOKES POLARIMETRY BY DR. THEODORE C. OAKBERG APPLICATION NOTE PHOTOELASTIC MODULATORS

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1 STOKES POLARMETRY PHOTOELASTC MODULATORS APPLCATON NOTE T E C H N O L O G Y F O R P O L A R Z A T O N M E A S U R E M E N T STOKES POLARMETRY BY DR. THEODORE C. OAKBERG James Kemp s version of the photoelastic modulator was invented for use as a polarimeter, particularl for use in astronom. The basic problem is measuring net polariation components in what is predominantl an unpolaried light source. Dr. Kemp was able to measure a polariation component of light less than 0 6 below the level of the total light intensit. The polariation state of a light source is represented b four numerical quantities called the Stokes parameters.,2 These correspond to intensities of the light beam after it has passed through certain devices such as polaried prisms or films and wave plates. These are defined in Figure. To man scientists a polarimeter is a device for measuring a change in the plane of polariation of a linearl polaried light beam. For small angle rotations, this measurement can be done more simpl and with greater precision using the techniques described in the application note Optical Rotation. - total intensit of light beam Q = - 45 U = - V = DETECTOR FGURE. DEFNTON OF THE STOKES PARAMETER Page 45 -

2 STOKES POLARMETRY PHOTOELASTC MODULATORS APPLCATON NOTE SMPLFED POLARMETER A simplified polarimeter optical setup is shown in Figure 2. This setup would be suitable for situations in which the direction of the linear polariation component is known beforehand. The polarimeter should be aligned so that the passing ais of the modulator is at 45 degrees to the known linear polariation direction, as shown. The polarier is oriented at right angles to the plane of the incident linear polariation component. 45 PEM Controller Modulator 0 f Reference 2f Reference Lock-in, f Polarier Sstem Computer 45 AC Signal Lock-in, 2f Detector Signal Conditioner The circular polariation component will produce a signal at the modulator frequenc, f. f the sense of the circular polariation is reversed, this will be shown b an output of opposite sign from the lock-in amplifier. This signal is proportional to Stokes Parameter V. The linear polariation component will give a signal at twice the modulator frequenc, 2f. A linearl polaried component at right angles to the direction shown will produce a lock-in output with opposite sign. This signal is proportional to Stokes Parameter U. FGURE 2. SMPLFED POLARMETER SET-UP A linear component of polariation which is at 45 degrees to the direction shown will produce no 2f signal in the lock-in amplifier. f there is no such component, the Stokes parameter Q is ero. f there is such a component, this simplified polarimeter cannot detect it. Figure 2 assumes that the light source is monochromatic or nearl so. PEM-based modulators need some spectral selection of the light being measured. f a wavelength selecting device such as a monochromator or interference filter is used, it should be placed between the polarier and the detector. GENERAL POLARMETERS Rotator-Based Polarimeter The setup above is not sufficient for determining the complete polariation state in situations where the linear polariation direction is not initiall defined. Thus, two measurements at 45 degrees with respect to each other must be made. This is a requirement of all general purpose polarimeters. With a PEM, there are at least two was of accomplishing this. The first method is to provide a means of rotating the entire polarimeter apparatus (Figure 2) through 45 degrees. A measurement in each of the two positions must be made. This is an acceptable and straightforward method Page 2

3 STOKES POLARMETRY PHOTOELASTC MODULATORS APPLCATON NOTE Fractional polariations: 2f (0 ) linear = Q 2 + U 2 polariation U 2f (45 ) = tan - U 2 Q f (0 ) = f (45 ) circular polariation = TABLE. STOKES PARAMETERS WTH ROTATNG POLARMETER provided that the light source is stead and does not change over the time required for both measurements. For a rotator-based polarimeter, the modulator, polarier and other detector would be mounted so the can be rotated together. Two measurements would be taken, with the angular positions of the polarimeter assembl differing b 45 degrees. Modern sstems would utilie a computer which would drive a motoried rotator and also process the data from the lock-in amplifiers and the DC meter. The relationships between the electronic outputs of the lock-ins and the DC meter, and the polariation state of the light source are given in Table. B using computer control of a single lock-in amplifier, it would be possible to make both f and 2f measurements sequentiall. Dual Modulator Polarimeter Two photoelastic modulators ma be used to provide a polarimeter with real time measurement capabilit. The two modulators are mounted with their modulator aes at 45 degrees with respect to each other. The polarier is mounted with its passing ais between the two modulator aes, or at 22.5 degrees with each modulator ais. The modulators must operate at different frequencies, tpicall a frequenc separation of 2 to 5 kh is used. Modulator Modulator Polarier 45, F 0, F Detector Signal Conditioner REFERENCE ELECTRONC HEAD CONTROLLER f ELECTRONC HEAD CONTROLLER f 2 REFERENCE AC SGNAL LOCK-N, f, 45 to all lock-in amplifiers LOCK-N, 2f, 0 LOCK-N, 2f 2, 0 V 2f, 45 V f, 45 V 2f2, 0 SYSTEM COMPUTER DC SGNAL FGURE 3. DUAL MODULATOR POLARMETER SET-UP Page 3

4 STOKES POLARMETRY PHOTOELASTC MODULATORS APPLCATON NOTE Figure 3 shows the optical configuration for a dual-modulator polarimeter. As mentioned, the modulator aes of the two modulators are at 45 degrees, with the polarier passing ais at 22.5 degrees with each modulator. The angular designations for each modulator are determined b which angular direction of polaried light each modulator subsstem is sensitive to. The relationships between the electronic output voltages and the appropriate polariation parameters are given in Table. The outputs of the two modulator sstems are equivalent to the two measurements with the rotator-based sstem. The measurement of the Stokes parameter could in principle be accomplished b using a single detector with an optical sstem to restrict the field of view and to select the appropriate spectral bandwidth. There is much benefit to measuring through the same optical sstem as the polarimeter. To measure with this setup, it is important that the retardation amplitude of both PEMs be adjusted to a specific value. This value is A = waves = radians. For these PEM retardation values, the intensit at the detector is independent of PEM retardation and VDC is proportional to the Stokes parameter. USE OF WAVEPLATES f the light source being measured is monochromatic or nearl so, waveplates ma be used to simplif the polarimeter sstem significantl. Two such uses are described below. Polarimeter Using Half-Wave Plate Rotating a small component such as a waveplate is much simpler than rotating a whole polarimeter apparatus. The half-wave plate ehibits the propert of rotating an linear polariation component to the opposite side of the fast ais. The half-wave plate is placed initiall with its fast ais parallel to the modulator ais. n this position Q and V ma be measured, although the algebraic signs of the lock-in outputs will be reversed, compared with the polarimeter without the waveplate. The waveplate is then rotated b 22.5 degrees for the measurement of the Stokes parameter U. Thus the 45 degree component is at 0 degrees with respect to the modulator ais, the 0 degree component is at 45 degrees. Thus the two measurements are sufficient for measuring the two linear parameters Q and U. Linear Polarimeter Using Quarter-Wave Plate f linear polarimetr is intended and there is no desire to measure the circular polariation components, the addition of a quarter-wave plate can be used to make a linear polarimeter which has no moving parts. The waveplate is then placed with the fast ais at 45 degrees with the modulator ais. The 45 degree polariation component (Stokes parameter U) is unaffected, and is detected b a lock-in amplifier at twice the modulator frequenc. The component at 0 degrees (Stokes parameter Q) is converted b the waveplate to circularl polaried light. This circular light is then detected b the lock-in amplifier at the modulator frequenc. Page 4

5 STOKES POLARMETRY PHOTOELASTC MODULATORS APPLCATON NOTE References:. Kemp, James C. Polaried Light and its nteraction with Modulating Devices - A Methodolog Review, Hinds nternational, nc., Januar Kliger, Lewis and Randall. Polaried Light in Optics and Spectroscop, Academic Press, Kemp, James C. Photoelastic modulator polarimeter in astronom, SPE Conference, San Diego, August Kemp, James C. and Barbour, Mark. A Photoelastic Modulator Polarimeter at Pine Mountain Observator, Publication of the Astronomical Societ of the Pacific, 93:52-525, August Kemp, James C., Henson, G.D., and Powell, E.R. The optical polariation of the sun measured at a sensitivit of parts in 0 million, Nature, V. 326, No. 60, pp , March 9, Kemp, James C. Detecting polaried light at levels below ppm. SPE Conference, Los Angeles, Januar 988. Hinds nstruments, nc / 7245 NW Evergreen Pkw / Hillsboro, OR 9724 / USA T: / F: / sales@hindsinstruments.com / PEMlabs is a Trademark of Hinds nstruments, nc. Manufactured in USA 2005, 2009 Hinds nstruments, nc. All rights reserved. Printed in USA Page 5