6 Properties of polarized light - polarimetry

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1 6 Properties of polarized light - polarimetr Supervisors : J.Geandrot, O.Frantz This practical work aims to stud some phenomena caused b the transversalit of light : dichroism, birefingence, rotating power. Objectives : Evaluation criteria : To discover and to eplain some phenomena caused b the vectorial nature of light. To verif Biot s law, using a Laurent polarimeter. Clarit of analses Correct dilution and dissolution Uncertainties Meticulous measuring and cleaning of our tables Be careful, the first manipulations are fun but do not waste our time because the last section (6.2 Polarimetr) is quite long. 6.1 Production of polarized light An electromagnetic wave is the propagation of the field [ E, B ] in vaccuum or in a material medium. The stud of the onl electric field is enough to deduce the properties of the magnetic field. The wave is transverse (the electric field is perpendicular to the direction of wave propagation) and the direction of the electric field is called polarization of the wave, b convention. The electrical field can be studied using a sine wave model : E = E = E 0 cos(2π ν (t z/c) + ϕ 0 ) E = E 0 cos(2π ν (t z/c) + ϕ 0 ) E z = 0 This wave is propagating along (Oz). ϕ 0 and ϕ 0 are the phase offsets of the waves. Visible light, X-ras, gamma ras, infrared, ultraviolet light and radio waves are electromagnetic waves. A progressive sine wave whose frequenc is ν has a temporal period T = 1/ν and a spatial period (wavelength) λ = c/ν. 43

2 6 Properties of polarized light - polarimetr A wave is plane polarized (linearl polarized) when E keeps a constant direction. E z Plane polarized wave, polarized along (O), propagating along (Oz) Front view A frequentl used coordinate sstem relates to the plane made b the propagation direction and a vector which is perpendicular to the plane of a reflecting surface : plane of incidence. The component of the electric field parallel to this plane is termed p-like (parallel) and the component perpendicular to this plane is termed s-like (from senkrecht, German for perpendicular). Polarized light with its electric field along the plane of incidence is thus denoted p-polarized, while light whose electric field is normal to the plane of incidence is called s-polarized. A wave is circularl polarized when its two components have a quadrature phase shift ( ϕ = ±90 ) and when their magnitudes are equal. Otherwise, it is ellipticall polarized : the electric field described an ellipse over time. E z Ellipticall polarized wave, propagating along (Oz) Front view Most common sources of visible light, including thermal radiation and fluorescence (but not lasers), produce light described as "incoherent". Radiation is produced independentl b a large number of atoms or molecules whose emissions are uncorrelated and generall of random polarizations. In this case the light is said to be unpolarized. One can polarize light, at least partiall, using natural phenomena (for eample, scattering b the sk or reflection on glass) Polarization using dichroism A dichroic material is either one which causes visible light to be split into distinct beams of different wavelengths (colours), or one in which light ras having different polarizations are absorbed differentl. A polarizer (or polariser) is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mied polarization into a beam with well-defined polarization, i.e. polarized light. A Polaroid polarizing filter is made from polvinl alcohol (PVA) plastic with an iodine doping. Stretching the sheet during manufacture causes the PVA chains to align in one particular direction. Valence electrons from the iodine dopant are able to move linearl along the polmer chains, but not 44

3 6.1 Production of polarized light transverse to them. So incident light which is polarized in parallel to the chains is absorbed b the sheet ; light polarized perpendicularl to the chains is transmitted. z Polarizer, passing direction along (O) An elliptical polarized wave becomes linearl polarized. When a second polarizer is placed after the first one, with perpendicular passing directions, no light is transmitted : the polarizers are crossed. The second polarizer is generall called an analzer. This propert can be used to determine whether light is polarized or not : if, at a certain angle, no light is transmitted through a polarizer then the light is linearl polarized, perpendicularl to this angle Polarization b reflection at Brewster s angle When light encounters a boundar between two media with different refractive indices, some of it is usuall reflected. When unpolarized light is incident from medium 1 on a medium 2 at Brewster s angle i B, defined b the relation tan i B = n 2 /n 1, the light that is reflected is perfectl s-polarized. The phsical mechanism for this can be qualitativel understood from the wa electric dipoles in the media respond to light. One can imagine that light incident on the surface is absorbed and then reradiated b oscillating electric dipoles at the interface between the two media. The polarization of freel propagating light is alwas perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in the polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate an energ in the direction of the dipole moment. If the refracted light is p-polarized and propagates eactl perpendicularl to the direction in which the light is predicted to be specularl reflected, the dipoles point along the specular reflection direction and therefore no light can be reflected Circular polarization Circular polarizers, also referred to as circular polarizing filters, can be used to create circularl polarized light or alternativel to selectivel absorb or pass clockwise (right handed) and counter-clockwise (left handed) circularl polarized light. The are used as polarizing filters in photograph to reduce oblique reflections from non-metallic surfaces, and are the lenses of the 3D glasses worn to watch some stereoscopic movies (3D), where the polarization of light is used to differentiate which image should be seen b the left and right ee. 45

4 6 Properties of polarized light - polarimetr There are several was to create circularl polarized light, the cheapest and most common involves using a linear polarizer followed b a quarter-wave plate. The linearl polarized light leaving the linear polarizer is transformed into circularl polarized light b the quarter-wave plate. The transmission ais of the linear polarizer needs to be half wa (45 ) between the fast and slow aes of the quarter-wave plate. 3D-glasses consist of two circular polarizers, which are of opposite handedness, mounted in reverse so that circularl polarized light becomes linearl polarized before being filtrated. A tpical waveplate is simpl a birefringent crstal with a carefull chosen orientation and thickness. The light travels at different speeds depending on the direction of its electric field. There are two neutral aes, one fast, one slow. The polarization of a linearl polarized wave along a neutral ais is left unchanged. A quarter-wave plate creates a dela of λ/4 between the fast and the slow components, i.e. ϕ = 90. E = E 0 cos(2π ν (t z/c)) E = E 0 cos(2π ν (t z/c)) E z = 0 linear polarization E = E 0 cos(2π ν (t z/c)) E = E 0 sin(2π ν (t z/c)) E z = 0 circular polarization Change in polarization b delaing the E component of Polarization b birefringence Birefringence is the optical propert of a material having a refractive inde that depends on the polarization and propagation direction of light. Crstals with asmmetric crstal structures are often birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereb a ra of light, when incident upon a birefringent material, is split b polarization into two ras taking slightl different paths. 6.2 Polarimetr In 1817, drawing on the work of Arago, Biot studied the effects of certain solutions on the polarization of light. He thus lad down the following laws : Some isotropic transparent material, in which a monochromatic, linearl polarized, light beam travels, rotates the plane of polarization around the propagation direction of the beam. This substance is said to be opticall active. A detrorotator medium causes linearl polarized light to rotate to the right. A levorotator medium causes linearl polarized light to rotate to the left. The angle α (degrees) of optical rotation is proportional to path length l (dm), concentration C (g.cm 3 ) and specific rotation [α], which depends on the material, temperature and wavelength. α = [α] l C Please be careful to use these units as the specific rotation is usuall given with them. 46

5 6.2 Polarimetr Laurent s polarimeter Laurent s polarimeter precisel measures the polarization direction of a light beam. It is made of a linear polarizer, a half-wave plate in the central part of the beam, a tank (length l) and a second linear polarizer (analzer). A half-wave plate transforms a linearl polarized light into another linearl polarized light, whose polarization direction is smmetrical with respect to its fast ais. When the analzer is perfectl balanced with the halfwave plate, the observed disc is uniform and dark. Without an opticall active solution, the polarization direction does not turn. The measured angle is close to zero (calibration stage). With the solution, the polarization direction turns through an α angle. As a consequence, the analzer has to be turned through the same α angle to get the uniform and dark disc back. Laurent s polarimeter : successive images observed in the eepiece near the direction of polarization. A vernier improves the accurac of the measured angle. Two sets of markings are engraved on the device : a fied one and a moveable one (the vernier). The vernier consists of 20 graduations spread over 19 others. As a consequence, each marking is shifted b 1/20 = 0,05, which defines its accurac. If the zero of the vernier is shifted b p/20 from a main tick, then, b progressive shifting, the p-th scale of the vernier coincides perfectl with a graduation of the fied part. This tick of the vernier is finall added to the main measure, after the decimal point, to increase its accurac. vernier main ticks The zero of the vernier is between the 3rd and the 4th of the main graduation. The first coincidence between graduations takes place at the 6th of the vernier. The result of the measurement is 3,60 ± 0,03 degrees. (which is consistent with what is being measured with the naked ee) Sucrose s specific rotation As the angle of rotation is proportional to the concentration of the opticall active compound, we will prepare three solutions of sucrose with different concentrations : 160 g/l, 80 g/l and 40 g/l. The first one is made b dissolving sugar into tap water, using a weighing scale and 47

6 6 Properties of polarized light - polarimetr a volumetric flask. Make sure ou mi the solution until all sugar is dissolved. Store this first solution as it will be diluted to prepare the others. Once our solution is read, pour it into the analsing tube. Tr to minimize the presence of air in it. Use the bulge to capture the remaining bubble and thus avoid refraction in the path of light. Be careful, the glass lid is fragile and we do not have spare ones. Afterwards, place the tube in the polarimeter, turn the analzer until ou get the dark, uniform disc. Finall read the angle thanks to the vernier. 6.3 Tasks Preparation Read the preceding tet. Write down the words ou do not understand, with their translation and pronunciation. A dictionar can be useful ( Calculate the tpical value of Brewster s angle i B for an air-glass interface. How can ou find the neutral ais of a quarter-wave plate? (using two crossed polarizers) Provide a drawing with a legend. How do ou check that light is linearl polarized? How do ou check that light is circularl polarized? (using a quarter-wave plate and an analzer). Provide drawings. Find the tpical specific rotation of sucrose on the internet. What does it depend on? Manipulations Polarization using dichroism (6.1.1) (10 ) Look through two polarizers while rotating one of them. What happens? Place a linear polarizer in front of each of our ees. Make sure these two polarizer are crossed. Look at ourself in a mirror. Close an ee. Do ou observe something unusual? Polarization b reflection at Brewster s angle (6.1.2) (10 ) Observe light, as reflected b a window, through a polarizer (used as an analzer). glass i object analzer Is the light polarized? Tr for i = 0 or i i B and conclude. If polarized, in which plane (s or p)? 48

7 6.3 Tasks Circular polarization (6.1.3) (30 ) Find the neutral ais of the quarter waveplate. Look at ourself in a mirror, wearing now a pair of 3D-glasses. Close an ee. What do ou observe? Find an eplanation (what does a mirror do on circularl polarized light?). In the following, we want to check how is made a pair of 3D-glasses. Confirm the linear polarization of light traveling from outside to inside. What is the polarization direction? Verif that light traveling from inside to outside is not linearl polarized. Using a quarterwave plate and an analzer, prove that light traveling from inside to outside is circularl polarized. Polarization b birefringence (6.1.4) (10 ) Look at some tet through the given crstal. What happens? Eplain using birefringence propert. Place a polarizer/analzer between the ee and the crstal. What do ou observe when the passing direction of the analzer changes? Conclude on the link between polarization and birefringence of this crstal. Sucrose s specific rotation (6.2.2) (60 ) How much sugar should ou dissolve in the flask in order to obtain a concentration of 160 g/l? Prepare the three solutions and for each one of them find the angle α of optical rotation thanks to the Laurent polarimeter. Identif the sources of uncertaint on α and C. Quantif them. Plot α vs concentration C (four points). Do not forget to show uncertainties. Does the Biot s law appl here? If it does, give specific rotation of sucrose and tell whether it is detrorotator or levorotator. 49

Waves, Polarization, and Coherence

05-0-4 Waves, Polarization, and Coherence Lecture 6 Biophotonics Jae Gwan Kim jaekim@gist.ac.kr, X 0 School of nformation and Communication ngineering Gwangju nstitute of Sciences and Technolog Outline