Experiment 3 – The Polarization of Light 1Experiment 3The Polarizationof Light1 IntroductionIn this experiment, we will study various polarizations of light. Thesewill include linearly polarized, circularly polarized, elliptically polar-ized and unpolarized light. The polarization of light will be describedquantitatively by the degree of polarization. We will also study the re-flection of linearly polarized light from a plane surface. In these studieswe will use a photodetector and a computer to acquire the data.2 Background - see Hecht, Chap. 82.1 Types of PolarizationThe electric field of a propagating transverse electromagnetic wave liesin a plane normal to the direction of propagation. Consider a wavepropagating along ˆz. For most of this discussion, we shall consider awave at a particular instant in time and e xamine the orientation of theelectric field vector in our x − y coordinate system.2.1.1 Polarized LightA general expression for the E-field is:E = ˆxE0xcos(kz − ωt) + ˆyE0ycos(kz − ωt + φ). (1)where φ is a phase shift between the ˆx and ˆy directions. If φ = 0, theelectric field oscillates along a line. This is linearly polarized light. Theangle of the polarization is determined by the relative magnitudes ofE0xand E0y. If φ = ±π/2, and E0x= E0ythe electric field vector tracesout a circle in the x − y plane. This describes circularly polarized light.Experiment 3 – The Polarization of Light 2If φ 6= 0, ±π/2 and/or E0x6= E0y, the light is elliptically polarized. Theelectric field traces out an ellipse, that in general can have any majorto minor axis ratio and an arbitrary angle.2.1.2 ”Unpolarized” LightIf light is monochromatic, it is polarized. It must be some formof elliptically polarized light (where we consider linear and circular tobe limiting cases.) For light to be ”unpolarized” requires a randomphase variation between the x and y components of the field, and sometime averaging. All light is always fully polarized at any instant intime. Unpolarized light is only possible if there are multiple frequenciespresent. Our HeNe lasers may or may not be fully polarized. They tendto lase in a few ”modes” with orthogonal polarizations, producing lightseparated in frequency by ∼ 1 G Hz (note this is only a part in 105ofthe optical frequency, so it still looks monochromatic). We will learnmore about lasers later in the course, but at the moment, what youneed to know is that over time (minutes to hours) the amount of lightin the two modes can drift. If it is all in one mode, the laser will b elinearly polarized. If it lases in both modes with equal intensity, it willappear unpolarized (because any measurement we make will averageover many cycles of the difference frequency). This drift will be animpediment to your measurements, and some of you w ill be lucky andwill have much more stable lasers than others. To do experiments wewill put one polarizer in front of the laser to make it linearly polarized,but how much light is transmitted through this polarizer will dependon the state of the laser (and may change in time!).2.2 Malus’s LawConsider polarized light of intensity I(0) incident on an ideal linearpolarizer. Let the transmission axis of this polarizer be at an angle of θwith respect to the initial polarization. Only light with it’s electric fieldvector parallel to the axis of the polarizer will be transmitted throughthe polarizer.The intensity of the light emerging from the second polarizer is givenby Malus’ Law:I(θ) = I(0) cos2(θ). (2)To go one step further, consider the situation where light from the firstpolarizer is incident on a second polarizer whose transmission axis is atan angle of ψ with respect to the initial polarization. The intensity oflight emerging from the second polarizer is given byI(ψ) = I(0) cos2(θ) cos2(θ − ψ). (3)Experiment 3 – The Polarization of Light 32.3 Degree of PolarizationThe degree of polarization is basically a measure of the extent to whichthe light we are studying is polarized and is given by:V =Imax− IminImax+ Imin, (4)where Iminand Imaxare the minimum and maximum intensities of thelight, respectively. For partially polarized light, this can also be writtenas:V =IpIp+ Iup, (5)where Ipis the intensity of the polarized portion and Iupis the intensityof the unpolarized portion. Sometimes V is called the fringe visibility.2.4 Reflection of Linearly Polarized LightWhen linearly polarized light is incident on a plane surface, the amountof light reflected, the reflectance (R), depends on the angle of incidenceand the orientation of the polarization vector relative to the scatteringplane. This is described by the Fresnel equations:Rk=tan (θi− θt)tan (θi+ θt)2(6)R⊥=sin (θi− θt)sin (θi+ θt)2. (7)One consequence of Eq. 6 is that when θi+ θt= π/2, tan (θi+ θt) →∞ and Rk→ 0. This occurs when θi= θBwhere θBis called Brewster’sangle and θt= β. Substituting θBand β into Eq. 6, subject to θB+β =π2leads totan θB=ntn0. (8)At θBonly light with its E-field perpendicular to the scattering planewill be reflected. Consequently, it is possible to produce polarized lightfrom unpolarized light by allowing it strike an interface at Brewster’sangle.3 ExperimentYou are supplied with 3 polarizers, one on a motorized rotation stage.You will have to deal with the laser drifts, so you will need to makestability measurements to disentangle effects due to the laser from yourExperiment 3 – The Polarization of Light 4measurements. Using the data acquisition system, measure the inten-sity stability of your laser, and then the time-dependent polarizationstate of your laser.Measure Brewster’s angle for the block of glass supplied. The polar-izers’ axes are not marked, so you will need to figure out how to assurethat the polarization of the beam striking the block is parallel to theplane of incidence.Verify Malus’ Law for one and two polarizers. A demonstration thatmystifies many observers is that placing a polarizer in between twocrossed polarizers allows light to be transmitted that was previouslyblocked. Set up this system and figure out why this is so.Go in the hallway and look at the light reflected off the floor. Is itpolarized, and if so, along what direction?If you have or can borrow polarizing sunglasses, measure their po-larization properties.Multiple scattering of light can affect the polarization state.