Chapter 8 Experiment 6: Light Polarization WARNING This experiment will employ Class III(a) lasers as a coherent, monochromatic light source. The student must read and understand the laser safety instructions on page 90 before attending this week’s laboratory. 8.1 Introduction We might recall that light is “transverse electro-magnetic waves”. James Clerk Maxwell’s electrodynamics equations describe these waves in detail. Transverse waves have the E and B vectors perpendicular to the direction of wave propagation. Out of 3-dimensional space, this still leaves two dimensions (or two degrees of freedom) in which the vectors might point; they can point in any radial direction around the light ‘rays’. These two degrees of freedom are represented mathematically by two orthogonal coordinate axes. These two coordinates are the basis for specifying the polarization of the light. The electric field vector E can be specified completely using only these two coordinates. Although the same is true for the magnetic field vector, the electrons in dielectrics get moved by the electric field; they experience an electric force −eE. Since their velocities are much smaller than light-speed, any magnetic force is much smaller and their random velocities generally average to zero quickly anyway. (The positively charged nuclei are thousands of times heavier than the electrons so that their response to the waves are neglected; their accelerations are thousands of times less.) This leads us to specify the polarization pˆ of the light to be the direction of the electric field, E(t) = E(t) pˆ. We also know that sinusoidal waves are equal parts positive and negative so that there is no difference between positive and negative polarization, pˆ ⇔ −pˆ. Linear polarization has the polarization vector pˆ a fixed unit vector in space and time. 109 CHAPTER 8: EXPERIMENT 6 Figure 8.1: A polaroid absorbs oscillating electric fields parallel to its grain. This can polarize natural light or it can check whether light is already polarized. Polarized light will be absorbed when its electric field is parallel to the polaroid’s grain. This is the most common form of polarization and the one we will be studying in this lab. If the plane of vibration rotates around the direction of propagation, then the light is said to be elliptically polarized. If the major and minor axes of an ellipse are equal, the ellipse is a circle and the same is true for circularly polarized light. Depending on the direction of rotation the light may be right- or left-circularly polarized. These two rotation directions are also independent of each other and form an alternate basis for specifying a general polarization. An ordinary light source consists of a very large number of randomly oriented atomic emitters. Each excited atom radiates a polarized wave train of roughly 10−8 s duration (in other words imagine a sinusoidal wave about 3 m long). New wave trains are constantly emitted and the overall polarization changes in a completely unpredictable fashion. These wave trains make up natural light. It is also known as unpolarized light, but this is a bit of a misnomer since, in actuality, every wave train is polarized but the wave trains’ polarization planes are randomly oriented in space (i.e. are different polarization states). The set of all wave trains has every possible polarization in equal abundance. In this lab you will 1) study the phenomenon of light polarization, 2) compare our observations to Malus’ law and to Brewster’s law 3) learn about the function and use of a semiconductor diode laser, and 4) learn about the function and use of a PIN photodiode light detector. Light’s polarization can be used to manipulate light. Just as changing its wavelength inside different dielectrics allows us to bend and to focus light, placing optical elements between two polarizers allows us to choose whether the light passes the second polarizer. For example, liquid crystals (nematic fluids) rotate the polarization of light so that we can choose with an electric field whether the polarization matches the second polarizer and is 110 CHAPTER 8: EXPERIMENT 6 Figure 8.2: A photograph of the light detector and shape wheel. We will use one of the circular apertures. transmitted. Many materials exhibit electro-optical or magneto-optical effects that can also be used in this manner. Birefringent (or dual index of refraction) crystals can be cut to exactly the right length to form half-wave plates or quarter-wave plates whose orientation relative to the incident polarization affects the polarization state of the transmitted light. Finally, light reflected from dielectric surfaces is partially polarized. Light reflected at the Brewster’s angle from a dielectric surface is completely polarized. We will observe the Brewster’s angle for Lucite as part of today’s experiment. Checkpoint What property of electro-magnetic radiation determines its polarization? Checkpoint What is a wavetrain? What is the plane of vibration of light? What is the difference between polarized and natural light? 111 CHAPTER 8: EXPERIMENT 6 Checkpoint Is the light emitted by most light sources polarized? Explain. What is circularly polarized light? 8.2 Polarizers An optical device whose input is natural light and whose output is some form of polarized light is known as a “polarizer.” We know a variety of ways to polarize light. All of these techniques have in common some form of asymmetry associated with the way they operate. Three such techniques are discussed next. 1. Wire-Gridiron Polarizer. Imagine that an unpolarized electromagnetic wave impinges on a gridiron of very fine wire from the left. (See Figure 8.1.) The electric field can be resolved into two orthogonal components; in this case, one chosen to be parallel to the wires and the other perpendicular to them. The y-component of the field drives the conduction electrons along the length of each wire, thus generating a current. This current heats the wires so that energy is transferred from the field to the grid. In contrast the electrons are not free to move very far in the x-direction and the corresponding field component of the waves is essentially unaltered as it propagates through the grid. The transmission axis of the grid is accordingly perpendicular to the axes of the wires. The green arrows in Figure 8.1 indicate the polarization axis. 2. A Polaroid is a molecular analog to the wire gridiron. A sheet of clear polyvinyl alcohol is heated and stretched in a single direction, its long hydrocarbon molecules becoming aligned in the process. The sheet is then dipped into an ink solution rich in iodine. The iodine impregnates the plastic and attaches to the straight long-chain polymeric molecules, effectively forming a chain of its own. The conducting electrons associated with the iodine can move along the chain as if they were long thin wires. The component of E in an incident wave which is parallel to the molecules drives the electrons, does work on them, and is strongly absorbed. The transmission axis of the polarizer is therefore perpendicular to the direction in which the film was stretched. 3. A polarizing beam-splitter separates an incoming beam of light into a transmitted, horizontally polarized beam and a reflected, vertically polarized beam. These polarizers make use of Brewster’s law that will be studied today. Checkpoint How can you produce a beam of linearly polarized light? How can you establish if a beam of light is linearly polarized? How does a polaroid film polarize a beam of light? 112 CHAPTER 8: EXPERIMENT 6 8.2.1 Malus’s Law How do you determine experimen- tally whether or not a device is ac- tually a linear polarizer? Consider Figure 8.1 where natural (unpolar- ized) light is incident on an ideal linear polarizer. Only light with a specific orientation (polarization state) will be transmitted. That state will have an orientation par- allel to a specific direction which we call the transmission axis of the polarizer. In Figure 8.1 the trans- mission axis is depicted by green arrows. In other words, only the component of the optical field par- allel to the transmission axis will pass through the device unaffected. If the polarizer is rotated about the z-axis the amount of transmitted light will be unchanged because of the complete symmetry of unpolar- ized light. Now suppose that we introduce a second possibly iden- tical ideal polarizer, or analyzer, whose transmission axis is vertical. If the amplitude of the electric field transmitted by the polarizer is E0, Figure 8.3: The polarization light perpendicular to only its component parallel to the the plane of incidence is unaffected by reflections at transmission axis of the analyzer dielectric surfaces. will be passed on (assuming 100% efficiency). This component will have magnitude E0 cos θ. The observed intensity is the square of the amplitude, consequently 2 I(θ) = I0 cos θ. (8.1) This is known as Malus’s law, having first been published in 1809 by Etienne Malus, military engineer and captain of the army of Napoleon. Observe that I(90◦) = 0. This arises from the fact that the electric field that has passed through the polarizer is perpendicular to the transmission axis of the analyzer (two devices so arranged are said to be “crossed”). 113 CHAPTER 8: EXPERIMENT 6 Checkpoint What is the relation between polarizer orientation and transmitted light if the incident light is linearly polarized? Checkpoint What happens to the polarization of light that doesn’t pass the polarizer? Checkpoint What is Malus’ law? 8.2.2 Malus’ Law First, place the lens in the beam path very near the laser and place one polaroid very near the lens.