1. Objective Experiment 5 Polarization and Modulation of Light Understanding the definition of polarized and un-polarized light. Understanding polarizer and analzer definition, Maluse s law. Retarding plates definition and application 2. Theor Polarized light: A propagating light (Electromagnetic wave; EM) has its electric and magnetic fields. These fields are perpendicular to one another as well as to the propagation direction. Polarization of an EM wave (light) describes the behavior of the electric field vector of the light as it propagates through a medium. If light wave has E-field oscillating in random directions (but perpendicular to the propagation direction) is called unpolarized. If the direction of E-field oscillation is well defined, it is called polarized (Figure 1). Figure 1. If the E-field oscillates at all time within a well-defined line, it said that EM is linearl polarized. In a linearl polarized light, the E-field vibrations and propagating direction (z axis here) defines a plane of vibrations shown in figure 2.a. The E-field oscillations in the plane of polarization can be represented b the superposition of two fields Ex and E with the right magnitude and phase (Figure 2.b, figure 2.c) E ( z, t) E cos( t kz) x xo
E ( z, t) E cos( t kz ) o Where Ø is the phase difference between Ex and E, which defines the dela between Ex and E. Plane of polarization E x E ^ E x ^ x ^ xe x z E ^ (a) (b) (c) E E Figure (a) A 2. lina) earl Electric polarized field in a wave linearl has polarized its electric wave field oscillates oscillations along a line defined perpendicular along a to line propagation direction. b) E field oscillations are in the plane of polarization. c) E-field represented b Ex and E. An EM wave (light) can be polarized b passing through a polarizer such as Polaroid sheet. This polarizer will onl pass E-fields oscillating along a preferred direction, called transmission axis. Malus s law: Suppose that a linearl polarized light from a polarizer is incident on a second identical polarizer as shown in figure 3. B rotating the transmission axis of the second polarizer the polarization state of the incident light can be analzed. If the transmission axis of the second polarizer is at angle θ to the E-field of the first polarizer then E cosθ of the field will be allowed to pass through the analzer as in figure 3. As Irradiance or intensit of the light passing through the analzer is proportional to square of electric field (E cosθ) 2, the irradiance, I, at an angle is then given b Malus s Law: I(θ) = I(0) cos 2 (θ) Malus s law relates the intensit of a linearl polarized light passing through a second polarizer to the angle between the transmission axis and E-field vector.
Figure 3. Randoml polarized light is incident on polarizer 1 with transmission axis TA1. Light is linearl polarized along TA1 and becomes incident on polarizer 2 (called analzer) with transmission axis TA2 at an angle θ to TA1. Detector at the end measures the intensit of the light. Experimental procedure. 1. Launch the laser into a power meter detector, bolted on the breadboard at a distance about one meter from the laser. Record the maximum power of the laser. 2. Mount the polarizer (Polaroid sheet) in a rotation stage and bolt on the breadboard ver close to the laser. Rotate the sheet to get the maximum power. Record this power. Explain the differences in power values? 3. Mount the second polarizer (called analzer) in between the first one and detector. 4. Rotate the analzer to get the maximum power. Record the angle on the rotational stage, call it θ = 0. Explain the direction of the transmission axis of the second polarizer with respect to the first one at this point. 5. Rotate the stage of the analzer in steps of 10 until θ = 90 o. Record the powers at each step. 6. Rotate back the stage to θ = 0, check the power. Now rotate the stage in step of -10 until θ = -90 o. 7. Estimate the photosensitive device area. Then calculate the light intensit from the data recorded in steps of 5 and 6.
8. Sketch the calculated light intensities with respect to θ. Explain the results. 9. Sketch calculated light intensities with respect to cos 2 θ. Explain the results. Retarding Plates In crstalline materials the electronic polarization depends on the crstal direction. As a result the refractive index of a crstal, and the velocit of the light in a crstal depends on the direction of light propagation and the on the state of its polarization. Noncrstalline materials like glasses and cubic crstals have the same refractive index in all directions. These materials are called opticall isotropic. The refractive index of most crstals depends on the direction of light propagation and the on the state of its polarization. These materials are called opticall anisotropic. These materials are also called birefringent (double refraction) because an incident light beam is doubl refracted. There is a special direction in a birefringent crstal which all waves with different polarization experience the same refractive index (travel with the same phase velocit). This axis is called Optic Axis. Optic axis of a crstal is the direction in which a travelling light experience no birefringence (double refraction) and all the waves have the same phase velocit whatever their polarization is (figure 4). Figure 4. a) A birefringent crstal plate with the optic axis parallel to the plate surface. b) Optic axis perpendicular to plate surface. There is a phase difference between E and Eǁ in the first case. The phase difference of 180 is a half-wavelength retardation which means that E ǁ is delaed b 180 with respect to E and is called a half-wave plate retarder. A quarter wave-plate retarder provides quarter wavelength retardation. (Figure 5)
Figure 5. Input and output light polarization through half and quarter wave plate retarders. We can build an intensit modulator b inserting a polarizer and an analzer before and after a retarding plate. (Figure 6)
Retarding plate Analzer Polarizer Figure 6. Intensit Modulator contains 1) Polarizer 2) Retarding plate 3) Analzer all mounted on rotating stages. Experimental procedure: 1. Mount the polarizer (Polaroid sheet) in a rotation stage and bolt on the breadboard ver close to the laser. Turn on the laser, then rotate the polarizer to get the maximum power. Record this power. 2. Mount the second polarizer (called analzer) in between the first one and detector. Rotate the analzer until ou get the maximum power, record the angle of the analzer. 3. Remove the analzer carefull without an rotation. 4. Mount a retarding plate in another rotating stage and bolt it on the breadboard between the polarizer and detector. 3. Rotate the plate to find the optic axis (ou should get the maximum power). Record the power and the angle. 4. Mount the analzer again (at the same position of step 2) in between the retarding plate and detector. What is the power? Explain. 5. Rotate the analzer to get the maximum power again. Compare the results with previous experiment. Explain what ou have observed.