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Lab 2 Manual University of Toronto Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE318 – Fundamentals of Optics Lab #2 THE POLARIZATION OF LIGHT CAUTION: ● NEVER LOOK DIRECTLY INTO A LASER BEAM. IT IS HARMFUL TO YOUR EYES. ● NEVER TOUCH THE SURFACES OF OPTICAL ELEMENTS. ● HANDLE ALL OPTICAL ELEMENTS WITH CARE. Apparatus: • He-Ne laser • Photodetector and power meter • Depolarizer • Linear Polarizers • Half waveplate at 633nm • Quarter waveplate at 633nm • Rotary assembly with sample holder • Calcite beam displacer • Optical rail (2 meter in length) • A board marked with cross arrows. Most optical elements used in this lab have already been mounted and attached to posts. To handle these elements, you should hold the mount or the post. Reference: • "Introduction to Optics" by Pedrotti, 3rd Ed o Section 4-9, 15-1, 15-2, 15-4, 15-5, by Pedrotti • "Optics" by Hecht, 4th Ed o Chapter 4 1 PART I: LINEAR POLARIZERS Background: Light is a transverse electromagnetic wave. The electric and magnetic fields oscillate in directions perpendicular to the direction of propagation. The polarization state of light refers to the direction of the electric field oscillation. Linearly polarized light has the electric field oscillates along one linear direction (Fig. 1a). Circularly polarized light is characterized by a constant electric field rotating in the plane perpendicular to the direction of propagation (Fig. 1b). Elliptically polarized light also has a rotating electric field, but its amplitude is not constant (Fig. 1c). Finally, light can also be randomly polarized, where the direction of polarization changes rapidly with time, as it does for light emitted from most incandescent light sources. (a) (b) (c) y y y E x x x Fig. 1 Electric field of (a) linearly-polarized, (b) circularly-polarized, and (c) elliptically-polarized light that are propagating in the z-direction. The direction of the arrowhead indicates the direction of the electric field. The polarization state of light can be analyzed via a combination of linear polarizer and light power detector. Each linear polarizer has a transmission axis. Maximum power transmission occurs when the polarization direction of light is aligned with this axis. Light polarized in other directions is absorbed (either partially or completely depending on the polarization direction) by the polaroid material of the polarizer. Therefore, if randomly polarized light enters the polarizer, the transmitted light is linearly polarized. Although the transmission should ideally be zero if the polarization direction is perpendicular to this axis, there is always some leakage due to the non-ideal construction of the polarizer. Nevertheless, minimum power transmission should be observed. For circularly polarized light, the power transmission through a linear polarizer is constant regardless of the direction of its transmission axis. This is because circular polarization can be considered as a superposition of two orthogonal linear polarizations of equal amplitude. Regardless of the direction of the transmission axis, circularly polarized light can always be decomposed into two linear polarizations of equal amplitude, where one is aligned with the transmission axis and one is perpendicular to it. Therefore, the total transmission of circularly polarized light through an ideal linear polarizer is always 50%. 2 For elliptically polarized light, the power transmission varies as the transmission axis of the polarizer is rotated. The maximum transmission is achieved when the polarizer’s transmission axis is aligned with the major axis of the ellipse, while minimum transmission occurs when the axis is aligned with the minor axis of the ellipse. Procedure: The transmission axis of polarizer used in this experiment has been calibrated to be along the 0 and 180 degree marks on center scale (dotted line in Fig. 2). Fig. 2 Transmission axis of calibrated polarizer 1. Alignment and basic observations a. Place the He-Ne laser source on the left end of the optical rail. b. Place the marked board after the laser. Observe the position of the laser spot on the board as you move the board from a position very close to laser to a position at the far end of the optical rail. Adjust the laser position such that the laser beam is aligned parallel to the optical rail. c. Place a mounted polarizer between the laser and the board. Adjust the height of the polarizer such that the laser light is incident on the center of the polarizer. i. Observe the brightness of the transmitted light while rotating the polarizer using the coarse control on its mount. What conclusion you can draw in terms of the polarization state of the He-Ne laser source used in this lab? 3 ii. Insert a depolarizer between the laser and the polarizer, rotate the polarizer again and observe the change in brightness of the transmitted light. iii. Insert another polarizer between the first polarizer and the board. Set the transmission axis of first polarizer to the vertical direction. Rotate the second polarizer and observe change in brightness. 2. Characterization of polarizer performance a. Principal transmittance (k1) is defined as the maximum transmission of a linear polarizer. i. For measurement accuracy, use a screen board to block the entrance of the detector and zero the reading before taking the measurement. ii. Place two polarizers after the laser source. Place the photodetector after the second polarizer and align the heights of the components. iii. Rotate the second polarizer until the maximum optical power is obtained on power meter. Record the power reading (P1). DO NOT FORGET TO WRITE DOWN THE UNITS! iv. Remove the second polarizer but keep the first polarizer and the photodetector unchanged. Measure the optical power passing through the first polarizer (P0). DO NOT FORGET TO WRITE DOWN THE UNITS! v. Calculate the k1 = P1/P0. Express k1 in dB scale using the following formula: k1(dB)=10log10(P1/P0). DO NOT FORGET TO WRITE DOWN “dB” as the unit for k1(dB). b. Minor transmittance (k2) is defined as the minimum transmission of a linear polarizer. Use the same set-up as step (a) to measure k2 of the polarizer. i. For measurement accuracy, use a screen board to block the entrance of the detector and zero the reading before taking the measurement. ii. Rotate the second polarizer until the minimum optical power is obtained on power meter. Record the power reading (P2). DO NOT FORGET TO WRITE DOWN THE UNITS! iii. Calculate the k2 = P2/P0. Express it in dB scale as well. DO NOT FORGET TO WRITE DOWN “dB” as the unit for k2(dB). 4 c. Calculate the total transmittance of unpolarised light, which is defined as (k1+k2)/2. [Question: should you use linear or dB scale for the k’s when you apply this formula?] d. Calculate the extinction ratio of the polarizer, which is defined as k1/k2 (linear scale). Express the extinction ratio in dB scale. [Question: How do you obtain the extinction ratio in dB scale?] 3. Confirmation of the law of Malus When unpolarized light incident on two polarizers oriented at an angle θ with 2 respect each other, the total transmitted irradiance is given by I(θ) = Iocos (θ), where Io is the irradiance of light after the first polarizer. This is known as Malus' law. Unpolarized light θ Fig. 3 Schematic of the set up for confirming the law of Malus. The red arrow indicates the direction of polarization. a. Set up the laser, two polarizers, and the photodetector on the optical rail. Set both polarizer axes to the 0° degree mark on center scale (i.e. transmission axis is along vertical polarization). b. Use the detector to measure the optical power passing through the second polarizer I(θ) by rotating the second polarizer from 0° to 180°. Record the readings in Table 1. c. Remove the second polarizer and measure Io. d. Calculate I(θ)/Io and then normalize these values with respect to I(0°)/Io. Table 1. Results for the confirmation of Malus’ law. 0° 20° 40° 60° 80° 90° 100° 120° 140° 160° 180° I(θ)(mW) I(θ)/Io Normalized 1 I(θ)/Io 2 cos (θ) 2 e. Use excel to plot the normalized I(θ)/Io and compare it against cos (θ). 5 PART II: BIREFRINGENCE Background: Many crystalline substances are optically anisotropic, meaning that their optical properties are directionally dependent. As light travels through an anisotropic medium, it is splitted into two principal electromagnetic vibrations, an ordinary ray (o-wave) and an extraordinary ray (e-wave), which are perpendicular to each other and perpendicular to the direction that the waves propagate. This phenomenon is known as birefringence or double refraction. The birefringence of the material can be quantified as ∆� = �$ − �& where ne and no are refractive indices experienced by the e-wave and o-wave respectively. Procedure: Calcite is a common naturally birefringent crystal. A long piece of calcite crystal (called the beam displacer) is provided for this experiment. 1. Draw a small dot on a piece of white paper. 2. Hold the calcite crystal (be careful in handling it and touch only the unpolished sides, not the end facets.) vertically in the air above the dot. Looking through the calcite crystal, how many dots do you see? Now rotate the crystal slowly and observe how the pattern changes. CAUTION: ● NEVER LOOK DIRECTLY INTO A LASER BEAM. IT IS HARMFUL TO YOUR EYES. Laser Depolarizer Calcite Fig. 4 Set-up for the birefringence experiment. 3. Set up the laser, depolarizer, rotary assembly, and viewing screen. Carefully place the calcite crystal on the rotary assembly. Adjust the height of the assembly such 6 that the laser light incidents normally on the crystal surface. Look from the side of the crystal and observe how the light beam is transmitted in the crystal.
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