Polarization II: Waveplates

PHYS430-530, Department of Physics, Northern Illinois University (Dated: November 4, 2019) The polarization of light − conventionally taken as describing the direction of the electric ﬁeld in time − plays an important role in many electromagnetic phenomena. Wave plates can be used to manipulate the polarization state of an incoming wave.

I. INTRODUCTION & OBJECTIVES

The purpose of this lab is to demonstrate the effect of wave plates to affect the polarization state of an incoming wave. Specifically we will be using quarter-wave λ/4 plates, and half-wave λ/2 plates to alter the polarization of an incoming linearly-polarized wave. The quarter-wave and half-wave plates are also known as retardation plates. A retardation plate has a propagation axis (taken to bez ˆ normal to the surface of the plate. It also has a slow and a fast axis, which are taken to be in the plane orthogonal to the propagation axis. In addition the slow and fast axis are generally orthogonal to FIG. 2. Photograph of the experimental setup used in this each other. The slow and fast axis have a different index laboratory. of refraction referred to as ns and nf respectively. As light travels through these retardation plates with the wave (CW) beams or sources. light propagating alongz ˆ, the light will exit the plate with its two field components (in the waveplate basis) having experienced a different phase shift resulting in a II. EXPERIMENTAL APPARATUS & phase difference δϕ = 2πdλ(ns − nf ). The half-wave METHODS plate (δϕ = π) can changes the polarization direction of linearly polarized light, while the quarter-wave plate A. Overview (δϕ = π/2) converts linearly polarized to circularly polarized light. The experimental setup consists of a source (a laser with associated collimation system), a polaroid polarizer to ensure the laser beam is linearly-polarized a quarter or half waveplate, a Glan-Thompson prism polarizer to analyze the final polarization, and a detection system comprising a diode and associated electronics; see Fig.2. Each of the system is described below.

B. Source

The source include a HeNe laser followed by a collimator-iris system. A assembly consisting of a lens and an iris collimate the beam to a large radius (5 m) FIG. 1. Conﬁguration and notations associated to the two and the iris clip the laser beam to the desired size. cases considered in the theory section: a λ/2 (a) and λ/4 (b) waveplate. C. Polarizers The main goal of this laboratory is to measured the intensity transmitted through the two conﬁguration de- In this lab you will use a couple of polarizers already scribed above. You will also use a laser and a photodi- used in the previous lab (on polarizer). ode to measure the signal. One technique implemented in the setup is the use of an optical chopper to modulate • A Glan-Thompson prism consists of two right- the laser beam and provide a baseline to the diode for angled calcite prisms that are cemented together by an intensity measurement. Such optical-chopping tech- their long faces. The optical axes of the calcite crys- nique is commonly used when charactering continuous- tals are parallel and aligned perpendicular to the 2

E. Detection system

The detection system consists of four items: A pho- todiode which detects the laser beam and produce an electrical signal. The diode is connected to an oscilloscope where the output can be measured. In addition an amplifier is inserted between the oscilloscope and diode. To continuously get a reference signal the laser beam intensity is mechanically modulated using an optical chopper (consisting of a rotating wheel with holes). in the absence of any component the signal measured on the scope consists of square-tooth trace with it maximum FIG. 3. Photograph of the λ/2 (b) and λ/4 (c) waveplates. and minimum respectively corresponding to the cases of laser on and off (i.e. blocked by the chopper). Therefore a measure of the peak-to-peak height provide a quantity plane of reflection. Birefringence splits light enter- proportional to the laser intensity I ∝ E2. In the fol- ing the prism into two rays, experiencing different lowing we will call this signal the diode signal and you refractive indices; the p-polarized ordinary ray is will record its value in Volt using the oscilloscope. An totally internally reflected from the calcite?cement absolute measurement of the power on the diode could interface, leaving the s-polarized extraordinary ray in principle be possible but would required a precise cal- to be transmitted. The prism can therefore be used ibration of the diode (not available for this lab). as a polarizing beam splitter.

III. EXPERIMENTAL PROCEDURE • A polaroid polarizer consists of many microscopic crystals of iodoquinine sulphate (herapathite) em- bedded in a transparent nitrocellulose polymer Before starting, you should familiarize yourself with film. The needle-like crystals are aligned during the experimental setup and identify each of the system manufacture of the film by stretching or by apply- (laser, a collimator with iris, optical chopper, and detec- ing electric or magnetic fields. With the crystals tion system). In a first step, you should make sure none aligned, the sheet is dichroic: it tends to absorb of the polarizers are in the path. Check the beam laser light which is polarized parallel to the direction of beam is align all the way and hit the detector area of crystal alignment, but to transmit light which is the diode. Adjust the iris size to ensure the full beam is polarized perpendicular to it. If the wave interacts contained within the diode’s detection area. Make sure with a line of crystals as in a sheet of polaroid, your turn on the amplifier (and dial a rotation frequency any varying electric field in the direction parallel for the chopper). to the line of the crystals will cause a current to flow along this line. The electrons moving in this current will collide with other particles and re-emit A. Data taking the light backwards and forwards. This will cancel the incident wave causing little or no transmission 1. Check incoming polarization: Set the analyzer through the sheet. The component of the electric Glan-Thompson prism in front of the diode and field perpendicular to the line of crystals however align it to make sure the laser beam passes through can cause only small movements in the electrons as its center. they can’t move very much from side to side. This means there will be little change in the perpendic- (a) Set the angle of the Glan-Thompson prism to ular component of the field leading to transmission ensure the radiation is polarized in the hori- of the part of the light wave polarized perpendicu- zontal plane. lar to the crystals only, hence allowing the material to be used as a light polarizer. (b) Place one of the polaroid polarizers down- stream of the collimating lens and tune its angle to zero the intensity of the signal on the diode. This will ensure the incoming laser beam is predominantly vertically polarized. Record the polaroid polarizer angle and D. Waveplates the Glan-Thompson prism angle. Note: for the remaining of the experiment the In this lab you will use a couple of waveplate pictured polaroid polarizer angle should not be in Fig.3. The λ/2 and λ/4 waveplates are labelled. changed. 3

2. λ/2 waveplate: Insert the half-wave plate down- B. Analysis stream of the polaroid polarizer.

(a) record the angle of the waveplate θwp and ro- From the data taken you should be able to recover tate the Glan-Thompson prism until the signal find out the impact of the different waveplates on the detected by the diode vanishes and record the polarization. corresponding Glan-Thompson prism angle θa (b) vary the angle of the waveplate by 15◦ and 1. λ/2 waveplate: repeat step 2(a) (c) repeat steps 2(a), and 2(b) for few values until (a) Plot the recorded diode signal as a function of ◦ you have done a full 180 on the waveplate. the angle of the Glan-Thompson prism for the different angles of the waveplate. At the end your measurement you should have several tables giving the angle θa and θwp. (b) Discuss your observations and conclude on the 3. λ/4 waveplate: Replace the λ/2 waveplate with effect of the λ/2 waveplate especially that the the λ/4. final polarization in linear and rotated by an angle that depends on θwp. How if the polar- (a) Make sure that without the λ/4 waveplate the ization rotation angle related to θwp. analyzer is “crossed”, i.e. the light is extin- guished. The insert the λ/4 waveplate so that the marked direction is vertical. What do you 2. λ/4 waveplate: observe? ◦ (b) Rotate the λ/4 waveplate by θwp = 15 and (a) Plot the recorded diode signal as a function of ◦ the analyzer through 360 . What do you ob- the angle of the Glan-Thompson prism I(θa) serve? Record the signal intensity as you vary for the seven value of θ0 you selected ◦ the analyzer angle θa in step of 20 . (b) Discuss the conditions for a circularly polar- (c) Repeat step 3(b) for several waveplate angles ized wave to be produced after the λ/4 wave- (that is by changing the marked direction in plate and confirm you have produced such a ◦ polarization at one of the angles above (which incremental steps of 15 (you should do θwp = 0, 15, 30, 45, 60, 75 and 90◦. one? and how do you confirm the wave is circularly polarized?) At the end your measurement you should have several tables giving the angle θa and θwp.