E The oscillating E-field defines the polarization of the wave. B

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1 This sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning. A. Describing Electromagnetic Waves: An electromagnetic wave consists of oscillating E and B fields, perpendicular to each other, with the direction of propagation perpendicular to both E and B. Polarization refers to the E E The oscillating E-field defines the polarization of the wave. B The plane of polarization is shown by the gray arrows. t t direction of oscillation of the E-field and we need not consider the B-field since to state its direction would be redundant. The wave above would be called vertically polarized and is one example of linear polarization. Light from a lamp has waves traveling in all directions, each with its own random polarization and is called unpolarized light since there is no single plane of polarization. Said another way, all polarizations are present in equal amounts, with random phase relationships, and random amplitudes and wavelengths. If things are not random and there is a plane with larger amplitudes then the light is partially polarized in the direction of the aforementioned plane. In this lab we will only consider light of one wavelength that is linearly polarized. B. Making and Detecting Linearly Polarized Light: Turn on your polarimeter and look down into the top polarizer. While rotating the top polarizer through 360 observe the intensity of the transmitted light. 1. Find the transmission axis of the bottom polarizer with the small polarizer (mounted in a black plastic ring) from your box. This one has its transmission axis marked with two groves in the plastic. Explain your procedure and use a piece of masking tape to mark it on the rim of the polarimeter. Find the transmission axis of the top polarizer in a similar way and mark it in the same way. 2. What is the angle between the transmission axes of the two polarizers when there is Maximum transmission? What about no transmission?

2 C. The Amplitude of the Transmitted E-Field: The light coming from the bottom polarizer is linearly polarized. Consider the case in which this linearly polarized EM wave s E-field vector makes an angle θ with the transmission axis of the analyzer. The analyzer transmits oscillations in one direction (along the transmission axis) and absorbs those that are perpendicular to that direction. For angles not 0º or 90º with respect to the transmission axis the polarizer transmits the component of the E-field along the transmission axis and absorbs the rest. 1. Write the space- and time-dependent E-field shown above as a vector sum of two electric field vectors, one oscillating in a plane parallel to the analyzer transmission axis, ŷ, and the other oscillating in a plane perpendicular to the analyzer transmission axis, ˆx. θ 2. Write down the space- and time-dependent E-field of the EM wave transmitted by the analyzer. What is its polarization angle with respect to the analyzer s transmission axis? Explain. 3. What is the ratio of the amplitude of the E-field of the EM wave transmitted by the polarizer to the amplitude of the E-field of the incident EM wave? Explain. 4. Why might it be useful to decompose the E-field into two parts when it passes through an analyzer? How would you do this if the analyzer was not aligned with the y-axis? Explain.

3 5. Set the analyzer so that no light is transmitted. Now insert a third polarizer between them and rotate it. How many degrees of rotation does it take to go from light to dark? Explain this effect by thinking about the E-field components transmitted at the second and then third polarizer. D. Superposition and Polarization: Note that above you separated a polarization state into two perpendicular components, one absorbed and one transmitted. It is also possible to assemble a polarization state from two perpendicular polarization states. That is, the components themselves can be thought of as two independent polarization states. 1. Add the two polarization states shown in the diagram to find the angle and amplitude of the superposition state. Give the angle with respect to vertical and the amplitude in terms of E o. Draw the result in the diagram. (This is similar to Monday s group problem.) 4E o 3E o 2. The diagram above shows these two waves at an instant when both E-fields are at maximum. Are these two waves in phase with each other? Explain. The 3-D diagram shows how the components behave in time. t

4 E. Circular Polarization: Consider the case where the horizontal component is time-delayed, or phase shifted by one quarter of a period. That is, the horizontal component starts later in time as illustrated by the 3-D diagram below. Let both amplitudes be E o here. t o t1 t2 t3 t4 t t 5 1. Use the axes below to draw the components of each polarization as it varies in time. Also draw the vector sum on each axis. y x t o t 1 t 2 t 3 t 4 t 5 2. Describe the time-dependence of the total E-field (direction and magnitude). Does it oscillate?

5 3. Now consider the case where the horizontal component is time-advanced, or phase shifted by one quarter of a period. That is, the horizontal component starts earlier in time as illustrated by the 3-D diagram below. Let both amplitudes be E o here. t o t1 t2 t3 t4 t t 5 4. Use the axes below to draw the components of each polarization as it varies in time and draw the vector sum on each axis. y x t o t 1 t 2 t 3 t 4 t 5 5. Describe the behavior of the E-field and compare it to the previous example.

6 The two polarization states you just worked with are called right and left circular. They can be described by an E-field that rotates clockwise or counterclockwise with a constant magnitude. 6. Consider these two circular polarization states as components of a single polarization state. That is, add them graphically as you did the two linear polarizations. See the Arkansas Do Nothing demo with your TA. y x t o t 1 t 2 t 3 t 4 t 5 7. Write down the space- and time-dependent E-field of the EM wave that is the superposition of these two circular polarizations. What is its polarization angle with respect to y-axis?

7 F. Sugar Molecules: Sugars come in two varieties; left-handed (CCW) and right-handed (CW), and are like screw threads in this way. You will use Karo syrup, with is made of right-handed sugars only, since it is produced biologically. If you don t know what Karo syrup is, ask your Mother. Right circularly polarized and left circularly polarized light propagate at different speeds in such a chiral solution. This results in a time delay of one component relative to the other after passing through the solution. The time delay depends on the sugar concentration and the length of solution the light passes through. Consider the case when linearly polarized light is shined through the solution. Remember from the previous section that linearly polarized light can be thought of as a superposition of equal amplitude right and left circularly polarized components. The effects you will see are what you get when you add circularly polarized light of one variety with a time delayed circular polarization of the other variety. Get a set of four jars of Karo syrup, being careful not to tip them as the syrup will cling to the side and take time to run back down into the jar. 1. Place the large jar (lid off, open end up) on the polarizer and spend some time rotating the analyzer while looking through the polarizers and syrup. You should see colors in the syrup. In what order do the colors appear as you rotate the analyzer clockwise? 2. Place a filter (colored transparency) under the syrup so you are only looking at one color. Rotate the analyzer so that the light outside the jar is extinguished. Now rotate the analyzer left or right until the light through the syrup is extinguished. Record the difference. Filter color: Relative rotation (deg): 3. Do this for the other jars and record all your data below. Sugar depth Blue angle Green angle Red angle Other angle

8 4. Plot the data for each color on the axes below. Use a reasonable scale on the axes and put each color on the graph. Polarization Rotation Sugar Depth 5. Below are two circular polarizations with the CCW component delayed by π/2 (90º). They are drawn at various times like in previous examples. What is their sum or superposition state? Is it linear? If so, what is the angle it makes with the vertical? y x t o t 1 t 2 t 3 t 4 t 5 6. Write down a relation between the phase delay of the CCW component and the angle of the resulting linear polarization with respect to the y-axis (see above).

9 To understand the light as it passes through the Karo, we think of it a superposition of right and left-circularly polarized light. This works, because (as in E-6 and F-5) adding two equalamplitude circularly polarized EM waves together gives a linear polarized wave. The polarization direction depends on the phase difference of the circularly polarized waves. The effect of the Karo syrup is to create a difference in propagation speed between the left- and right-handed circular polarization, since it has only right-handed sugars. Since they travel at different speeds, they arrive at the top of the Karo at different times, but they are oscillating up and down in time at with exactly the same period. This leads to a phase difference between right and left-handed polarization components. 7. Suppose that the CW component moves.0001% more slowly than the CCW component (take v CCW =3x10 8 m/s). (Remember,.0001% is a factor of =10-6 ). What is the time delay of the CW component relative to the CW component after traversing 10 cm of Karo? 8. The wavelength of red light is ~ 700 nm. What is the time oscillation period? 9. What fraction of this oscillation period is the time delay calculated in 7? 10. What phase shift and polarization rotation does this correspond to? 11. Explain whether this change in polarization rotation with wavelength is qualitatively consistent with your measurements for different colors of light.

10 G. Making and Detecting Circularly Polarized Light, λ/4 Wave Plates: There should be two λ/4 wave plates in your kit. They have an E-axis (extraordinary) and an O-axis (ordinary). Polarization components parallel to the E-axis exit the plate delayed in time with respect to components parallel to the O-axis by ¼ of a cycle. Follow the directions in the manual for Experiment 5 and 6 and answer the four questions below that are about the same as the four in the text. (two in Exp. 5 and two in Exp. 6) 1. Use the hint in the manual to explain why a λ/4 plate rotated between crossed polarizers can cause extinctions separated by 90º? Hint #2: λ/4 plates do not always make circularly polarized light. 2. Rotate the λ/4 wave plate so it looks bright. (See Hint #2 above) Leave the λ/4 wave plate in this position and rotate the analyzer through 2π radians and explain why the brightness remains relatively constant.

11 Now do experiment 6 in the lab manual and answer the two following questions. 3. Explain the behavior when rotating the analyzer with the plates positioned with their optic axes aligned. (The bottom one needs to be set to create circularly polarized light before the second is placed on top.) 4. Explain the behavior when rotating the analyzer with the plates positioned with their optic axes at 90º with respect to each other. (The bottom one needs to be set to create circularly polarized light before the second is placed on top.)