ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 6: Polarization Original: Professor McLeod SUMMARY: In this lab you will become familiar with the basics of polarization and learn to use common optical elements to manipulate polarization via diatenuation (polarizers), retardation (wave plates) and Fresnel reflection (polarization beam splitting). This will give you the required background to construct a remote sensing apparatus that can detect the concentration of sugar in a liquid (e.g. for non-invasive diabetes monitoring). PRELAB [20 POINTS TOTAL; 5 POINTS EXTRA CREDIT]: Note: Virtually all of the HW problems in the text are good for understanding, so if you are having trouble, try problems with the solutions in the back. HOMEWORK PROBLEM 1: Pedrotti 3 14-9. HOMEWORK PROBLEM 2: Pedrotti 3 14-1. If this is illuminated by a linear polarization parallel to what is the output Jones vector? HOMEWORK PROBLEM 3: Derive the Jones matrix for a half-wave plate at an arbitrary angle If this is illuminated by a linear polarization parallel to what is the Jones vector of the output? Compare the output polarization states and total power transmitted of problems 2 and 3. HOMEWORK PROBLEM 4: Pedrotti 3 15-16. Note that the use of the phrase specific rotation here is incorrect. Take part (b) to be asking for in units of degrees / mm ala Table 15-2. HOMEWORK PROBLEM 5: Students traditionally have trouble visualizing the different states of polarization and their interaction with waveplates and polarizers. This problem will attempt to help you with this visualization. It covers the same concepts as the previous problems but does not use the compact notation of Jones. The problem description is long, but the problem simple. Take some time and understand each step. The polarization of light is the curve made by the tip of the E-field vector in the plane normal to propagation as a function of time. Lissajous figures, commonly shown in EE labs as an introduction to oscilloscopes, are a way of visualizing these curves. Use an applet (e.g. http://fipsgold.physik.uni-kl.de/software/java/lissajous/index.html) to observe the following polarization states and answer the associated questions. Always leave the temporal frequency (or period) of the x and y components to be the same. a) Leave the relative phase delay between the x and y components phi=zero and explore different relative amplitudes. What polarization state is this? b) Now set the phase delay (phi) equal to + and -90 degrees and the amplitudes equal. What polarization state is this? Version 1.2, 8/18/12 McLeod and Gopinath 1
c) Finally, what state do you generate if you don t obey the conditions of a and b? That is, arbitrary angle and/or unequal amplitudes? Make sure you understand how one state evolves into another as you change the knobs. d) Polarizer function: Set up an arbitrary elliptical state. Now imagine this is sent into a polarizer. This is a material that strongly absorbs one linear (x or y) polarization but not the other (y or x). Assume our polarizer attenuates the y component and passes the x component. Simulate this by setting the amplitude of the y component (Ay) equal to zero. What is the output state? Do this as many times as needed with different input states (once may be sufficient). What if you input a non-zero amplitude but get zero amplitude (no light) out what was the input state? What can you conclude about the input state if you were to rotate your polarizer yet always get the same total power transmission? Hint: The input state is one you explored in (a-c). e) Half wave plate function: Set up linear polarization at 45 degrees and state the general conditions on amplitude and relative phase. Now imagine that this is the input wave to a crystal that will delay (change the phase) of both the x and y components. The absolute (total, common) delay isn t very important it doesn t change the shape of the polarization curve. The relative delay (the difference introduced to the x and y components) does change the polarization. A half wave plate introduce a half wave (, 180 degrees, /2) of x relative to y. Simulate this by adding 180 degrees to phi. What is the polarization state that emerges from the crystal? f) Quarter wave plate function: Set up the same 45-degree linear polarization as in (e). Now imagine cutting the crystal from (e) in half lengthwise so we only get a quarter wave (, 90 degrees, /4) delay between Ex and Ey. Simulate this by adding 90 degrees to phi. What is the polarization state that emerges from the crystal? Now imagine rotating the crystal by 90 degrees so that if (for example) we previously delayed x, now we delay y. Simulate this by changing phi to -90 degrees. What is the polarization state and how does it differ from the previous case? Can you think of a way to tell the difference between these two states in the lab using waveplates or polarizers? Hint: Work on this a bit, but the answer is actually no. g) Write down the Jones vector described by the Lissajous app using the variables in the app. What variables didn t you use? These are assumed by the Jones method. DESIGN PROBLEM [EXTRA CREDIT - 5 POINTS]: Create a matlab utility using Jones vectors to plot the output power as some component in an optical train is rotated through 360 degrees. Define a library of Jones vectors including standard input polarizations including various linear and circular states. Similarly, define a library of common components including polarizers, quarter-wave plates, half-wave plates and an optically active plate with some rotary power. Finally, define the rotation matrix R with the rotation expressed as a variable theta. Then create a for loop over theta into which you can cut and paste a set of Jones calculations to calculate the output power from an experiment as theta is changed. After the loop, plot the power versus theta. This will make most of the post-lab very efficient. Turn in your code for credit with a sample plot. Version 1.2, 8/18/12 McLeod and Gopinath 2
TECHNICAL RESOURCES: TEXTBOOK: Chapters 14 & 15 LECTURE NOTES: Lecture 6, Polarization. EQUIPMENT AVAILABLE: A collimated, spatially-filtered, JDS Uniphase 1103P-3020 helium neon laser. The laser wavelength is 633 nm. Polarizing components: (2) sheet polarizers, (1) quarter and half wave plates, (1) polarizing beam splitter. A flat glass plate (microscope slide) as a Brewster-angle beam sampler. A stressed plastic part such as a transparent spoon or a piece of transparent tape on a glass slide. A test chamber for fluids with windows on opposite ends Sucrose solutions (Karo syrup) of 0, and approximately 0.1, 0.2 and 0.4 g/cm 3 concentration. LAB PROCEDURE: STEP 1: ANALOG OPTICAL ROUTING VIA LINEAR POLARIZATION ANGLE In the collimated beam, place the half-wave plate (on a rotation stage) followed by the polarizing beam splitter. Observe that you can control the intensity out the two paths via rotation of the half-wave plate. Mount the microscope slide so you can reflect the beam off of one of its 1 mm edges. Be careful of the sharp edges, particularly in the dark. This arrangement allows you to easily separate the front surface from the back surface reflections. Insert the slide into either the transmitted or reflected path and rotate the glass by turning the post in the post holder, observing the intensity of the reflection from the front air/glass interface. Observe and record Brewster s angle in one of the two paths and use this to unambiguously identify the polarizations in the two paths. Remove the slide. Adjust the half-wave plate for minimum transmission and maximum reflection. Which of these conditions gives you the most sensitivity on the rotation? Record the angle of rotation from the half-wave plate mount. Then adjust for minimum transmission and maximum reflection. Note the amount of rotation between this setting and the previous. Version 1.2, 8/18/12 McLeod and Gopinath 3
Transmitted Collimate HWP PBS Reflected Figure 1. Setup for step 1. In your lab book: 1. Use your measurement of Brewster s angle to calculate the index of refraction of the glass. Estimate your accuracy via an estimate of the accuracy of your angle measurement. 2. Use Jones matrices to predict the intensity efficiency of the transmission and reflection ports for an ideal half-wave plate and polarizing beam splitter combination. Make a plot of both efficiencies and their sum as a function of halfwave plate rotation angle. Comment on why the sum must have the form shown. Compare your measured angles of the half-wave plate to this plot. STEP 2: CIRCULAR POLARIZATION Place the quarter-wave plate, then the sheet polarizer after the polarizing beam splitter. Rotate the quarter-wave plate and observe the output after the polarizer. Can you adjust for nearly zero transmission as you did in step 2? Collimate HWP PBS QWP Polarizer Figure 2. Setup for step 2 (a). Replace the polarizer with a mirror and observe the output from the reflected beam splitter port (see figure). Rotate the quarter-wave plate and observe the output. Record the quarter-wave plate angles which result in minimum and maximum transmission from the reflected polarization beam splitter port. This is sometimes referred to as an isolator, although it is not a true isolator which is a non-reciprocal device. Version 1.2, 8/18/12 McLeod and Gopinath 4
Collimate HWP PBS QWP Mirror Figure 3. Setup for step 2 (b). In your lab book: 1. Use Jones matrices to explain both results. Hint: In the second case, if you unfold the optical path by removing the mirror and copying components in the order they are encountered, the double-pass through the quarter-wave plate becomes a single pass through two identical quarter-wave plates. This considerably simplifies the analysis. 2. Extra credit: If the isolator were configured for maximum power through the reflected port and thus minimum power directed back to the laser, where would the power go if a mirror were put at the top of figure 4, sending the light backwards? A true isolator would still protect the laser does this arrangement? STEP 3: STRESS TESTING VIA POLARIZATION Place a polarizer after the beam splitter and rotate it for minimum transmission. Then insert a molded clear plastic part such as a spoon or a piece of transparent tape on a glass slide. Observe the results in both the transmitted and reflected paths. Collimate HWP PBS Plastic part Polarizer Figure 5. Setup for step 3. In your lab book: Using the same Jones matrix model from above, explain what you observe. Compare the output to the interferograms of the previous lab. STEP 4: CHEMICAL SENSING VIA OPTICAL ROTATION Many organic molecules have a spiral shape DNA is one of the most famous. These molecules thus have two possible forms: left- and right-handed. For reasons that are still a mystery to biologists, life on earth uses just one of these forms for each particular molecule. Thus, a solution of (say) sugar will contain only one handedness of sugar. Version 1.2, 8/18/12 McLeod and Gopinath 5
The other, mirror-image form can have similar properties including taste, but our bodies cannot digest it. A circularly-polarized electromagnetic wave propagating along such a spiral molecule will experience a different index of refraction (or speed of propagation) depending on whether the handedness of the wave and molecule are the same or opposite. This is referred to as circular birefringence or optical activity. In the prelab problem 4, you showed that a linearly-polarized wave incident on such an optically-active material will exhibit a rotation of the plane of polarization as it propagates. This rotation can be detected and used to measure the amount or type of a spiral molecule in solution. Since this can be done without physically touching the liquid, it is used by diabetics to monitor their blood-sugar and for measurements of the composition of the atmosphere. Set up the simple measurement system below and adjust the polarizer for minimum transmission. This is your zero angle. Fill your test chamber with each solution in turn and again adjust for minimum transmission. Record each angle of rotation from zero. Collimate HWP PBS Test chamber Polarizer Figure 6. Setup for step 4. Figure 7. Sucrose molecule, C 12 H 22 O 11 or cane sugar (Wikipedia). In your lab book: Plot your rotation angle vs the actual sugar concentrations, c. This notation is slightly different than used in the book, but more standard. Using a linear fit to this data, extract the specific rotary power (aka specific rotation) 20 C 633nm 20 C 633nm Lc of sucrose given the relation Version 1.2, 8/18/12 McLeod and Gopinath 6
where the length of the sample, L, is defined to be in units of dm = 10 cm by historical convention. Danger: Many sources including our textbook use incorrect units for the specific rotation (e.g. compare eq 15-4 to table 15-2 and then to problem 15-15). Compare your value to the published data for sucruose of 20 C 590nm 66. 5 g dm 3 cm Can this experiment tell the difference between solutions of different handedness? Version 1.2, 8/18/12 McLeod and Gopinath 7
Grading Expectations Lab Report 6: Polarization (100 total points) Name Name and group members. Abstract (10 points). Introduction (10 points) Methods (35 points) 1. ANALOG OPTICAL ROUTING VIA LINEAR POLARIZATION ANGLE, 10 pts a. Figure of setup, 4 pts b. Description, 6 pts 2. CIRCULAR POLARIZATION, 10 pts a. Figures for parts 2(a) and 2(b), 6 pts b. Description, 4 pts 3. STRESS TESTING VIA POLARIZATION, 8 pts a. Figure of setup, 4 pts b. Description, 4 pts 4. CHEMICAL SENSING VIA OPTICAL ROTATION 7 pts a. Figure, 3 pts b. Description, 4 pts Results and Analysis (35 points) 1. ANALOG OPTICAL ROUTING VIA LINEAR POLARIZATION ANGLE, 12 pts a. Measurement of Brewster's angle and calculation of index of refraction Description, 2 pts Accuracy estimate, 1 pt b. Jones matrices to predict efficiency of transmission reflection Description, 2 pts Plots of efficiencies and sums, 1 pt Comment on form of sum, 1 pt Comparison with measured angles, 1 pt 2. CIRCULAR POLARIZATION, 10 pts a. Jones matrices to explain step/figure 2(a) Explanation of what expect, 2 pts Comparison with results, 1 pt b. Jones matrices to explain step/figure 2(b). Explanation of what expect, 2 pts Comparison with results, 1 pt Version 1.2, 8/18/12 McLeod and Gopinath 8
c. Extra credit [4 extra points total]: Explanation of insertion of mirror in figure 4 Explanation of where power would go, 2 pts Does this protect the laser?, 2 pts 3. STRESS TESTING VIA POLARIZATION, 5 pts a. Jones matrices Explanation of what expect, 2 pts Comparison with interferograms of previous lab, 1 pt 4. CHEMICAL SENSING VIA OPTICAL ROTATION, 8 pts a. Plot rotation angle versus sugar concentration, 2 pts b. Extract rotary power, 2 pts c. Compare with published data, 2 pts d. Solutions with handedness explanation, 2 pts e. Conclusion (10 points) Summary of lab report f. References Include any references that you used. Version 1.2, 8/18/12 McLeod and Gopinath 9