Engineering Sciences 151. Electromagnetic Communication Laboratory Assignment 4 Fall Term

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1 Engineering Sciences 151 Electromagnetic Communication Laboratory Assignment 4 Fall Term OBJECTIVES: To build familiarity with interference phenomena and interferometric measurement techniques; to use a Mach-Zehnder interferometer to measure the index of refraction of glass and polyacrylate materials at microwave frequencies; to use a Michelson interferometer to study the light emission spectrum of sodium vapor. INTRODUCTION: The notion of interference is perhaps the single most important concept in wave propagation. It is the basis for nearly all high-frequency measurements and signal processing schemes. To observe interference effects we need to have two signals, say, E A and E B, that are derived from the same signal source and that are, thus, time synchronous, follow two distinct paths d A and d B to impinge upon a single observation point. At that point, the total field is the sum of the two component fields and is give by E = E A exp( jβ d A ) + E B exp(jβ d B ) = E exp( jφ ) where E = E A + E B + EA E B cos[ β(d A d B ) + ( φ A φ B )] and φ = arctan E sin β d + φ A A A E A cos β d A + φ A [ ] + E B sin[ β d B +φ B ] [ ] + E B cos[ βd B +φ B ]. In these circumstances, the magnitude of the total field varies continuously between a maximum of and a minimum of E A + E B + E A E B = E A + E B ("constructive" interference) E A + E B E A E B = E A E B ("destructive" interference) as a function of the phase difference β ( d A d B ). An interferometer is a device designed to produce such an "interference pattern" by systematically changing the effective path difference. There are many different types of interferometers! Standing waves on transmission lines are one particularly significance example of an interference phenomenon and, thus, we have already studied some aspects of interferometry in considerable detail. In fact, the slotted line used in Laboratory Assignment 3 is effectively an interferometer which measures the interference of "leftpropagating" and "right-propagating" waves. More precisely, the resonant section or resonator studied in Section 1h of that assignment is an example of a so called Fabry-Perot interferometer. In this laboratory assignment we study two other famous and extremely useful interferometric configurations.

2 PAGE- THE MACH -ZEHNDER INTERFEROMETER: A MICROWAVE VERSION EXPERIMENTAL SETUP EQUIPMENT: Sweep Signal Generator: 8-1 GHz, Dorado International Corp. Model G4-197 Variable phase shifter, Hewlett-Packard, Model X885A Variable attenuator, Hewlett-Packard, Model X38A Slotted line section, Hewlett-Packard, Model 809B Detector mount, Hewlett-Packard, Model X485B Microwave isolators, Cascade Research Corp. and Microwave Associates Low-noise Preamplifier, Stanford Research Systems, Model SR MHz Dual-channel oscilloscope, Tektronix, Model 13A Miscellaneous X-band waveguide components BACKGROUND AND THEORY OF MEASUREMENTS: The Mach-Zehnder interferometric configuration has emerged as the basis of some of the most important switching devices in high data-rate fiber optic communication systems. In the microwave version of a Mach-Zehnder interferometer, illustrated above, the signal emitted from the signal generator is carried by coaxial cable to a coax-waveguide transition where it is re-radiated into X-band waveguide. This beam then splits into two, essentially, equal beams at the H-plane tee junction. After propagating along two distinct path, the two beams again merge in a second H-plane tee. The resultant beam propagates out of the third arm of the tee and impinges on a crystal detector. The output of the detector depends on the magnitude of the sum (i.e. the interference) of the two signals. Thus, when the effective path difference is an odd number of half-wavelengths, the output will be zero or a minimum and when it is an even number of half-wavelengths, the output will be a maximum. The relative phase and magnitude of the signal propagating in the lower (reference) path may be precisely adjusted by means of the

3 PAGE-3 variable phase shifter and attenuator. The inclusion of microwave isolators (essentially true one-way windows ) within the configuration helps to minimize the troublesome cumulative effects of multiple reflections from various waveguide discontinuities. MEASUREMENTS: 1. Set the Dorado signal generator so that output signal is a 1 khz AM modulated sinusoid at some convenient mid X-band frequency, say 10 GHz. The output of the tunable detector should be amplified in one channel of the tuned amplifier and observed on the dual-channel oscilloscope (Of course, you should tune the detector to obtain maximum output). The output of the slotted line detector should be amplified in the other channel of the tuned amplifier and observed on the dual-channel oscilloscope as well. With the test section empty adjust the phase shifter and attenuator to obtain a null output from the interferometer. Near the null setting, increase the gain of the preamp and notice how an exceedingly small phase change gives a very large change in the output amplitude. In fact, notice that the null is very sensitive to mechanical deformations of the interferometer! It is this high phase sensitivity which makes the Mach-Zehnder configuration so useful as the basis of fast pulse modulators. In this regard, also notice that the balance of the interferometer shifts when the location and penetration the slotted line probe are varied.. Again with the test section empty and the signal generator set to 10 GHz use the slotted line section to measure the VSWR and, thus, determine the reflectivity of the microwave horn. Note the locations of the maxima and minima using the end of the horn as a reference. 3. With the test section still empty and the signal generator set to 10 GHz, carefully re-measure and record the phase shift and attenuation necessary to null the interferometer: also, re-measure and record the reflectivity of the horn. Then mount a polyacrylate (viz. Lucite or Plexiglas ) sheet orthogonal to the waveguide axis. Measure and record the change in phase shift and attenuation necessary to once again null the interferometer (We suggest that you introduce the material into the test section in small steps and re-null the interferometer after each step). Also measure the change in reflectivity of the horn to estimate the amount of power reflected by the sheet. To quote from the Dorado manual (with minor editing): Frequency setting: Press the "F(MHz)". Its LED turns on. Current frequency value is displayed on F panel. A blinking digit shows discreteness of frequency re-tuning. Set a necessary increment with "<--" and "-->" buttons and, turning knob "TUNE", set a frequency value. Output signal level setting: Press the "P" button. Panel P displays an output signal current value. A blinking digit shows discreteness of output signal. Set a necessary increment with "<--" and "-->" buttons and, turning knob "TUNE", set a P out value. AM mode setting: Press and hold AM button. Look at P panel values: "0" - AM turned off. "BP" - internal AM with 1kHz modulation freq. "BH" - external AM with modulation frequency from 0 to 3 khz When internal or external AM modes are selected, P panel displays a percent modulation current value in the range from 0 to 30%. "AM"'s button LED turns on.

4 PAGE-4 4. Repeat the measurements in 3.) with a sheet of plate glass. REPORT: 1. Estimate the effective input impedance of the microwave horn at 10 GHz.. Calculate the polyacrylate's index of refraction and attenuation constant at 10 GHz. 3. Calculate the plate glass's index of refraction and attenuation constant at 10 GHz. THE MICHELSON INTERFEROMETER: AN OPTICAL VERSION EXPERIMENTAL SETUP Warning: Do not touch any optical surfaces! In particular, contaminants from your fingers will permanently destroy the usefulness of any front-surface mirror. EQUIPMENT: Michelson interferometer, The Ealing Corp., Model He-Ne Laser, Spectra-Physics, Inc., Model A vintage sodium vapor lamp A microscope objective. An optical diffuser Assorted optical components and mounting hardware

5 PAGE-5 BACKGROUND AND THEORY OF MEASUREMENTS: The Michelson interferometer is a versatile instrument of the utmost historical and technical importance. One of these instruments, built with the greatest care and having extremely long path lengths (11 meters) was used by Michelson and Morley in 1887 to perform one of the most celebrated of all scientific experiments. Their observations formed the basis of Einstein's theory of relativity a few years later. Another was later used by Michelson to measure the standard meter (in Paris) in terms of the wavelength of cadmium light. Such interferometers are now routinely used for frequency discrimination in fiber optic communication systems. In the present experiments, we use a Michelson interferometer to measure (1) the (average) wavelength of the familiar yellow emission spectrum of sodium vapor and () the small difference in wavelength between the two components of yellow sodium light. The figure above shows the basic design of the interferometer. For stability, all optical components are mounted on a base which consists a rigid aluminum casting, stiffened by webs around the edge and ribbing under the essential optical mounting points. Incident light is transmitted through plate P 1 to the partly silvered surface. At this point, half the beam is reflected to M 1 and the other half is transmitted to M (passing through the compensator plate P on the way). Mirrors M 1 and M reflect the light back to the half silvered plate, and half of each beam reaches the observation point, the remainder being directed back to the source and lost. Mirror M 1 can be translated toward or away from the observer by means of a precision, micrometer-driven movement. Looking through plate P 1 toward the mirror M 1, the observer sees light reflected from both the real mirror M 1 and the image of the mirror M. M is adjustable with tilt screws so that its image can be made accurately parallel to M 1. It is the spacing of M 1 and M (or its image) which determines the interference or "fringe" pattern. It is clearly possible in this instrument to reduce the effective difference in path length (d 1 - d ) to zero or, in fact, to make it negative, essentially moving one of the mirrors through the other! As indicated, the mirror M 1 may be traversed 5mm along the viewing axis to establish the correct path length conditions. Movement is by a micrometer head working through a pivoted beam against a parallel, "backlash-free" spring action. The micrometer has a 8mm milled head, 5mm of movement, and a vernier reading to 0.01mm. Since the beam provides a 5:1 reduction in motion, the micrometer measures motion of the mirror to 0.00mm. If the two mirrors, M 1 and M, are accurately parallel the interference pattern is observed as a series of concentric circles or fringes. The wavelength of monochromatic light is determined in terms of the number of circular fringes disappearing into or appearing from the center of the pattern. The relation is d a d b = (m a ) λ where d a and d b are two positions of the mirror M 1, (m a ) is the difference in the corresponding orders of interference (number of fringes), and λ is, of course, the wavelength. Some of this discussion is taken from Optics: Experiments and Demonstrations, C. Harvey Palmer (The Johns Hopkins Press, Baltimore, 196)

6 PAGE-6 The wavelength difference between two closely spaced spectral lines such as the two components of the so called "sodium D line" is determined from their average wavelength and the "visibility" of the fringes. At certain positions of mirror M 1, you will observe that the fringes are clear and sharp whereas at intermediate positions, they are very indistinct. This change in visibility is due to the fact that there are two sets of fringes which are not identical (see figure below). At some positions, the two sets of fringes are in step and the overall fringe pattern sharp, whereas at the intermediate positions the two sets are out of step so that the overall pattern is washing out. The separation of the positions of maximum (or minimum) visibility of the fringe pattern is a measure of the wavelength difference. "visibility" max. min. max. λ λ' d a λ < λ' d b Fringe visibility with two wavelengths To find an expression for that wavelength difference, let the two wavelengths and their interference orders be distinguished by primed and unprimed symbols. Suppose that d a is a position where both sets are in step (maximum visibility) then d a = m a λ = m a λ If M 1 is translated from d a through a fringe visibility minimum to the next fringe visibility maximum, that new position d b is given by. d b = m b λ = m b λ In traversing this distance, the shorter wavelength will have given rise to (m a ) fringes and the longer wavelength to one less fringe (see figure) - i.e. m a = m a m b +1 Thus, eliminating the interference order, we find that

7 PAGE-7 λ = λ λ (d a d b ) MEASUREMENTS: 1. Use the He-Ne laser to align the interferometer. Follow the multiply reflected laser beam through the interferometer and adjust mirrors so that principal output beams are colinear. Need I say it, yes: Do not look directly into the laser output beam or into one of the specularly reflected secondary laser beams. After aligning the laser beams, spread the input beam with a microscope objective and observe the interference fringes produced by the laser. When the fringes are found, adjust the tilt screws very carefully so that the fringes become circular and their common center lies at the center of the field of view. Now slowly translate M 1 in the direction that makes the fringes move inward and disappear in the center. As exact path equality is approached, the fringes become much broader and the circular shape of the fringes becomes badly distorted. Thus, the point of exact path equality is somewhat uncertain. However, when the point is reached where the fringes begin to move outward from the center, the point of path equality has been passed.. Turn off the laser and move the sodium vapor lamp into position to measure the average wavelength of the yellow spectral component. Beginning near the point of path equality, move M 1 in either direction until the fringes are as sharp as possible. Moving M 1 in one direction to reduce the effects of backlash record the micrometer readings for every tenth fringe for a total of 00 fringes. 3. The expression above gives the difference in wavelength of the closely spaced sodium spectral lines in terms of the distance between two successive fringe visibility maxima or minima. The exact positions of the maxima or minima are, however, difficult to determine. In order to obtain a good value for the wavelength difference, about 0 minima should be observed. Begin at a position where the path difference is rather small and move the mirror M 1 through successive minima merely observing the field without recording data. Return M 1 back beyond the starting point and after removing backlash, record the micrometer readings for at least 0 successive minima. REPORT: 1. Explain the circular shape of the interference pattern.. Would it be possible to observe a fringe pattern with white light? Discuss. 3. Using a method of differences, calculate from your data the average wavelength of the sodium vapor D line (i.e. use the micrometer difference for 0 and 100 fringes, 10 and 110 fringes, 0 and 10 fringes, etc.) 4. Again using a similar method of differences, calculate from your data the splitting of the sodium vapor D line.

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