4500T101 - (8) Optical Terminology (14) Arrayed Waveguide...

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Unformatted text preview: (8) Optical Terminology (14) Arrayed Waveguide Grating Router Name (Please Print) (14) Fourier Transform Infrared Spectrometer (16) Light Measurement (15) Total Internal Reflection (15) Paraxial Ray Approximation (18) Refraction at Convex Spherical Surface E C E 4500 First Examination February 12, 2001 Rules for exam: 43!» UI 9°“? 10. 11. 12. 13. 14. 15. . The time allowed is 60 minutes. The test will start at 9:00am (rather than at 9:05am) and end at 10:00am (rather than at 9:55am). . Answer all questions. The value of each question is given in parentheses by the question. There are a total of 100 points possible. . All work must be shown for full credit. . Put your final answers in the locations specified. . You may use the six new single—sided 8 1/2" x 11" information sheets that you have prepared. Some physical constants are given below. . You may use one "book of math tables." You may use a "pocket calculator" that can be put in a normal-size pocket and requires no external electrical power. You may not use portable, lap-top, or notebook computers nor wireless or network connections. . You may not use any reference materials other than those listed above. Therefore, you may not use the class notes, any other textbooks, homework problems, reprints of papers, journals, prayer books, etc. There is to be no sharing of anything. If excess information is given in a question, ignore the unneeded information. If too little information is given in a question, assume the information needed and clearly note this with your work. Any changes to the examination will be written on the chalk board. Check the chalk board periodically during the examination. Any acts of dishonesty will be referred to the Dean of Students without prior discussion. The official written Institute procedures on academic honesty (entitled "Maintaining Academic Honesty" and available from the Dean of Students Office) will be followed in all cases. Have a happy exam! h = 6.6260755 x10‘34joule-sec c = 2.99792458x108meter/sec Table 1 STANDARD LUMINOSITY DATA Wavelength Luminous efiicacy Wavelength Luminous eflicacy (8) Optical Terminology State in words the meaning of the acronyms listed below. Put your answers in the spaces provided. DVD H DBR EDFA FWHM = (14) Arrayed Waveguide Grating Router An arrayed waveguide grating router is used as a wavelength demultiplexer. That is, a series of wavelengths that are multiplexed together in a single fiber are separated into individual waveguides by the arrayed waveguide grating router. The arrayed wave- guide output section from the combined channel waveguides of an arrayed waveguide grating router is shown below. The output ends of the channel waveguides lie along a circle of radius R as shown. This arrayed channel waveguide output may be well approx- imated as if it were a metallic curved reflection grating illuminated by a point source from the center of curvature (indicated by the dot). Under this approximation, state quantitatively the locations of the individual fo— cused wavelengths. This should be the locations where the output channel waveguides are placed to receive the demultiplexed wavelengths. Do not use the paraxial ray ap- proximation. In addition to this statement, indicate these locations on the diagram. SLAB § WAVEGUIDE :1 :l COUPUNG ARRAYED REG'ON CHANNEL :I WAVEGUIDES _—_:::_:I g (14) Fourier Transform Infrared Spectrometer A Fourier Transform Infrared (FTIR) spectrometer is based on a Michelson in- terferometer. An FTIR spectrometer is capable of determining the spectral content of a light source. This is accomplished by scanning one of the mirrors of the Michelson inter— ferometer and recording the output interferogram as a function of the optical path dif- ference between the two interfering beams. For the case of two narrow linewidth wave- lengths (represented by their wavenumbers, where wavenumber = 1 /wavelength) in the source (upper left figure), the resulting interferogram is shown (at upper right). Zero optical path difference is at the left edge of the graph. A Fourier transform relationship exists between the spectrum in wavenumber space and the interferogram in optical path difference space. For the same FTIR instrument in a second case, the source is changed and now consists of two narrow linewidth wavelengths (lower left figure) that are closer together in wavelength (and wavenumber). Sketch the new resulting interferogram for this source in the lower right figure. Put zero optical path difference at the left edge of the graph. INTENSITY INTENSITY <— INTENSITY INTENSITY WAVENUMBER OPTICAL PATH DIFFERENCE Light Measurement Radiance An important quantity in light measurement is “radiance.” Using complete sen- tence(s), define what is meant by “radiance.” Give the mks units of “radiance.” Apparent Brightness Four light sources of freespace wavelengths 500nm, 520nm, 600 nm, and 650nm each emit 2.0 milliwatts with the same beam divergence and beam geometry. Which source appears brightest? Check the one correct answer below. 500 nm 520 nm 600 nm 650 nm Illuminance An illumination of 100 footcandles at a wavelength of 500nm corresponds to which of the following irradiance values? Check the one correct answer. 2.935 x 10'4 watts/m2 3.16 x 10’3 watts/m2 0.455 watts/m2 4.90 watts /m2 (15) Total Internal Reflection The prism shown below is to be used in air as a totally internally reflecting prism. ' 45° 45° Calculate, showing all work, the range of values of the index of refraction, n, in order for total internal reflection to occur for the normally incident ray shown. Express the indices of refraction accurately to the nearest 0.0001. Put your final answers in the spaces provided below. (15) Paraxial Ray Approximation A thin prism of index of refraction n and apex angle <15 is used in air to deviate a light beam. The apex angle 4) is small. The angle of incidence oz is small. Using the paraxial ray approximation, develop an expression for the angular de- viation 6 in radians for this case of small ¢ and small a. Put your final answer in the space provided. (18) Refraction at Convex Spherical Surface The interface between two lossless dielectric regions is a convex spherical surface as shown in the diagram. The spherical surface has a radius of curvature of 50 mm. The index of refraction of the left-hand region is 1.5. The index of refraction of the right- hand region is 1.0. An object is located on the axis of the optical system 200 mm to the left of the spherical surface. Calculate, showing all work, the location of the image and the linear magnifica- tion. Express your answers accurately to four significant figures. Specify whether the image is left or right of the interface. Specify whether it is a real or virtual image. Put your final answers in the spaces provided. Using a distance between tick marks of 50 mm, draw on the above diagram, the object, the parallel ray, the chief ray, the focal ray, and the image. Image distance from interface = mm The image is to the (left) (right) of the interface. (Circle one.) Linear magnification = The image is (real) (virtual). (Circle one.) Optical Terminology DVD 2 Digital Versatile Disk or Digital Video Disk DBR = Distributed Bragg Reflector EDFA = Erbium-Doped Fiber Amplifier FWHM = Full Width at Half Maximum Arrayed Waveguide Grating Router Under the approximation as a metallic curved reflection grating illuminated by a point source from the center of curvature, the arrayed channel waveguide outputs are focused on the circumference of a Rowland circle. The diameter of the Rowland circle is equal to the radius of curvature, R, of the curved grating. The center of the Rowland circle is midway between the center of curvature and the center of the grating. Fourier Transform Infrared Spectrometer Two wavenurnbers (wavelengths) in a source constructively interfere when there is zero optical path difference between them. However, they destructively interfere after the optical path difference is great enough so that they are out of phase. For two wave- lengths that are closer together, a greater optical path difference is required for them to be out of phase. INTENSITY INTENSITY <- INTENSITY INTENSITY WAVENUMBER OPTICAL PATH DIFFERENCE Light Measurement Radiance Radiance is the radiant power output per unit solid angle per unit projected area. The mks units of radiance are watt /steradian-meter2. Apparent Brightness The 520nm light source appears brightest. Illuminance . _ 1001m/ft2 _ 2 Irradlance ‘ (O.323)(680lm/w)(12in/ft)2(25.4 x 10'3m/in)2 ’ 4'90 w/m Total Internal Reflection nmm sin 61 = nm-r sin 90° nmin = l/sin 01 = 1/sin 45° 2 1.414214 nmax = 00 Paraxial Ray Approximation The deviation, 6, is given by 6 = a — ¢ + sin—1 {n sin[¢ — sin—1(sina/n)]} In the paraxial ray approximation, 6=oz—¢+n(¢—a/n) or 5=¢(n—1) Refraction at Convex Spherical Surface R = +50mm, m = 1.50, 712 = 1.00, s = 200mm an f1 = — = n2 - 721 R f2 = L = —100mm 712 — n1 n1 n2 le—nl s + 3’ _ R R2 - 8’ = m _ n _ m = —07.143 mm. R s 7118, . . . m = — = 0.4286 (uprlght vu‘tual Image) ...
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This note was uploaded on 04/29/2008 for the course ECE 4500 taught by Professor Gaylord during the Spring '08 term at Georgia Institute of Technology.

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4500T101 - (8) Optical Terminology (14) Arrayed Waveguide...

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