4500T305 - General Questions Interference Filter (20) (22)...

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Unformatted text preview: General Questions Interference Filter (20) (22) Name (Please Print) Rectangular Aperture (22) Grating Beamsplitter (18) Fourier Hologram (18) E C E 4500 Third Hour Examination May 5, 2005 Rules for exam: LII-ka ooqu 10. 11. 12. 13. 14. 15. . The time allowed is 60 minutes. The test will start at 3:00pm (rather than at 2:50pm). 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 six new single-sided 8 1/2" x 11" information sheets that you have prepared in your own handwriting. Your information sheets may not include photocopied material. You may also use the six single—sided information‘sheets that you prepared for the first examination and the six single—sided information sheets that you prepared for the second examination. Some physical constants are given below. . You may use one "book of math tables" or calculus textbook. . You may use a "pocket calculator" that can be put in a normal-size pocket and requires no external electrical power. Graphing calculators and programmable calculators are acceptable. You may not use portable, hand-held, lap-top, or notebook computers or 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 textbooks, homework problems, reprints of papers, journals, pray'er 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 board. Check the 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 = 299792458 X108meter/sec e = 1.6021773349x 101966111 k = 1.38065812x10'23joule/K General Optical Engineering Questions 1. An asymmetric slab waveguide has thickness h, cover index n6, film index n f, and substrate index n8. Light lof freespace wavelength /\ is propagating in this waveguide both as a TEo mode and as a T E1 mode. It is desired to make the TEl mode become cutoff. However, it is desired to retain the TEo mode as a propagating mode. How can this be accomplished? (Circle one best answer.) a) increase A b) decrease h c) increase ns (1) increase 120 e) decrease n f f) all of the above g) none of the above 2. An asymmetric slab waveguide has thickness h, cover index nc, film index n f, and substrate index ns. Light of freespace wavelength A is propagating in this waveguide both as a TED mode and as a TEl mode. For these modes, (Circle one best answer.) a) group velocity of TE; mode < phase velocity of TED mode b) phase velocity of TEO mode < phase velocity of TE1 mode c) The TE1 mode is less tightly bound than the TED mode. (1) The propagation constant fl is smaller for the TE1 mode than for the TEO mode. e) all of the above f) none of the above 3. A symmetric slab waveguide has a film of refractive index nf and cover and substrate of refractive index of he : n3. The thickness of the film is h. For a T E0 mode excited in this waveguide at a freespace wavelength of A, the thickness at cutoff for the T E0 mode is (Circle one best answer.) a) 0 b) A/nf c) A/ns d) A/nc e) (n; — min/(n3: — n3) 0 (mic/mam; — nan/(n3 — mg) g) 00 4. A thin slab in air of thickness d and refractive index n with flat and parallel surfaces will strongly reflect normally incident light of freespace wavelength A for m being an in- teger if a) 2nd 2 m/\ b) 2nd 2 (m — %)/\ c)nd = mA yd) nd 2 (m — %)/\ e) 4nd 2 mA f) 4nd = (m — §),\ g) all of the above h) none of the above Interference Filter It is desired to use a “one half wavelength” thick interference filter in air to scan the freespace wavelength range around A0. The interference filter is specified to pass A, at normal incidence. The specified wavelength As > /\0. The one-half-wavelength layer in the interference filter has a refractive index n. This layer is surrounded by glass of refractive index 711 as shown in the figure. Calculate, showing all work, the angle of incidence in air, a()\0), needed to pass freespace wavelength A0. Express your answer as a function of A0, A3, and n only (elimi— nate any angles of refraction). Put your analytic expression in the space provided. (1 (A0) : (analytic expression) Calculate, showing all work, the angular tuning rate of the filter (the rate of change of the wavelength transmitted per unit change in the angle of incidence a) at wavelength A0. Put your analytic expression in the space provided. Angular tuning rate : (analytic expression) If a particular interference filter in air has a specified wavelength of As = 520 nm, n z 1.4, and n1 2 1.5, calculate, showing all work, the required angle of incidence to pass light of 514.5 nm. Express your answer in degrees. For this same case, calcu- late, showing all work, the angular tuning rate of the filter. Express your answer in nm/ degree. Express your answers accurately to four significant figures. Put your an— swers in the spaces provided. 0: (A0 : 514.5 nm) 2 degree Angular tuning rate 2 nm/ degree Diffraction by a Rectangular Aperture ' A rectangular aperture has a width of LI and a height of Ly. The amplitude transmittance of the rectangular aperture is given by t(a:,y) = rect(m/L$,y/Ly) where 'rect(x / Lw, y / Ly) is the two—dimensional rectangular function for which rect(:I:/Lm,y/Ly) = l for —Lx/2S$S+Lm/2 and—Ly/ZSyS-l-Ly/Z = O for x<—L$/2, x>+Lx/2, yg< —Ly/2, y>+Ly/2 This rectangular aperture is coherently illuminated in air at normal incidence by light of freespace wavelength A. Develop, showing all work, the radiant intensity (analytic ex— pression) in the far field. Express your answer as a function of A, Lx, Ly, 0x (the far— field angle in the x—direction), fly (the far—field angle in the y-direction), and I (0) (the radiant intensity for 0 2 0y 2 0) only (eliminate all other variables). Put your final answer in the space provided. I(0z,0y) ll (analytic expression) DVD Grating Beamsplitter For-a DVD tracking system it is desired to split a single laser beam of freespace wavelength 840 nm into three beams of the same wavelength. One of the beams is to be undeviated. The other two beams are to be at an angle of 5 degrees on either side of the undeviated beam. This is to be accomplished by having the original beam normally inci— dent upon a grating. The grating consists of a periodic series of transparent and opaque stripes (or “line pairs”). Calculate, showing all work, the spatial frequency of the needed grating. Express your answer in “line pairs per millimeter.” Express your answer accurately to the, near- est 0.1 line pairs per millimeter. Put your final answer in the space provided. Spatial frequency of grating 2 line pairs/ mm Making a Fourier Transform Hologram A transparency of amplitude transmittance A(a:, y) is coherently illuminated with collimated light of a freespace wavelength A as shown in the diagram. It is desired to make a Fourier transtrm hologram of A(:I:, y). Fourier transform lens of focal length fl is available to use. Draw on the diagram the optical components and light beams re- quired to make a Fourier transform hologram. Label all components. Label important dimensions. Label the Fourier transform hologram. Object Reconstructing a Fourier Transform Hologram It is desired to reconstruct A(a;, y) from the Fourier transform hologram of A(m, y) as recorded in the previous question. A Fourier transform lensof focal length f2 is avail- A able to use for the reconstruction. Draw on the diagram below the optical components and light beams required to reconstruct the Fourier transform hologram. Label all com— ponents. Label important dimensions. Label the Fourier transform hologram. Label the reconstruction of A(a:, General Optical Engineering Questions 1. An asymmetric slab waveguide has thickness h, cover index nc, film index n f, and substrate index n3. Light of freespace wavelength A is propagating in this waveguide both as a TEO mode and as a TE1 mode. It is desired to make the TE1 mode become cutoff. However, it is desired to retain the TEo mode as a propagating mode. How can this be accomplished? f) all of the above 2. 'An asymmetric slab waveguide has thickness h, cover index nc, film index nf, and substrate index ns. Light of freespace wavelength A is propagating in this waveguide both as a TEo mode and as a TE1 mode. For these modes, e) all of the above 3. A symmetric slab waveguide has a film of refractive index nf and cover and substrate - of refractive index of 71C 2 n3. The thickness of the film is h. For a TEo mode excited in this waveguide at a freespace wavelength of A, the thickness at cutoff for the TED mode is a) 0 4. A thin slab in air of thickness d and refractive index n with flat and parallel surfaces will strongly reflect normally incident light of freespace wavelength /\ for m being an in- teger if b) 2nd 2 (m — %))\ Interference Filter 2ndcosfl = mA For [3 = 0 and m = 1, then 2nd 2 /\s Therefore As 003,8 = A0 From Snell’s law sina = nsinfi and so cosfl = (1—sinzfl)1/2 and so As(1 _ saga 1/2 = A0 or <1— — sina : n[1 — filzr/z a = a()\0) = SM 1{n [1 — filial/2} or alternatively a = sin—1 (n sin ,6) a = a()\0) = sin_1{nsin[(cos“1(§3)]} Differentiate to obtain the tuning rate 2 Ag (1 — Si::a)_1/2(—2 3:17;“ Cosoz) _)\s sinicosa/(l _ Vsig2a)1/2 3L? 3|? 3L? || __ A sin2a 12 ) 2n (n2 —- sinza or alternatively dAQ _ _ A - _ _ A - da — fifimacosa) — mszn2a For numerical example A0 = 514.5 nm, As = 520nm, n = 1.4 a()\o) = 11.72° “fl—M = —53.33 nm/md O! m da ——0.931 nm/ degree Diffraction by a Rectangular Aperture Amplitude transmittance t(a:, y) = rect(a:/L$,y/VLy) t(m,y) = rect(a:/Lx)-rect(y/Ly) Two-dimensional Fourier transform - +00 +00 F(k,;, kg) = / / t(:1:, y) e_j2"(k’ $+kywdw dy V w y =~—OO =~OO for even function +00 +00 F(kz, kg) = f / rect(x/L$) - motel/Ly) cos (kzrc) cos(k,,y)dx dy $=—oo yz—oo . / and separable in a: and y F(k$,ky) = foo 122—00 +00 rect(:z: / L1) cos (kxaz) da: - / 'rect(y/Ly) cos(kyy) dy y=—oo and so DVD Grating Bearnsplitter A = 840nm OIL] : +50 3:1 z ’50 The forward—diffracted—order grating equation n1 sinfi’ — n3 sinflg’ = Form=1,ns=1,0’=0,z‘=+1, and 11=—5° 1 _ 31211071 K — _ A 1 Spatial frequency of grating = —— = 000010376 line pairs/mm = 103.76 line pairs/mm A Making. a Fourier Transform Hologram A transparency of amplitude transmittance A(:I:, y) is coherently illuminated with collimated light of a freespace wavelength A as shown in the diagram. It is desired to make a Fourier transform hologram of A(:z:, y). A Fourier transform lens of focal length fl is availableto use. Draw on the diagram the optical components and light beams re— quired to make a Fourier transform hologram. Label all components. Label important dimensions. Label the Fourier transform hologram. Fourier Transform Fourier Transform Reconstructing a Fourier Transform Hologram It is desired to reconstruct A(:c, y) from the Fourier transform hologram of A(:r, y) as recorded in the previous question. A Fourier transform lens of focal length f2 is avail- able to use for the reconstruction. Draw on the diagram below the optical components and light beams required to reconstruct the Fourier transform hologram. Label all com— ponents. Label important dimensions. Label the Fourier transform hologram. Label the reconstruction of A(a:, y). Fourier . r Fourier Twat..st m Transform Reconstruction Hologram ...
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4500T305 - General Questions Interference Filter (20) (22)...

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