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Unformatted text preview: FINAL EXAM Course# ECE 716 Name g d L gg‘F / 0 4/9
Quarter Autumn 2006 This exam is being administered under the Electrical Engineering Honor
Code. You may use THREE 8.5” x 11” pieces of paper with anything you want
written anywhere on them, a ruler, and your calculator. If you are lacking a
physical constant you may ask for it. If there is an equation you already know
exists, you can ask for that too as long as you describe it well enough so I know
you're not fishing. If you don't get an answer, but need it to complete the next problem, then
write down that you didn't get the result, that you're assuming (choose a
reasonable value), and proceed. Make sure ou make this clear, however. Show all your work. mil If
you get a ridiculous answer, write down that you recognize it's ridiculous and
speculate as to why (if you don't have time to find your mistake). If part (b) relies /" on having part (a) correct, and you couldn't do (a), then write down "assume the
answer to "a" is ...", and continue. There are __total points on this exam; all questions are not weighted
evenly. You havel hour and 48 minutes to ﬁnish the exam. page 1 of 11 1‘” f WU 3 {ﬂu K
() 1. A plane wave whose phase fronts form an angle of 10° with
respect to the xaxis and are parallel to the y axis is incident on a lens/’for focal length f=20 cm as shown below. () a) Find the (x, y, z) coordinates of the point image formed.
Explain your reasoning. ear) W) (DMI‘YVLL’C\ rmwci'rd V0») J [06‘
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frequency of this plane wave in the plane 220? )
l m 9 = mm
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‘ 6 page 3 of 12 1. Continued. ‘1» 0 k (I—[)2~—y2 d) A wave described by E = Bogﬂu» __.’P_ 6 [ Ill—6°) "—7
I» «.0 L'W’e’” is incident on the same lens above. The lens causes the beam to collapse to a point
source. Find the location of the point source created by the lens. If the
second point source is am image of the source of the original beam, What
is the magnification? Is the image real or imaginary? (“)7 wév)‘. ﬁl/wri WW l W 47‘9““ all) ‘Wéﬂ" £10m ac; ,9 AMT 5 cvvlf H9,—
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{hr dt w) flag," WC 3 R CV) ’N/ (“' Z J “>5 rcwtw ("m4 4 (3“ l, 4 :1 MW V57] page 4 of 12 O 2. For each of the optical situations below, indicate which of the suggested
matrices, if any, describes it. Explain your reasoning.
dashed lines is an unspecifiled optical system, and th
out of (right) the system are shown. The region between the
e rays going into (left) and [0 B]
C Y) “57¢ 0 if and? (Vb (on. (Ct Flam waw Hewlett} cm a 0 3. A hologram is constructed using a plane wave reference and an off axis point source object as shown below. This is similar to the system on the
second midterm except for the location of the object. () a) The hologram is then reconstructed using the same plane wave
used to make it. Sketch on the ﬁgure above the phasefronts for all the beams you 5L
expect from reconstruction, and label them. ‘ l 1276‘
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M\‘ (yr [‘1 5‘ UKK(s ) va \CVLCL" rye , l’\' l. glow F or,“ LC Ck () b) Can this hologram be thought of as two superimposed lenses?
Explain. You score for this problem will depend on the quality of your
explanation, not just whether you have some general idea. Use the back of this
sheet if needed. (On the midterm I received some very sketchy answers). VCSwﬁkatl/(v) ”A 54“" ‘11 Writ“W 2/ 0%) dL/K‘n} LUCJ‘ MAO/(£9 71/ (7‘7“Sn A lfm)‘ (cmufvl’f Cx fkdtm Mat <67}? HA l’ﬁ CK fur«l ft'uvtc, TlA‘I lnclaj‘rw (W (rtccl1/ +WQ j/lriu‘t cup mph/(J v' 0'“ ply" (at/f:
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hf {ncdxwuy (x [1611 l‘ // L) I ‘ 3. Continued () C) Suppose the same hologram is reconstructed with the object
beam (the point source) instead. Sketch and label below the principle beam and
the E00 beam (we never had a good name for it):__pon’t worry about the conjugate
beam. “ Lao ,Vc._v‘.,_____._,c  page 6 of 11 0 4. A GaAs verticalcavity surface—emitting diode laser (A4520 nm)
produces a round Gaussian beam waist of wo=25 um. , 3’59W4V J F' . , .
() a) 1nd the Raylelgh range (I n W01 : ﬂ (”(1%“) “ML 2 , at. (J (A («AM 1 ‘ / ..__ .
7 5 ) A0 {/Loﬂo‘ ‘f...
:3}, MM () b) Find the farfield divergence angle and indicate your units
(degrees or radians) av 11de Lgiv‘trircwt ($3 ’) bafffﬁz‘uta/V #:H 61%  *6} 3
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9’ 71% L W Local. will“,
“"‘W 'le (Znaf‘ual [l t l ﬂy as? of 3;“; ‘1 810%; ”UV/V ”7 () c) We wish to couple as much as possible of this light into a fiber, Q
using a lens to reimage the beam waist on the ﬁber tip. If the lens will be 5991131 S m m
away from the waist, what should the diameter of the lens be? Explain your choice.
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Mn? «N / page80f12 “a “lime, :4: ”iv ‘qéyﬁ (,{o Vu’ﬁC/Jii’x{j I /{ 0 6. We said in class that the Gaussian beam diverges the least of all possible beams. There is a type of beam called the Bessel beam, however, that
doesn’t diffract at all— its phasefront is planar everywhere. The Gaussian beam is
a solution to the paraxial wave equation, but the Bessel beam is an exact solution
of the fullup wave equation. Furthermore, the Gaussian beam has a ﬁnite RMS width, but the Bessel beam’s RMS width is inﬁnite. The drawing below compares
the two proﬁles. Gaussian beam Explain why it is not possible to generate a true nondiffracting Bessel beam in the laboratory. Why will any physically realizable beam necessarily
diffract? Sly“: \“l/L @(SSdI Liam (S tW,+lV\l+€ (\A w€‘(l(\/ ‘14 wIll 1’le Fob
l2); HVWC aft/(J i"\ Aux] Pky$i(u,Q 57Il(m’ F‘L‘C ‘FrvALLJVVV‘ Wulkrw" page 9 of 11 O 7. Sometimes reﬂections that come back from an optical system have to
be defeated. For example, in launching light into a fiber, the Fresnel reﬂection,
although small, can mess up the oscillation of the laser if the reﬂections get back
into the laser. Below is a trick commonly used to stop them. . . i reflection
mcndent linear polarizer QWP FA/lx
@ 45° () a) When light reﬂects from a material of higher refractive index (such as the face of the fiber), one polarization (call it x) is phaseshifted by 7:
radians; the other polarization is not phase—shifted. When the LCP light is
reﬂected from the face of the fiber, will it come back as RCP or LCP? Lcr: [f l a ‘j “5 {5 tam: y m flan. 31cm
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, ) ; Y, a v» 315%” “term “1 " page 10 of 11 7. Continued b) Show that the system shown will prevent any reﬂected light. we Mjw (w (oi/La AW) «M HA “1“ Warsaw, He A4,,
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axis is?) ‘4’?) wt Wt‘ﬁkrsx Fol Exow’JL/ (ﬂy “I Fist runa wtx 01"“?
(ﬂ«L‘rt‘ be L‘ Q “0 (wish: (VOW—QYCJWh’g (”m/J ‘{/LL( wkh f/Luv Ova/(a PLEDGE: N0 aid received, given, or observed. 5' d L LA I Q N’S page 12 of 12 ...
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