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e894as4g - ENSC 460/894 Assignment 4(Nov 20 due Solutions j...

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Unformatted text preview: ENSC 460/894 Assignment 4 (Nov 20 due Nov 27 2003) Solutions j}; H 1 Assuming that the diffraction spreading (divergence) of a HeNe laser beam 51—“ — 0t =1: 0. 6328 um) can be approximated by assuming it is equivalent to the diffraction caused by a plane monochromatic wave incident on a circular aperture of diameter equal to the laser beam diameter, calculate the diver- gence for a2 mm-diameter beam. a . e;- 1.22 B -= 1.22 0 3:; ”m a 0.39 and ITiiTttt ‘e— ' 2 Calculate the refractive index difference per centimeter in lithium niobate . (LiNbog) for an applied field of 1000 Went. How long must a longitudinal l Pockels cell be to cause a phase change of 90° between the fast and slow rays 1. I for ruby laser light (it = 0.6943 um)? I _]_lilll-ll1 J—lL! in I- 11,- rnaE - l (30.3 x 1.11"12 11/11) (2.313(1000 V/cm) l o 2 l l l Ln -= 1.37 x to" I _l a ¢’_x(n8_ny)1 l-fln:'n’ ZAn-nx-n’ I I 1_ “Mg wovzgam flafldffz‘l ' ~44. __-1._IEJ 41': (1. 87 x 10 5 III-Iflllfiflflflfllflflfll | II:IIIIIIETHHTHHI'FMSV?ZflEE 3 What angle should a HeNe laser beam make relative to the normal to the I.- surface of an acousto-oPtical modulator operated at 40 MHz with an acoust- I.- ical wavelength of 60 p.111? What 15 the shift in frequency of the optical wave, l.- assuming the optical wave has a prepagation component in the same direction I as the acoustical wave? I 11110 = 21. sin 9 Let in = 1 . ——*‘“*. I I A l l l | -10 -1 0.633 use a o _ . e = sin fia- sin 2)(60 um) 0.00528 I I I | I | I Affi’f'=-4OHHZ TTI—I l | ._..—-— . 4 A Solid laser 'coasisis of mirrors separated by 50 cm with a laser rod 10 cm i— ' i . in length with a refractive index of 1.5 and a Q-switch with a length of 2"”; H. ___.§_;%_ cm and a refractive index of 1.45. What is the frequency spacing betweeri _ .Q_;-_J_ axial modes for this laser? __———i——i __*___1__#_# HWW . 1 l I” ar-z—E L-nML+nL+[50cm-L -L°] 4 L = (1.5)(10 cm) 4- (1.45)(2.5 cm) 4- 37.5 cm - 56.2 cm I: ‘ i 5f“ 3 2510mm 3 - 267 MHz +— ' _ . I | ' i . . i l e _= _.__ {”4 f E '. i-ri-fiiw-J—i—i'“ 7+ __-—1E—:—«1——1!5.:3L,—ii_i—T"t—11-15 \H EIL'F. in... y-rv m‘ to!“ JI—Imz-Il-vm 3."? -' }1..--. (-1 A "I 5(a) Using the energy balance approach, estimate the power required to pro- duce a spot weld 3 mm in diameter and 1 mm deep in low-carbon steel 'with a 1-s pulse from a C0; laser. 9 = 7-35 glcm”, K = 0.07 cmzls C = 0.7 Jig K, k = 0.4 W/cm K Estimated values near the melting point are Tm = 1809 K . L; = 13.8 ”/1110! Assume 60% reflectance. e uniform irradiance' model. Remember, at ‘ this depth the temperatUre is only about 35% of the surface temperature. (c) According to the unime irradiance model, how long does it take to reach Tm at the surface for the power deduced in part (a)? 2?.1; “" " " ""T‘ _ _ :. ._-r -.._.- _ _ w- —- _ rain 4,. , Hum” ("l-m 1 gm)“ - ' £- 371 _ _ -. . ' magma}:- -; “Al-1mm:— ——.___ 6 Low-carbon steel of S-mm thickness is to be cut with a laser at a Speed of 1.25 mimin with a 0.5-mm kerf. Using energy balance, estimate the power that must Be coupled into the material. k = 0.4 W/cm K p = 7.86 glcm3 C = 0.50 J/g K Ln = 350 kJ/mol L; = 13.8 kJ/mol i‘ = 3135K -.I_- MM'IfllHWI ' L_ 1.! .11...l;l_,t,,.,., , , Iimmmm-—i 7 Mild steel is to be welded with a multikilowatt C0; laser. Using the" model M of Swift-Hook and Gick, estimate the power required to produce a weld of _ 2-mrn width and 4.5-mrn depth at l m/min. K = 0.09 cmzls _ k = 0.4 W/cm K --—— = 1309 K _____ .r/Iu1m‘vllmfi: w "my/mnaam w "—2.... _J’ IWIH‘IIIHIIH - mumm— m— KIN-ILHI/ H17— 'J ’ x; ,.m, (I If 1 8 Holes are to be drilled in 0.5-mm-thick nickel with a diameter of 0.13 mm. usmg a pulsed Nd—YAG laser with a 4-kW peak power output. Use energy balance to estimate the energy needed and the pulse length, assuming a nearly square pulse. Show that the time to reach vaporization at the surface is neg- ; ligible, based on the results of the uniform irradiance model. k = 0.91 chm K —- c = o 44 Jig K — p = s 9 glam3 — L, = 79s Jig -— L = 6303 Jig — T - 1726K l l _ _ AV .fl‘fllfli’lflill’flfll lilY/L‘l __ ...
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