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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 mmdiameter 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 _]_lilllll1 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 lﬂn:'n’ ZAnnxn’ I
I 1_ “Mg wovzgam ﬂaﬂdffz‘l ' ~44. __1._IEJ 41': (1. 87 x 10 5 IIIIﬂllﬁﬂﬂﬂﬂlﬂﬂﬂl 
II:IIIIIIETHHTHHI'FMSV?ZﬂEE 3 What angle should a HeNe laser beam make relative to the normal to the I.
surface of an acoustooPtical 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 Qswitch 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”
arz—E LnML+nL+[50cmL 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 '. iriﬁiwJ—i—i'“
7+ __—1E—:—«1——1!5.:3L,—ii_i—T"t—1115 \H EIL'F. in... yrv
m‘ to!“ JI—ImzIlvm 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 lowcarbon steel
'with a 1s pulse from a C0; laser. 9 = 735 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”
("lm 1 gm)“  ' £ 371 _ _ . . ' magma}: ; “Al1mm:— ——.___ 6 Lowcarbon steel of Smm thickness is to be cut with a laser at a Speed of
1.25 mimin with a 0.5mm 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 SwiftHook and Gick, estimate the power required to produce a weld of _
2mrn width and 4.5mrn 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—
KINILHI/ H17—
'J ’ x; ,.m, (I If 1 8 Holes are to be drilled in 0.5mmthick nickel with a diameter of 0.13 mm.
usmg a pulsed Nd—YAG laser with a 4kW 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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 Spring '10
 Chapmann

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