Optics Tutorial LAK
Transcript of Optics Tutorial LAK
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Basic OpticsLaura KranendonkERC, UW Madison
2004
Table of Contents
Basic Optics
1. Introduction 1
2. Proerties o! Li"#t.. 1
a. Co$or 1%. &ectra$ Po'er 2
c. Po$ari(ation. 4
). *tica$ +undaenta$s. 4a. +erat-s Princi$e
%. &ne$$-s La'. /c. +resne$ Euations.
d. Etendue e. Co#erence 11
!. &catterin". 1)
Optical Laboratory Toolbox
1. Introduction. 1
2. Creatin" Li"#t.. 1a. Lasers.. 1
%. LE3s.. 1
). 3irectin" Li"#t.. 1a. LensesMirrors. 1
%. +i%ers.. 22
4. Contro$$in" Wa5e$en"t#. 24
a. 3i!!raction 6ratin". 24%. Eta$ons.. 2/
c. 7aronic 6eneration 2
. Measurin" Li"#t.. 28a. 3etectors.. 28
%. Caeras39es 28
Appendix1. &I Pre!i:es.. 2
2. Laser C$assi!ications.. 2
). Cornin" &M+;28 *tica$ +i%er Product 3ata s#eet
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Basic Optics
Introduction
In 1/0, t#e !irst Ru%9 $aser 'as %ui$t >1?, oenin" t#e door !or an9 ne' otica$
in5entions and researc# toics. Mec#anica$ en"ineers in articu$ar are current$9 'orkin"on otica$ et#ods !or easurin" !$uid and "as roerties, easurin" ec#anica$
stresses, and anu!acturin" tec#niues. In order to understand t#ese ne' de5e$oents,
a %asic understandin" o! $i"#t and $i"#t roerties is reuired. @#ese notes are eanton$9 as a re5ie' o! $i"#t toics in order to understand rinci$es coon$9 used in t#e
ec#anica$ en"ineer-s otica$ $a%orator9. @#e #9sics %e#ind t#e ateria$s %ein"
resented are "enera$$9 co5ered in introductor9 #9sics courses.
Properties of Light
Aisi%$e $i"#t is a sa$$ art o! t#e e$ectroa"netic sectru. E$ectroa"netic 'a5es
#a5e e$ectric and a"netic !ie$ds erendicu$ar to t#e direction o! otion. @#e9 are a%$e
to tra5e$ t#rou"# a 5acuu or a ediu. @#ere are se5era$ roerties coon$9 used todescri%e $i"#t suc# as co$or B'a5e$en"t#, 'a5enu%er, !reuenc9, ener"9, and o'er
Bintensit9.
Figure 1.1 E$ectroa"netic sectru, #ttD#9er#9sics.#9;astr."su.edu#%asees1.#t$
Wa5e$en"t# BD easured in nanoeters Bn, icroeters B, or an"stros B , 1 0.1 n, t#e distance !ro one eak to t#e ne:t.
+reuenc9 B!D easured in 7ert( B7(, 17( 1s;1. +reuenc9 is t#e in5erse o! t#e tie
it 'ou$d take a 'a5e to tra5e$ 1 'a5e$en"t#. @o ca$cu$ate !reuenc9 !ro 'a5e$en"t#D
fc= B1.1&eed o! $i"#t in a 5acuu Bc ) : 108s
Wa5enu%er BD easured in in5erse centieters Bc;1. @#e 'a5enu%er is #o'
an9 'a5es !it in t#e distance o! 1 c.
2
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Ener"9 BED easured in Fo$e, F#oton, or e$ectron 5o$t BeA, 1eA1./ : 10;1F er
#oton or er o$e o! #otons. Ener"9 o! t#e 'a5e can %e ca$cu$ated direct$9 !ro t#e
'a5e$en"t# or !reuenc9 usin" t#e !o$$o'in" euationD
chhfE == B1.2
P$anck-s constant, h/./2/ : 10;)4
Fs.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple 1.1
a. Consider a 10 n 'a5e. W#at are t#e !reuenc9, 'a5enu%er and
ener"9 Bin a 5acuuG
Frequency:
( ) Hz
s
Hz
m
nm
nms
mcf 14
8
10H4.11
1H
10
1H
10
1H
10H)=
==
1$% T&'
Wavenumber:
=
cm
m
m
nm
nm 100
1H
10
1H
10
1
(%)1.(1c#*1
Energy:
( )
==
sxJsxhfE
1104.1H10/2/./ 14)4 1.+,)x1-*1$/photon
%. Consider t#e dia"ra %e$o'. W#at is , , and !G
W#en ca$cu$atin" di!!erences, it is iortant con5ert into coon unitsbeforetakin" t#e di!!erence.
00n;/00n 1--n#
cm
m
m
nm
nmnm 100
1H
10
1H
00
1
/00
1 +0,-.$)c#
*1
)
>n?
P
>W?
/00 00
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nm
mW.. in
0001.0
1=
=
1- 3/n#
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
Po$ari(ationD W#en t#e e$ectroa"netic 'a5es coosin" a $i"#t %ea 5i%rate in t#esae direction, t#e $i"#t is said to %e o$ari(ed. Po$ari(ed $i"#t is "enera$$9 c$assi!ied into
2 "rous deendin" on #o' t#e e$ectric 'a5es are a$i"ned 'it# t#e $ane o! incidence.
@#e $ane o! incidence is t#e $ane coosin" t#e incident, re!$ected, and transitted
ra9s. @rans5erse a"netic B@M, ara$$e$ BJJ, P, and * are a$$ 'a9s to re!er to 'a5es t#atare o$ari(ed suc# t#at t#e e$ectric !ie$d is in t#e $ane o! incidence. @rans5erse e$ectric
B@E, erendicu$ar B , &, and E are a$$ 'a9s to re!er to o$ari(ation erendicu$ar tot#e $ane o! incidence. @#e o$ari(ation o! $i"#t can a!!ect an9 asects o! otics.Materia$s can #a5e di!!erent roerties !or di!!erent o$ari(ations, suc# as inde:es o!
re!raction B%ire!rin"ents or re!$ecti5it9. In addition to t#ese o$ari(ed cases, $i"#t can %e
rando$9 o$ari(ed Ba$so ca$$ed natura$ $i"#t, or circu$ar$9 or e$$itica$$9 o$ari(ed.
Figure 1.0Para$$e$ o$ari(ation dia"ra.
Figure 1.%Perendicu$ar o$ari(ation dia"ra.
Optical Funda#entals
In t#is section, !undaenta$ otica$ rinci$es 'i$$ %e re5ie'ed in order to understand$i"#t %e#a5ior. *nce t#ese %asic rinci$es are understood, co$e: otica$ a$ications
W#en t#e e$ectric !ie$d
BE is ara$$e$ to t#eaer Bas dra'n, it is
ca$$edD @M, P, *, or JJ.
@#e ara$$e$ $ines are 1
reresentation o! t#iso$ari(ation.
Incident ra9 Re!$ected ra9
@ransitted ra9
W#en t#e e$ectric !ie$dBE is erendicu$ar to
t#e aer $ane, it is
ca$$edD @E, &, E, or .
@#e dots are 1
reresentation o! t#is
o$ari(ation.
Incident ra9 Re!$ected ra9
@ransitted ra9
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and too$s can %e studied. @#ere!ore, it is 5er9 iortant to #a5e a "ood understandin" o!
t#ese !undaenta$ rinci$es.
+erat-s Princi$e
+erat-s rinci$e states t#at $i"#t 'i$$ take at# 'it# t#e s#ortest tra5e$ tie to "o !ro
one oint to anot#er, as s#o'n in !i"ure 4.
Figure 1.) I$$ustration o! +erat-s rinci$e, $i"#t 'i$$ tra5e$ in a strai"#t $ine !ro one oint to anot#er
since a strai"#t $ine 'i$$ %e t#e uickest at#.
+erat-s rinci$e can %e used to s#o' t#e %e#a5ior o! re!$ection. 3eendin" on t#e
incident an"$e o! t#e $i"#t onto a sur!ace Bsa9 a irror, $i"#t 'i$$ on$9 re!$ect at t#at sae
incident an"$e. @#ere!oreD
ri = B1.)
Figure 1.(+erat-s rinci$e on a irror. @#e %ea !ro t#e das#ed at# is iossi%$e %ecause it is a
$on"er tra5e$ tie t#an t#e so$id $ine at#.
+erat-s rinci$e can a$so %e used to s#o' #o' a $ens !ocuses $i"#t. In order tounderstand t#is #enoenon, it is iortant to kno' t#at $i"#t tra5e$s at di!!erent seeds
deendin" on t#e inde: o! re!raction Bn o! t#e ateria$. 6$ass t9ica$$9 #as an inde: o!re!raction o! a%out 1., '#ereas air #as an inde: o! re!raction o! essentia$$9 1 Bc seedo! $i"#t in a 5acuu. @#e seed t#at $i"#t tra5e$s t#rou"# a ediu isD
n
cvlight= B1.4
In !i"ure /, it can t#en %e deduced t#at $i"#t 'i$$ tra5e$ !ro oint = to oint in t#esae aount o! tie Band t#ere!ore t#e s#ortest aount o! tie !or a$$ o! t#e $ines.
BHintD t#e t#ickest art o! t#e $ens #as t#e o5era$$ s#ortest at# $en"t#, %ut since t#e $i"#t
/
2
1
1
2
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'i$$ tra5e$ s$o'er in t#e "$ass, t#e o5era$$ tie to tra5e$ !ro = to 'i$$ %e t#e sae !or
t#e center$ine.
Figure 1. Li"#t at#'a9s t#rou"# a $ens, oint = and are at t'ice t#e !ocus $en"t# o! t#e $ens.
&ne$$-s La'
&ne$$-s $a' redicts t#e direction o! $i"#t as it tra5e$s t#rou"# di!!erent edius. &ne$$-s$a' can %e stated %9 t#e !o$$o'in" euation '#ere nis t#e inde: o! re!raction, and i, t,andrstand !or incident, transitted, and re!$ected.
ttii nn sinsin = B1.
Figure 1.,3ia"ra o! &ne$$-s $a', s#o'in" $i"#t tra5e$in" !ro air to "$ass.
@ota$ interna$ re!$ection can occur '#en $i"#t in a #i"# inde: ediu reac#es a $o'
inde: ediu Bni nt. In t#ese conditions, '#en t0o, t#e corresondin" incident
an"$e is ca$$ed t#e critica$ an"$e. =n9 incident ra9 at t#e critica$ an"$e or #i"#er 'i$$
cause tota$ interna$ re!$ection, eanin" a$$ o! t#e $i"#t is re!$ected and none is transitted.@#is 'i$$ %ecoe iortant '#en dea$in" 'it# !i%er otic ca%$es.
n"$ass
1.
nair
1
r
t
i
=
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"xa#ple 1.0
a. Consider a %ea tra5e$in" !ro air Bn1 to "$ass Bn1. at a )0oincident an"$e. &ketc# t#e s9ste, ca$cu$atin" t#e re!$ection and
transission an"$es.
ri = 0-oB+erat-s Princi$e
ttii nn sinsin = B&ne$$-s La'o
iti nn )0L.1L1 ===
( )
= )0sinH
.1
1sin 1t 1$.%
o
%. W#at is t#e critica$ an"$e Bonset o! tota$ interna$ re!$ection !or a"$assair inter!aceG inc;&e$enideair Bn2.G
@o !ind t#e onset o! tota$ interna$ re!$ection B@IR, set t#e transissionan"$e eua$ to 0o. @#ere!oreD
/lass:
( )
=
= 1H
1
.1sin0sinsin 11
i
ti
n
n %1.,o
0inc"1elenide:
( )
=
= 1H
1
.2sin0sinsin 11
i
t
i
n
n +0.),o
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+resne$-s Euations
@#e aount o! $i"#t t#at is transitted or re!$ected can %e deterined %9 t#e +resne$
euations. @#e ratio o! re!$ected to incident o'er Bor t#e !raction o! o'er re!$ecteddeends on t#e o$ari(ation o! t#e $i"#t, and can %e 'ritten asD
8
n"$ass
1.
nair
1
)0o
1.o
)0o
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2
JJcoscos
coscos
+
=itti
tiit
nn
nn2
BPara$$e$ o$ari(ed $i"#t B1./
2
coscos
coscos
+
=ttii
ttii
nn
nn2
BPerendicu$ar o$ari(ed $i"#t B1.
'#ic# can %e si$i!ied to
2
+
=ti
it
nn
nn2 '#en i0. 2is a$so ca$$ed t#e re!$ected
o'er coe!!icient. I! no $i"#t is a%sor%ed in t#e ateria$, transitted o'er can t#en %e
ca$cu$ated %9 initia$ o'er u$ti$ied %9D
C1B 23 = B1.8!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple 1.%
a. I! a 1W $aser %ea is directed t#rou"# a "$ass icroscoe s$ide,'#at is t#e transitted o'erG (4ssume there is no 5o6er absor5tion in
the glass)
Usin" t#e +resne$ euations, it is ossi%$e to ca$cu$ate t#e re!$ected o'er
coe!!icient !or %ot# t#e air"$ass inter!ace, and t#e "$ass air inter!ace. It
turns out t#at t#ese are t#e saeD
04.0.2
.0 22
=
=
+
=ti
it
nn
nn2
&ince t#ere is no a%sor%ance, t#e transitted o'er coe!!icient is t#en Nust1;2. @#ere!ore, /O B1;0.04 o! t#e o'er is transitted, or 0./W.
%. W#at 'ou$d %e t#e transitted o'er i! t#ere 'ere 0 icroscoe
s$ides %et'een t#e $aser and detectorG (4ssume an air ga5 bet6een eachslide)
Rea$i(in" t#at at eac# inter!ace, /O o! t#e o'er is transitted, and t#ereare a tota$ o! 100 inter!aces, it can %e deduced t#atD
01/.0C/.0B 100 ==3@#ere!ore, 1./O o! t#e ori"ina$ o'er or 0.01/W is transitted.
1W $aser
air"$ass inter!ace
"$assair inter!ace
Li"#t detector,
a%$e to easureo'er o! $i"#t
%ea.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
Figure 1.$Re!$ection 5ersus incident an"$e !or an air"$ass s9ste.
Euations B1.4 and B1. can %e $otted 5ersus incident an"$e, as s#o'n in !i"ure 1.. =t
/.4o, t#ere is no re!$ection !or one o! t#e o$ari(ations. @#is is a secia$ incident an"$ekno'n as re'ster-s an"$e. 9 aniu$atin" t#e incident an"$e, it is ossi%$e to o$ari(e
uno$ari(ed $i"#t.
"xa#ple 1.)
I! t#ere 'ere t#e sae 0 s$ides as in e:a$e 1.), %ut no' t#e incident
an"$e 'as at re'ster-s an"$e, '#at 'ou$d t#e transitted o'er %eG
(4ssume the light is un5olarized* and equal amounts of 5er5endicular and5arallel"5olarized light)
4ns6er:
=t re'ster-s an"$e, none o! t#e ara$$e$;o$ari(ed $i"#t 'i$$ %e re!$ectedB100O transission, or 0O net transission. +ro euation Bor !ro
t#e "ra# in !i"ure 8, t#e re!$ection !or 1 air"$ass and "$assair 0.14.
@#ere!ore, t#e erendicu$ar o$ari(ed $i"#t transits 8.1O B1;0.14 ateac# inter!ace, so o5er a$$ 100 inter!aces, 0.81100.84:10;8is transitted
Bessentially !.
*5era$$, t#e tota$ transission is t#en )-4.
Etendue
Etendue, a$so kno'n as t#e araeter roduct, can %e t#ou"#t o! as t#e ua$it9 o! $i"#t,and is uanti!ied %9 si(e u$ti$ied %9 di5er"ence. @#e sa$$er t#e etendue, t#e %etter
co$$iated t#e $i"#t can %e. Etendue is t#e otica$ eui5a$ent o! entro9 at %est it 'i$$
10
Reflection versus incident angle (air-glass interface)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
Incident Angle
Reflectance
RJJ
R
re'ster-san"$e/.4o
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reain constant, #o'e5er it 'i$$ ne5er iro5e. +i"ure 1.10 s#o's #o' etendue is
ca$cu$ated and "ra#ica$$9 reresented.
Figure 1.1- 6ra#ica$ reresentation o! etendue.
@#e sa$$est etendue ossi%$e is ca$$ed t#e di!!raction $iit. @#e di!!raction $iit is
'a5e$en"t# deendent, and can %e ca$cu$ated !ro t#e !o$$o'in" euation, '#ere dis t#e
sot si(eQ, t#e diaeter o! t#e $i"#t sourceD
( )
halfdH B1.8
@#e di!!raction $iit t#ere!ore $eads to t#e iniu sot si(e t#at a %ea cou$d roduce
Brat#er t#an an in!inite$9 sa$$ oint. Lasers are a%$e to roduce $i"#t t#at is neardi!!raction $iited. = "enuine increase in etendue is ca$$ed %ea steerin".
"xa#ple 1.(
a. Li"#t at /10 n, $ea5es a $aser at t#e di!!raction $iit. @#e$aser #as a 1 diaeter eittin" area. W#at is t#e di5er"ence
an"$e o! t#e $aserG
=halfdH
=
m
m
nm
m
m
nmhalf
1
10H
10
1H
1
1H
/10 /
11.1+)o
%. I! t#e $aser %ea 'ere co$$ected in a 1 c diaeter $ens at t#e !oca$$en"t#, #o' $ar"e 'ou$d t#e roNected sot %e 10 k !ro t#e $ensG
First* calculated the divergence angle leaving the lens:
( ) ( )2211 sinsin rr =
mmr
.02
11 =
=
11
!
a1
1
2
2
Etendue %est caseD
a1sinB
1a
2sinB
2
1tan;1Ba
2!
2tan;1Ba
1!
Li"#t source
a2
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cmr
o
.0
2.22
2
1
=
=
( )
=
=
m
cm
m
m
cm
m
r
r o
1
100H
10
1H
.0
2.22sinH.0sin
CsinBsin
/
1
2
1112
0.002o
Next* using trigonometry* figure outthe size of the s5ot:
( ) ( )o7r 002.0tanH10000tanH 2) == 0.) 2
)H r4 = -.%) #+
Co#erence
W#en 2 or ore $i"#t %eas are sueriosed on eac# ot#er, t#e9 #a5e t#e otentia$ to%e eit#er co#erent or inco#erent. W#en co#erent $i"#t #as t#e sae eaks and 5a$$e9s, it
constructi5e$9 inter!eres, '#ereas i! a eak $ines u 'it# a 5a$$e9, t#ere is destructi5e
inter!erence, '#ic# 'eakens t#e si"na$.
W#en 'a5es o! di!!erent 'a5e$en"t#s are tra5e$in" a$on" t#e sae at#, it is use!u$ tokno' at '#at $en"t# t#e 'a5es %ecoe inco#erent. @#is co#erence $en"t#- can %e
ca$cu$ated 'it# t#e !o$$o'in" euationD
=
2
c7 B1.
12
Destructive Interference
-1.5
0
1.5
0
Constructive Interference
-2
0
2
0 250
Incoherent Light
-1.2
0
1.2
0
Figure 1.11E:a$es o! destructi5e and constructi5e
inter!erence, and inco#erent $i"#t.
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"xa#ple 1.
@'o 10 W $asers eittin" 5er9 near$9 t#e sae co$or are arran"ed ass#o'n %e$o'. @#e to $aser is a !ree;runnin" $aser, and t#e %otto is a
sta%i$i(ed $aser t#e sta%i$i(ed $aser #as a si"ni!icant$9 sa$$er $ine'idt#.
@#e !u$$ 'idt# #a$! a:- B+W7M o! t#e to $aser is 0.1 c;1
, and t#e+W7M o! t#e $o'er $aser is )00 k7(. +W7M is t#e %and'idt# at #a$! t#ea:iu, since ost $asers and ot#er otica$ sources roduce 'a5es on a
6aussian cur5e +W7M is a "ood aro:iation o! %and'idt#.
+ree runnin" $aserD fr 00.01 n, +W7M 0.1c;1
&ta%i$i(ed $aserD s 00 n, +W7M )00 k7(
a. W#at is t#e co#erence $en"t# o! t#e 2 $asersG
Free running laser:
+
=
frfrfrfr
fr
nm
m
m
cmcm
H.0
1
H.0
1
10
1H
1
100H
1
fr 0.004 n
nm
m
nm
nm7 frc
222
,10
1H
004.0
01.00=
=
-.1 #
1tabilized laser:
+
=
ssss
cHz
Hz8Hz
H.0
1
H.0
1H
1
1000H
s4.:10;n
nm
m
nmx
nm7
s
s
sc
222
,10
1H
10.4
00
=
=
15--- #
%. @#e detector is not readin" a si"na$. W#9 cou$d t#is %eG
4ns6er:
1)
+ree runnin"
sta%a$i(ed
3etectorLasersD
%ea s$itter
irror
)0 c
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&ince t#e co#erence $en"t# in t#e !ree;runnin" $aser is s#orter t#an t#e at#
it is tra5e$in", t#e $i"#t %ecoes inco#erent, and t#ere!ore cannot a$i"n
'it# t#e sta%i$i(ed $aser.
&catterin"W#en $i"#t #its o$ecu$es, it can %ecoe scattered in se5era$ 'a9s. W#en $i"#t is
scattered %9 5er9 sa$$ o$ecu$es Bd SS e$astic BRa9$ei"# scatterin", ine$astic 'it#
increased ener"9 B=nti;&tokes Raan scatterin", or ine$astic 'it# decreased ener"9
B&tokes Raan scatterin" scatterin" can occur. W#en $i"#t is scattered %9 $ar"er
o$ecu$es Bd, Mie scatterin" occurs.
@#e incident o'er, densit9 o! o$ecu$es, 5o$ue o! interest, and co$$ection an"$e o! t#e
otics can deterine t#e scattered o'er !or eac# t9e o! scatterin". @#e euation !or
scattered o'er is as !o$$o'sD
=
n7.
.
9
s
B1.10
9
s
.
. ratio o! scattered o'er to incident o'er
di!!erentia$ scatterin" cross;section
&rHo$ecu$es
c2
so$id an"$e o! co$$ection >&r?, 1 &teradian 4Hradians
n o$ecu$ar densit9
(at standard tem5erature and 5ressure* air has a molecular density of:
#&+!
'
molecules;cm
$
)2ayleigh:
42
22 C1B4
o2ayleigh N
n=
B1.11
13.nmatN2ayleigh 1rmolec
cm
,00
2
28
2
10H4.8
!or en. B1.11, n re!racti5e inde: o! o$ecu$e
No nu%er densit9 at &@P
@#is in5erse re$ations#i 'it# 'a5e$en"t# can %e used to e:$ain '#9 durin" t#e da9, t#e
sk9 is %$ue and not red. =s t#e sun sets, t#e sun-s ra9s tra5e$ t#rou"# ore o! t#eatos#ere, a$$o'in" ore scatterin", causin" t#e sunset to %e a redder co$or.
2aman:
2ayleigh2aman
)10
-ie:
14
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2
2d-ie
=
d diaeter o! scatterin" o$ecu$e
Wa5e$en"t# c#an"es due to Raan scatterin" can %e ca$cu$ated %9 t#e !o$$o'in"euationsD
=nti;&tokes RaanDhEEE +=+ TL B1.12
&tokes RaanDh
EEE
= TL B1.1)
"xa#ple 1.,
= 1 W $aser at 00n is directed into air at roo teerature and
ressure. I! a detector cou$d ick u 10O o! t#e area o! a s#ere, and 1 c$on", #o' uc# o'er 'ou$d %e detected due to Ra9$ei"# scatterin"G
4ns6er:
=
2ayleigh9
s n7
.
.
n2.H101o$ecu$esc)
0.1H4 1.2/
71 c
=
1rmolecule
cmx
2ayleigh H104.8
228
.s 2.8/:10;8W
Conclusions
In t#is section, 'e #a5e de5e$oed t#e too$s necessar9 to understand #enoena dea$in"'it# otics. Wit# t#ese !undaenta$ rinci$es, 'e can no' o5e a#ead to $earnin"a%out t#e instruents used in otica$ $a%oratories, and ot#er otica$ a$ications.
1
L
Pin
3etector
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Optical Laboratory Toolbox
In t#e otica$ $a%orator9, it is iortant to %e a%$e to contro$ t#e direction, 'a5e$en"t#,
and sectra$ o'er o! $i"#t. Usin" t#e rinci$es de5e$oed in t#e re5ious section, it is
ossi%$e to do t#is in an9 'a9s. Lasers and LE3s can %e used to create $i"#t at seci!ic'a5e$en"t#s and o'ers. Lenses, irrors, and !i%er otics can %e used to direct $i"#t.
3i!!raction "ratin"s and eta$ons are e:a$es o! 'a9s to contro$ t#e 'a5e$en"t#. +ina$$9,
5arious detectors can %e used to easure $i"#t roerties.
Creating Light
W#en 'e t#ink o! arti!icia$ $i"#t sources, t#e !irst t#in" t#at coes to ind is ro%a%$9 a$i"#t %u$%. Li"#t %u$%s "i5e o!! inco#erent $i"#t o5er a 'ide ran"e o! 'a5e$en"t#s.
7eatin" eta$ !i$aents creates $i"#t in standard $i"#t %u$%s. W#en seci!ic 'a5e$en"t#s
or co#erent $i"#t is reuired, $asers or LE3-s are t#e usua$ et#od.
Lasers 7i"#t4$i!ication %9 1tiu$atedEission o!2adiationLasers roduce co#erent e$ectroa"netic 'a5es at narro' 'a5e$en"t# %ands, eit#er
continuous$9 or u$sed. @#ere are t#ree arts to a $aserD "ain ediu, u, and!eed%ack. @#e %asic idea %e#ind a $aser is t#at !irst atos in t#e "ain ediu are e:cited
to #i"#er t#an usua$ ener"9 states. *nce enou"# atos are e:cited, a #oton causes t#e
to dro to a $o'er ener"9 state. In "oin" !ro a #i"#er ener"9 state to a $o'er ener"9state, t#e atos "i5e o!! anot#er #oton at a seci!ic 'a5e$en"t#. @#ese #otons cascade
t#rou"#out t#e ediu %et'een irrors, causin" ore t#e rocess to continua$$9 reeat.
+ina$$9, one o! t#e irrors 'i$$ #a5e on$9 artia$ re!$ection, a$$o'in" a %ea to e:it t#e
ca5it9 Bsee !i"ure 2.1. Lasers #a5e t#e otentia$ to #a5e 5er9 #i"# o'er, and cou$d %edan"erous i! roer sa!et9 recautions are not used. =endi: ) %reaks do'n t#e t9es
o! $asers into c$assi!ications %ased on o'er and otentia$ #ar!u$ness.
Figure +.1 &i$i!ied dia"ra o! a Ru%9 $aser. Ru%9 B=$2*) Cr is t#e "ain ediu $as are used to
u t#e ru%9 to an e:cited state 'it# irrors on eit#er end o! t#e ca5it9.
Lasers are c$assi!ied accordin" to t#e ediu t#at is %ein" e:cited. @#e t#ree %asic
cate"ories are so$id Bi&e&Ru%9, "as Bi&e&7e;
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deterines t#e 'a5e$en"t# t#at t#e $aser roduces. 6ain edius can %e 5er9 di!!erent,
%ut essentia$$9 t#e9 a$$ need to do t#e sae t#in". +irst, a ou$ation in5ersionQ needs to
occur. Indi5idua$ atos nora$$9 are !ound in a "round ener"9 state. W#en 1 e$ectron ise:cited and o5es to a di!!erent or%itin" s#e$$, t#e ato #as an o5era$$ #i"#er ener"9
state. Pou$ation in5ersion occurs '#en t#ere are ore atos in t#e e:cited state t#an t#e
"round state. =n e:a$e o! a no%$e "as B
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Figure +.%@#e t#ree ain transitions, stiu$ated a%sor%ance, sontaneous eission, and stiu$ated
eission.
&oe atos #a5e etasta%$e states, '#ic# are sta%$e, #i"#;ener"9 states. Metasta%$estates are crucia$ !or $asers %ecause t#e9 a$$o's !or ou$ation in5ersion. 6ain edia is
$iited to o$ecu$es t#at #a5e etasta%$e states B"enera$$9 a rare occurrence. =s an
ato "oes !ro t#e etasta%$e state to a $o'er state, it re$eases a #oton 'it# seci!ic'a5e$en"t#. @#ere a9 %e a sa$$ ran"e o! ener"ies at t#e etasta%$e state t#at cause t#e
$aser to #a5e a ran"e o! 'a5e$en"t#s. 3eendin" on t#e a$ication, t#is can %e eit#er
%ene!icia$ or not. We 'i$$ see $ater in t#is c#ater #o' to aniu$ate 'a5e$en"t#s.
Pro%a%$9 t#e %est 'a9 to understand #o' $asers 'ork is to $ook at an aniation !ro oneo! t#e 'e%sites $isted in aendi: 4, #o'e5er !i"ure 2. "i5es a "enera$ o5er5ie' o! t#e
rocess. = $ist o! soe a5ai$a%$e $asers and t#eir 'a5e$en"t#s is $isted in aendi: 2.
18
&ontaneous Eission
#oton
6round &tate
E:cited &tate
&tiu$ated Eission
6round &tate
E:cited &tate
Ener"9@ransissions
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Figure +.) &tes in creatin" a $aser. @#e "ra9 dots reresent atos as t#e9 tra5e$ !ro natura$$9 occurrin"
"round states, to #i"#er etasta%$e states '#en stiu$ated %9 #otons. @#is !i"ure is si$i!ied !or c$arit9.
In actua$it9, eac# ato %ein" stiu$ated reuires 1 #oton, '#ereas on$9 1 #oton tota$ is s#o'n in t#is
dia"ra. @#e #otons %ounce %ack and !ort# %et'een t#e surroundin" irrors Bnot s#o'n, a$$o'in" t#e
stiu$ated eission to continue. @#e odd ato t#at 'ent to a #i"#er state is a rare occurrence it is s#o'n#ere to si$9 to i$$ustration '#at can #aen.
=s entioned %e!ore, $asers can %e eit#er u$sed or continuous. Pu$sed $asers #a5e a
$iit to #o' s#ort t#e9 can %e %ased on t#e 7eisen%er" Uncertaint9 Princi$e, '#ic# is
stated as !o$$o'sD
4hEt B2.1
'#ere tis t#e u$se duration, Eis t#e ener"9 Bree%erE
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11 0010.0.1//// +=+ cmcm 1////.010 c;1
=
+=
010.1////
1
.1////
111
0.0000)8 n
==
nm
m7c
22
10
1
0000)8.0
/00
$.) #
@#e $en"t# o! t#e u$se is Nust seed o! sound u$ti$ied %9 t#e u$se durationD
[ ] [ ]
==
ns
sns
smxtc7 55ulse
8
10
1H10H10)H 0 #
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
LE3s 7i"#tEittin"=iodes
LE3s are sii$ar to $asers, #o'e5er t#e9 use on$9 sontaneous eission rat#er t#an
stiu$ated. Reo5in" t#e irrors !ro a $aser "ets rid o! t#e stiu$ated eission. @#e
ain di!!erence t#ere!ore %et'een $asers and LE3s is t#at LE3s roduce inco#erent$i"#t. &ince LE3s are ore e!!icient t#an $i"#t %u$%s, and $ess #ar!u$ to t#e #uan e9e
t#en $asers, LE3s #a5e !ound an9 ractica$ a$ications suc# as %rake $i"#ts and sto
$i"#ts.
6irecting Light
*nce 'e #a5e $i"#t !ro a $i"#t source, 'e need to %e a%$e to accurate$9 contro$ '#ere ittra5e$s. @#ere are se5era$ 'a9s to do t#is. Lenses can %e used to co$$iate or !ocus $i"#t.
Mirrors are used to re!$ect $i"#t. +ina$$9, !i%er otic ca%$es are 5er9 use!u$ !or
trans!errin" $i"#t to seci!ic $ocations.
LensesLenses can %e used to eit#er !ocus or co$$iate $i"#t. = $ens can %e conca5e, con5e:, or
co%inations o! t#e 2. Co$$iated $i"#t coin" in t#rou"# a conca5e $ens 'i$$ !ocus att#e !oca$ $en"t# Bf. In "enera$, t#e 6aussian $ens !oru$a isD
=+fss io
111B2.)
and t#e a"ni!ication !ro t#e $ens isD
o
i
s
s-= B2.4
20
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Figure +.(3ia"ra !or 6aussian $ens !oru$aD B1so B1si B1!
Figure +. Lens secia$ case, a oint source at t#e !oca$ $en"t# co$$iates $i"#t. = oint source not on t#ecenter $ane B9et sti$$ at t#e !oca$ $en"t# 'i$$ co$$iate t#e $i"#t at an an"$e to t#e center $ane.
Figure +.,=n ia"e at t'ice t#e !oca$ $en"t# 'i$$ "i5e 1D1 ia"in".
@#e +;nu%er Bre!erred to asD +V or +V in industr9 o! a $ens isf;d, as s#o'n in !i"ure2.8. *t#er %e#a5iors o! $enses can %e deterined !ro &ne$$-s $a'. =na$9tica$$9, t#is can
21
f
2f
;2f "f f
d
so
si
i;con5e: $ens
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%e uite ri"orous, #o'e5er "ra#ica$ so$utions or ra9 tracin" so!t'are ro"ras can
si$i!9 t#e coutationa$ 'ork.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple +.+
6i5en an LE3 'it# a 100 diaeter eission area, and #a$!;an"$e di5er"ence
o! 20o, '#at +V $ens 'ou$d 9ou need to #a5e a di5er"ence #a$! an"$e o! a t9ica$$aser ointer, 0.01oG
4ns6er:+irst ca$cu$ate t#e iniu diaeter o! t#e $ens !ro %asic etendue rinci$esD
=
21,22
21,11 sinsin dd
( )( )01.0sin
20sin10100
sin
sin /
2
1,2
21,11
2
ox
d
d
=
=
0.1/
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%$urrin" o! t#e ia"e 'i$$ resu$t, '#ic# is kno'n as coa a%erration. +ie$d cur5ature
occurs '#en a $ens tends to !ocus on a cur5ed, rat#er t#an !$at $ane. W#en ia"e s#aes
do not actua$$9 corre$ate 'it# t#e actua$ s#ae o! t#e o%Nect, distortion is occurrin".3istortion is usua$$9 increased as t#e o%Nect is $aced !urt#er o!! t#e center a:is. +ina$$9,
c#roatic a%erration occurs '#en di!!erent 'a5e$en"t#s #a5e di!!erent %e#a5iors t#rou"#
t#e $ens, causin" di!!erent co$ors to !ocus at di!!erent oints. It is iortant to kno' t#ata$$ o! t#ese a%errations can %e eit#er e$iinated or inii(ed 'it# 5arious tec#niues
suc# as usin" u$ti$e $enses or t#e use o! as#erica$ irrors.
Mirrors
Mirrors are ade 'it# #i"#$9 re!$ecti5e sur!aces. +erat-s rinci$e can %e used to
deduce t#at t#e re!$ection an"$e is a$'a9s eua$ to t#e incident an"$e. =side !ro !$at
irrors, ara%o$ic s#aed irrors are coon$9 !ound in otica$ $a%oratories. Para%o$icirrors !ocus $i"#t to a oint.
+i%ers
= 5er9 use!u$ too$ in toda9-s otica$ too$%o: is t#e !i%er. +i%ers are essentia$$9 dra'n"$ass Bor soe transarent ediu 'it# a rotecti5e coatin". = sa$e dia"ra o! a
!i%er is "i5en in !i"ure 2..
Figure +.$ 3ia"ra o! !i%er otic ca%$e.
W#en $i"#t is directed into t#e core at sa$$ enou"# an"$es, tota$ interna$ re!$ection 'i$$
occur %et'een t#e core and c$addin" inter!ace. @#e nuerica$ aerture is t#e sine o! t#ea:iu #a$! an"$e t#at can %e directed at t#e core and tota$ interna$ re!$ection 'i$$ sti$$
occur Bsee !i"ure 2.10. @#e !o$$o'in" euation can t#ere!ore %e ca$cu$ated !ro &ne$$-$a'D
22
21sin claddingcore nnN4 =
= B2.
2)
Core, n1
C$addin", n2
u!!er
Facket
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Figure +.1- W#en $i"#t is "uided into a !i%er at an an"$e $ess t#en t#e #a$! an"$e, tota$ interna$ re!$ection
'i$$ occur, iro5in" $i"#t transission.
W#en t#e diaeter o! t#e !i%er core is sa$$ enou"#, 'a5es on$9 can tra5e$ in one at#.
@#ese !i%ers are ca$$ed sin"$e;ode !i%ers. =t $ar"er diaeters, 'a5es coin" in at
di!!erent an"$es can tra5e$ in di!!erent at#s, and are t#ere!ore tered u$ti;ode at#s.@#e nu%er o! odes a !i%er #as can %e deterined !roD
V odes 2
.0
=
dN4Nm B2./
3ue to t#e "enera$$9 $on" $en"t#s, attenuation B$oss due to scatterin" and a%sor%ance is acritica$ roert9 !or !i%ers. +i"ure 2.11 s#o's attenuations in deci%e$s er ki$oeter !or a
coon !i%er ateria$, si$ica. Po'er transission !or t#e $en"t# o! !i%er can %e t#en
ca$cu$ated.
10107
3
= B2.
'#ere is t#e $oss in deci%e$s er $en"t#Bdk, and 3is o'er out o5er initia$ o'er.
=endi: 4 is a roduct data s#eet !or Cornin"-s &M+;28 *tica$ +i%er B&M+ sin"$eode !i%er. 7oe!u$$9 %9 no' ost o! t#e roerties are c$ear.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple +.%
Usin" !i"ure 2.11, '#at is t#e transission Bratio o! outut to inut intensit9 o! a
10 k $en"t# o! !i%er at 80 nG =t 10 nG
4ns6er:+ro t#e !i"ure, at 80 n, t#ere is aro:iate$9 2 dk attenuation $oss,
10
10H2
80 10
=nm3 14 transission
at 10n t#ere is aro:iate$9 0.2 dk attenuation $oss
24
Core, n1.
C$addin", n1.48
Li"#t 'it#in t#is cone
is "uided a$on" !i%er
cr
12
12
12.2o
12
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10
10H2.0
10 10
=nm3 (0 4transission
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
Figure +.11 =ttenuation in !used si$ica Bcoon ateria$ o! !i%ers. +roD
#ttD'''.se.onas#.edu.auteac#in"sc)011e$ecXotB).d!Bro%a%$9 s#ou$d !ind a %etter "ra#
Controlling 3a7elength
Man9 ties, it is necessar9 to 'ork 'it# a seci!ic 'a5e$en"t# or to searate $i"#t %9
'a5e$en"t#. @#is is esecia$$9 use!u$ in sectrosco9 a$ications. @#ere arean9 'a9s to searate 'a5e$en"t#. @#is section 'i$$ descri%e soe o! t#e
ore strai"#t!or'ard et#odsD di!!raction "ratin"s, eta$ons, and #aronic
"eneration.
3i!!raction 6ratin"
W#en o$9c#roatic $i"#t is directed at a di!!raction "ratin", it is re!$ected as a s#eet.
@#e 'a5es sread out into t#e s#eet accordin" to 'a5e$en"t#. 3i!!raction "ratin"s areirrors 'it# 5er9 recise "roo5es cut into t#e. +i"ure 2.12 i$$ustrates t#e %e#a5ior o! a
di!!raction "ratin".
2
http://www.spme.monash.edu.au/teaching/msc3011/elec_&_opt(3).pdfhttp://www.spme.monash.edu.au/teaching/msc3011/elec_&_opt(3).pdf -
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Figure +.1+ 3ia"ra o! a di!!raction "ratin". @#e $i"#t is incident at an"$e , and $ea5es at discreet
an"$es .
@#e "ratin" euation is as !o$$o's, '#ere mis t#e orderD( ) sinsindm += B2.8
&o !or di!!erent 'a5e$en"t#s, t#ere are di!!erent an"$es, causin" t#e $i"#t s#eet. =s a
"enera$ ru$e o! t#u%, t#e ost e!!icient use o! t#e "ratin" occurs around t#e %$a(e
'a5e$en"t#.
+orD efficient>?laze?laze 0
2
)
)
2>
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple +.)
=n in!rared B1. diode $aser #as an eittin" area o! 1 : 1 eittin"
area. = !oca$ $en"t# $ens is used to co$$iate t#e $aser. @#e %ea isdirected at a 1200 " B"ratin" er i$$ieter "ratin". =t '#at an"$e does t#e
1storder di!!racted %ea coe %ack to'ards t#e $aser Bt#is is ca$$ed t#e Littro'
an"$eG4ns6er:
+irst, ca$cu$ate dD
[ ] mx&m
mmmm
gd 10))8
10001
12001 =
=
@#en, $u" into t#e "ratin" euationD( ) sinsin +=dm
kno'in"D = !or Littro' condition, and 1 Border 1 sin2= 2 (%.1(o
2/
%$a(e
incident an"$e
re!$ected an"$e
&u%scrits are t#e
order o! t#e "ratin"
d
o
;1
1
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
Eta$ons
=n eta$on can occur '#ene5er t#ere are airs o! !$at $ates searated %9 an otica$$9
contacted sacer Bsuc# as a $aser ca5it9, or e5en Nust a icroscoe s$ide. 3ue toconstructi5e and destructi5e inter!erence, eta$ons on$9 a$$o' certain 'a5e$en"t#s to %e
transitted. Man9 ties eta$ons are un'anted, #o'e5er eit#er usin" an"$ed sur!aces or
s#i!tin" t#e incident $i"#t to an an"$e can e$iinate t#e.
+ree &ectra$ Ran"e B+&R [ ]Hznd
c
2B2.
n inde: o! re!raction, d distance %et'een ara$$e$ $anes
+inesse B+ 2
2
1
B2.10
and'idt# +W7M B!u$$ 'idt# #a$! a: F
F12B2.11
Figure +.10 Eta$on dia"ra.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple +.(
W#at is t#e !ree sectra$ ran"e and +W7M o! a "$ass Bn1. icroscoe s$ide, 1
'ideG
4ns6er:
/101H.1H2 =
x
cF12 100 @7(
[ ]s
x
smx
fcfc
110100
10)
12
8
=== 0# 2 F89
2
+W7M
+&R
Wa5e$en"t#
@ransission
BO
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2
1
1
+
=n
n2 0.04
2
2F
=
1
0./4
[ ]
/4.0
)mm
F
F12
FWH- == %.),% #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
7aronic 6eneration
=side !ro searatin" 'a5e$en"t#s 'it# "ratin"s or usin" inter!erence as in eta$ons, it isossi%$e to i: 'a5e$en"t#s to "et ne' 'a5e$en"t#s. @#ese rocesses ust satis!9
ener"9 and oentu conser5ation B#o'e5er, not #oton conser5ation. +i"ure 2.14
deonstrations #o' di!!erentia$ and suation i:in" can occur.
Figure +.1% I$$ustration o! 2ndand )rd#aronic "eneration.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!"xa#ple +.
+ourt# #aronic "eneration is i$$ustrated in t#e !i"ure %e$o'. Ca$cu$ate t#e !ina$
'a5e$en"t# %9 er!orin" an ener"9 %a$ance. =$$ o! t#e inut %eas enter at10/4 n.
28
non$inear
cr9sta$Q
110/4 n
210/4 n
) )2 n
Ener"9 a$anceDE
in E
out
&econd 7aronic 6enerationD
110/4 n
210/4 n
) )2 n
Ener"9 a$anceD
Ein Eout
)21
hchchc=+
4)
hchchc=+
@#ird 7aronic 6enerationD
410/4 n ) n
non$inearcr9sta$Q
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4ns6er:
+irst, rea$i(e t#e das#ed $ine a%o5e can de!ine t#e s9ste. @#en, EinEoutD
out
hchc
=
1
4
out2 +(( n#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
:easuring Light
*nce 'e !ina$$9 #a5e $i"#t directed in t#e correct direction and at t#e desired 'a5e$en"t#,
it is usua$$9 iortant to %e a%$e to detect t#e $i"#t. Caeras can %e used !or 5isua$detection, and 5arious ot#er detectors can %e used to easure o'er, 'a5e$en"t#,
o$ari(ation, and co#erence. @#is section needs ore 'ork
Conclusion
In t#is section, 'e #a5e %een introduced to soe o! t#e %asic too$s used in an otics
$a%orator9. Li"#t %u$%s, $asers, and diodes can %e used to create $i"#t, irrors, $enses,
and !i%ers can %e used to direct $i"#t. 6ratin"s, eta$ons, and #aronic "eneration are
'a9s to aniu$ate t#e 'a5e$en"t#. +ina$$9, detectors and caeras are used to easure$i"#t intensit9. 9 no 'a9 #o'e5er did t#is c#ater contain a co$ete $ist o! otica$
too$s a5ai$a%$e. In t#e ne:t section, otica$ a$ications 'i$$ %e discussed to rea$i(e t#eotentia$ o! t#ese too$s.
2
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Appendix 1
&cienti!ic Units*tics !reuent$9 dea$s 'it# 5er9 $ar"e or 5er9 sa$$ nu%ers Bn, 67(, etc..
@#ere!ore, it is iortant to %ecoe !ai$iar 'it# t#e &I re!i:esD
@era @ 1012 Centi c 10;2 Pico 10;12
6i"a 6 10 Mi$$i M 10;) +eto ! 10;1
Me"a M 10/ Micro 10;/ =tto = 10;18
Ki$o k 10)
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7ere is anot#er descrition t#at re$ates t#e $aser c$assi!ications to coon $aser t9es and o'er $e5e$sD
C$ass I ; EYEMP@ L=&ER&, considered Tsa!eT !or intra%ea 5ie'in". Aisi%$e %ea.
Ma:iu o'er $ess t#an 0.4 W. @#is 'i$$ not cause daa"e e5en '#ere t#e entire
%ea enters t#e e9e and it is %ein" stared at continuous$9.
C$ass II ; L*W;P*WERE3 AI&ILE BCW *R 7I67 PUL&E R=@E L=&ER&, 'onTt
daa"e 9our e9e i! 5ie'ed oentari$9. Aisi%$e %ea.
Ma:iu o'er $ess t#an 1 W !or 7e
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Appendix % ; =seful 3ebsites
#ttDscience'or$d.'o$!ra.co#9sicstoics*tics.#t$#ttDicro.a"net.!su.edurier$i"#tandco$orinde:.#t$
#ttD'''.#o'stu!!'orks.co
#ttD'e%#9sics.#.sstate.eduNa5airror
http://scienceworld.wolfram.com/physics/topics/Optics.htmlhttp://www.howstuffworks.com/http://webphysics.ph.msstate.edu/javamirror/http://scienceworld.wolfram.com/physics/topics/Optics.htmlhttp://www.howstuffworks.com/http://webphysics.ph.msstate.edu/javamirror/