optical sources
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Optical Sources. History of Lasers. In 1917, Einstein predicted the existence of spontaneous and stimulated emission by which an atom can emit radiation. - PowerPoint PPT PresentationTRANSCRIPT
Optical Sources
History of Lasers
• In 1917, Einstein predicted the existence of spontaneous and stimulated emission by which an atom can emit radiation.
• To make use of the stimulated emission for the construction of coherent optical sources – Townes and Schawlow in the US and Basov and Prochorov in the USSR.
• In 1960- Maiman demonstrated the first laser.
The Einstein Coefficients
(1) )(
bygiven is eunit volumper unit timeper sabsorption undergoing
atoms ofnumber The . levelenergy higher the togo andradiation
incident theabsorbcan levelenergy lower in the atomAn (i)
/)(
.
and frequency between radiation incident theof eunit volumper
energy thebe )(Let ly.respective , and levelsenergy in the
present eunit volumper atoms ofnumber thebe and Let
112
2
1
21
21
21
uNBR
E
E
EE
d
duEE
NN
abs
N1
2
h
The Einstein Coefficients
m.equilibriu thermalof assumption
with theconsistentnot is sink whichor grow lenergy wil
radiation equal,not are they If ns. transitiodownward toequal be
should ns transitioupward ofnumber them,equilibriu At thermal
(3)
bygiven is eunit volumper unit timeper emissions stimulated undergoing
atoms ofnumber The. level the togo and frequency at emission
sspontaneou a make alsocan stateupper in the atomAn )(
(2) )(
bygiven is eunit volumper unit time
per emissions stimulated undergoing atoms ofnumber The emission.
stimulated is This level the togo and frequency at radiation emit
can levelenergy higher in the atoman process, reverse aIn )(
2
2
221
.1
2
ANR
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Eiii
uNBR
E
Eii
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The Einstein Coefficients
(6) 1
1)(
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density energy radiation the theory,sPlanck' toAccording
J/K.101.38constant sBoltzmann'
(5)
is and
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(4) )/(
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12
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The Einstein Coefficients
emission. stimulated
thedominatesemission sspontaneou and 1 , If
1)(
isemission stimulated
tosspontaneou of ratio them,equilibriu At thermal (ii)
atom.per rate absorption
theas same is atomper rateemission stimulated The (i)
ts.coefficienEinstein called are and tscoefficien The
thatsee we(6), and (4) Eq. Comparing
/
2
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32
30
3
21
1221
RTk
euBN
ANR
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:nsObservatio
Example 1
.incoherent is sources
light usual fromlight thehence and dominatesemission sspontaneou
re, temperatuat this and sfrequencie opticalat Therefore
101.08
1))101038.1/(109355.1210exp(1.054
1)k/2(exp R
bygiven isemission stimulated tosspontaneou ofnumber theof ratio The
109355.1)1055.1/(103/ imples microns 55.1
.J101.054 J/K,1038.1k Assume microns. 1.55
ofh wavelengtafor emission stimulated tosspontaneou of
number theof ratio theCalculate 1000k. Tat source opticalan Consider
4
3231434
B
1468
3423B
Tf
Hzcf
s
Population inversion
Light amplification can take place only if Rst> Rabs or
N2 > N1.
Under thermal equilibrium, it is N1 > N2 . Therefore, N2
should be increased by external means. The condition N2 > N1
is referred as population inversion.
Review of Semiconductor Physics
band. conduction intoget and gap band thecross to
energygain band valencein the electrons increases, re temperatuAs
eV. 1.1 gap band theSi,For .or
anby separated are bands twoThese full.nearly is band valence
theandempty nearly is band conduction res, temperatulowAt
in be tosaid isit atom, theof shelloutermost
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thereby,and atom theofout come and means externalby energy
gain can electron An bound.loosely somewhat are electrons These
atoms. gneighborin its with bondscovalent
makesit by which shell,outer itsin electronsfour has atom SiA
(Si)Silicon :Ex .insulators and conductors of osebetween th lie
thatproperties conduction have materialstor Semiconduc
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band gapenergy gap
nd. valence ba
band.conduction
Review of Semiconductor Physics
constant. some is and re temperatuabsolute is
const.,Boltzmann is energy, gap band is where
2exp
bygiven is isit ,impurities no
withmaterialperfect afor and ion concentratcarrier intrinsic
theasknown is holes and electrons ofion concentrat The
.or vacanciesof number equal behind leaves which band,
conductionin electrons free of ion concentrat a toleads This
KT
kE
Tk
EKnpn
n
holes p
n
Bg
B
gi
i
*
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Example 2
microns. 1.1278
)101.602181.1/(103106256.6/
/
.101.60218 1eV
i.e. 1V, ofbarrier potential a climb torequiredenergy theis eV 1
C.101.60218 chargeElectron
,106256.6 Assume emitted.radiation of wavelength
theCalculate eV. 1.1 is gap band thematerialtor semiconduc aFor
19834
19
19
34
g
g
Ehc
hchfE
J
Jsh
Direct and Indirect Band Gaps
momentum. of values
different at occur levelsenergy maximum band valenceand
minimum band conduction thematerials, gap-band-indirectFor
particle.another requiring without possible
is momentum ofon conservati , thereforeand momentum same
thehave holes and electrons thematerials, gap-band-directFor
momentum. theoffunction a as bandgap
theof shape on the depending materials
or either as classified are torsSemiconduc
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and -gap indirect-b
d-gapdirect-ban
P-N Junctions
. called are devicessuch and
called are junctionsSuch layer. middle the toconfined
be willholes and electrons gap, bandlower theof Because
it. gsurroundin layers an thesmaller th islayer thin middle thisof
gap band The layers. type-n and type-pbetween layer thin a
gsandwichinby solved becan problemt confinemencarrier The
realized. benot
can densitiescarrier high Therefore, junction. theofy vicinit
immediate the toconfinednot are carriers thebecause is This
microns). 10-(1region widerelatively aover occursion recombinat
hole-electron that ison homojuncti with theproblem The
. called is figure in theshown junction n -p The
reserostructudouble het
tionsheterojunc
onhomojuncti
*
*
p-type n-type
P-N Junctions
ons.homojuncti using devices in the than
higher is cturesheterostru doublein generationlight of efficiency
theTherefore, too.light, theconfine and s waveguidedielectric
asact cturesheterostru double theresult, a As layer. gsurroundin
theindex than refractivehigher slightly haslayer active The
layer). active asknown (alsolayer middle
the toholes and electrons theconfine tohelps difference bandgap
theFirstly, .benefecialdoubly istion heterojunc of use The
energy. gap banddifferent but layers, gsurroundin the
asconstant lattice same thehaslayer middle This design. device
on the depending doped benot may or may layer middle The
*
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*
Non-radiative recombination
rate.ion recombinat total and rate,
ionrecombinat radiativenon rate,ion recombinat radiative
as
define touseful isIt light.emit that pairs hole-electron of
number thereduce they since harmful are processes radiative-non All
light. producing
n rather thaenergy kinetic as holeor electron another given to is
energy released thetion,recomboinaAuger In the radiative.-non
areion recombinatAuger and defectsat ion recombinat example,
For ion.recombinat radiative-non called isit light, of form in the
not isn combinatio hole-electron during releasedenergy theIf
ion.recombinat radiative
called is This light. produce tocombinecan holes and Electrons
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iciencyuantum effinternal q
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1. to
5.0 InP, and GaAs assuch materials gap banddirect For
gap. bandindirect their of because sources optical
for suitablenot areBoth Ge. and Sifor 10 Typically,
materials. gap band
indirectfor offraction small a is whereastors,semiconduc
bandgap-directfor comparable are and ion timesRecombinat
,
as expressed becan efficiency quantum internal
theNow e.unit volumper carriersnumber theis where
/ ,/
definition theUsing
int
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rrnr
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Light emitting diode (LED)
• LED is a forward-biased p-n homojunction or heterojunction.
• Radiative recombination of electron-hole pairs in the depletion region generates light.
• For LEDs, radiative recombination of holes and electrons is dominated by spontaneous emission and stimulated emission is negligible.
• The emitted light is incoherent with a relatively wide spectral width (30-60 nm) and a relatively large angular spread.
• For bit rates less than 100-200 Mb/s together with multimode fibers, LEDs are usually the best light source.
• LEDs can not be used for long haul WDM systems because of their large spectral width.
LED: Light-Current Characteristics
. called is quantity The
)/(
bygiven
ispower emitted The interface. at the reflection internal totalto
duepower generated than theless is LED ofout comingpower The
power. optical
internalsimply or unit timeper generatedenergy photon theis
)/(
is unit timeper generatedenergy photon , rateion recombinat
radiative toequal is unit timeper generated photons of no. theSince
//
i.e. processes, radiative-non and radiative through unit timeper
recombined carriers of no. the toequal is )/( unit timeper
injected carriers of no. thestate,steady In the charge.electron is
where/ is rateinjection carrier the,current given aAt
intint
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iciencyuantum effexternal q
qIPP
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ext
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LED: Light-Current Characteristics
tyresponsivi calledquantity thedefine touseful also isIt
device. theacross drop voltage theis where, power, electrical
applied the topower optical emitted theof ratio theas
thedefine touseful isit view,ofpoint practical From
)1(
1
obtains one ivity, transmittFresnel eaccount th into
takingand to0over power optical thegIntegratin incidence. of
angle on the dependsch ivity whi transmittFresnelby multiplied be
should surface theescaping rays toingcorrespondpower optical The
.reflection internal totalundergo an greater th angles The surface.
LED theescapes material,tor semiconduc theof R.I. theis and angle critical
theis ))1sin( where angle of cone a within emittedlight The
0
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LED: Light-Current Characteristics
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current and power emitted of ratio
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Example 3
mW 29.2
)101310(*)10602.1(
)04.0(*)103(*)10(6.6256*0.77
)/( power Generated (ii)
77.0130/100 efficiency quantum Internal (i)
tyresponsivi (v) and emittedpower optical (iv)
efficiency quantum external (iii)power generated (ii)
efficiency quantum internal (i) Calculate 3.5. is material
LED theofindex refractive theandmA 40 iscurrent drive The
ly.respective ns, 100 and 30 of ion timesrecombinat radiative-non and
radiative has nm 1310 ofength peak wavel a emitting LEDA
9-19-
834-
intint
int
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Example 3
W/A0103.0
W/A /40412.0/P ty Responsivi (v)
mW. 0.412mW2.29*0141.0P power d(iv)Emitte
0.0141.
3.5(4.5)
1
)1(
1 efficiency quantum External (iii)
e
intexte
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Laser diode (LD)
• Laser diodes emit light through stimulated emission while LEDs emit light through spontaneous emission.
• Laser diodes can emit high powers (~100 mW) and also it is coherent.
• A relatively narrow angular spread of the output beam compared with LEDs permit high coupling efficiency.
• A relatively narrow spectral width of LD makes it a suitable candidate for wavelength division multiplexing (WDM) applications.
Laser diode (LD)• When a photon of energy hf impinges on the system, electrons in the
valence band can be excited to conduction band. This is called absorption.
• Electrons in the conduction band are also stimulated to make a transition to valence band in the presence of a photon of energy hf which is equal to the band gap energy. This is called stimulated emission.
• Electrons in the conduction band could emit a photon of energy hf without any external stimulation and go to valence band. This is spontaneous emission.
• The stimulated emission exceeds absorption only if the number of electrons in the excited state exceeds that in ground state. This condition is known as population inversion.
• Population inversion is achieved by various “pumping” techniques. In semiconductor lasers, population inversion is accomplished by injecting electrons into the semiconductor material.
Light Amplification by Stimulated Emission for TwoLevel Systems
time.
unitper emittedenergy ofamount net toequal be should This
(1)
is Sdz volume
theleaving unit timeper energy ofamount net theTherefore,
dz)S.I(z is Sdz volume
theleaving unit timeper energy ofamount theand I(z)S is Sdz
volume theentering unit timeper energy ofamount The ly.respective
dz,z and zat intensity opticalrepresent dz)I(z and I(z)Let
dz.z and zat situated S area of P and P planes woconsider t usLet 21
Sdzdz
dIdz)-I(z))S( I(z
z) z+dz)
P1 P2
z z+dz
Light Amplification by Stimulated Emission
)exp()0()(
have we(4), Eq. Solving
)/()B(
(4) ,
becomes (3) Eq. So,
linewidth.laser where
)(
by )(density energy
torelated is )( it volumedensity/un spectralenergy The
index. refractive ,/
by related areintensity and )(density energy The
(3) )()B(
have we(2), and Eqs.(1) Equating
(2) )()B(
is unit timeper emittedenergy of
amount net So, t.coefficienEinstein is where)( is
unit timeper absorbedenergy theand )(
isemission stimulated todue unit timeper emittedenergy The
lasers.for small isit sinceemission sspontaneou ignore usLet
12
12
12
1
2
zIzI
cnNN
Idz
dI
uv
u
nncI
uNNdz
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BSdzuBN
SdzuBN
Optical Feedback and Laser Threshold
. thecalled is threshold
reach the toneededcurrent minimum The achieved.not is threshold
theand negligible be gain will optical and achievednot isinversion
population small, iscurrent theIf . called isoperation
laser esustain th torequiredgain minimum The up. buildnot will
populationphoton thelosses,cavity for the compensate enough to large
not isgain optical theIf losses.cavity of becauselost isemission
stimulatedby generated photons offraction Certain :
cavity. (FP)Perot -Fabry called is
cavity optical This mirrors. by two formedcavity opticalan inside
mediumgain theplacingby provided isfeedback thelasersmost In
.oscillatoran intoamplifier an convertsit
is ingredientnecessary other The operation.laser
forenough not is aloneinversion populationby obtainedgain
optical The frequency. opticalat operating oscillatoran isLaser :
currentthreshold
gainthreshold
edbackoptical fe
ThresholdLaser
Feedback
Optical Feedback and Laser Threshold
(2) 1
ln2
1
sides,both on amplitudes equatingBy
(1) )2exp()exp(
i.e., trip,round
oneafter unchangedremain should waveplane thestate,steady In
.absorption and scattering assuch lossn propagatio theincludes that loss
internalan of because and mirrors at the reflection of because
)exp(by changes amplitude its time,same At the
medium.
gain in theconstant n propagatio theis /2 k where2kL,by
changes phase Its gain.power theis g where2L))exp((g/2)(by increases
amplitude its0), toL and L to0 from (i.e. tripround one During
L. be mirrors ebetween th distance theand and be mirrors of
tscoefficien reflection Let the . amplitude of waveplane aConsider
int21
int
0int210
int
int21
0
21
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totmirRRLg
EikLLRRgLE
LRR
n
RR
E
Optical Feedback and Laser Threshold
. tocorrespond sfrequencie These
cavity. theof frequciesresonant asknown set in the
sfrequencie of onematch must frequency laser that shows (3) Eq.
in vaccum.light of velocity is andfrequency is
(3) 2
or
index refractive is integer,an is where,24
22
(1) Eq. of sidesboth on phases equatingBy
ld.at thresho losscavity total
toequal be shouldgain optical that shows (2) Eq.
al modeslongitudin
f
f
cfnL
mcf
nmmnL
mkL
m
m
m
Example 4
cm 0.0155
))5.0*9.0/(1ln(100*2
101151.0
cm 01151.0)10ln(
dB 05.0))1.(exp(log 10
is 1cm oflength aover loss absorption The
1
ln2
1
is requiredgain minimum The
MHz. 42.87 spacing mode allongitudin theSo,
1,2,3.... MHz, 87.42
)101005.32/(1032/
bygiven are modes allongitudin The
required.gain minimum theand spacing mode
allongitudin theCalculate cm. 100 mirrorsbetween distance
and 0.5R 0.9, R 3.5, dB/cm, 05.0 t,coefficien
loss absorption :parameters following thehas diodelaser GaAsA
1-
1-10/5.0int
int10
21int
28
21int_
g
RRLg
mm
mnLmcf
n
m
dB
Optical Feedback and Laser Threshold
mode.dominant thebecomes andfirst
thresholdreaches losscavity smallest with themode allongitudin The
modes. allongitudindifferent for different are lossescavity
such that designed are laserstor semiconduc SLM
)(
called are lasersSuch operation. mode allongitudin
single achieve tosuppressed becan modeslaser theof
Some modes. allongitudin single have todesirable isit Therefore,
fiber. opticalin speedsdifferent with propagate modeslaser
different since dispersion todue distortion signal torise give lasers
moded-multi systems, WDMhaul long assuch nsapplicatioFor
lasers. moded-multi
called are lasersSuch cavity. theof modes allongitudin
severalin light emitsgenerally laser tor semiconduc FPA
lasers.SLMmode allongitudin
single
DFB and DBR Semiconductor lasers
length.cavity t the throughouoccursfeedback the
lasers, DFBin elaser whil a ofregion active theinside place take
not doesfeedback thelasers (DBR) In
modes. allongitudinother for lly substantia increases
and closest to modes allongitudin for the minimum are
lossescavity The 1.m with Eq.(4) satisfying h wavelengta
for maximum isty reflectivisuch that chosen is period Grating
1).(mn diffractio Braggorder -first for the
strongest is wavesbackward and forwardbetween coupling The
integer
medium theofindex refractive
h wavelengtspace free period, grating
(4) )2/(
i.e. condition, Bragg
satisfying ngthsfor waveleonly occurs reflection and
light incident thereflects grating Bragg The grating. internalan
usingn diffractio Braggby achieved is This length.cavity the
t throughouddistribute isbut facets, the tolocalizednot is
lasers (DFB) in feedback The
flectord Bragg redistribute
m
n
nm
d feedbackdistribute
B
B
B
B
B
Laser Diode Rate Equations
chargeelectron q layer, active theof thickness
.mechanismsion recombinat radiative-non
and sspontaneou from comingconstant timecombine
light of velocity group area,unit per current
lossmirror loss, absorption ,
losscavity ),/(1lifetimephoton
rateemission sspontaneou
emission stimulated of ratenet
density)(carrier eunit volumper electrons of no.
density)(photon eunit volumper photons of no. where
injection ion recombinat emission stimulated
(6)
lossphoton emission sspontaneou emission stimulated
(5)
bygiven are electrons and photons thegoverningequation rate The
intint
d
vJ
v
R
G
n
qd
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dt
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d
r
g
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m
rm
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Laser Diode Rate Equations
become
conditions statesteady under equations rate , threshold theaboveJust
(9)
bygiven is statesteady in density carrier levelinversion
population thehave toneeded density current thresholdthe
and 0)( small negligibly is photons of no. the, thresholdBelow
.0 settingby emission sspontaneou
neglect weif form simple a akessolution t The zero. to(6) and Eqs.(5)
in sderivative timeset thecan weconditins, statesteady Under
layer. active in the
power optical offraction factor t confinemen field optical
(8) )(
bygiven is emission stimulated of ratenet The
(7) )(
is density carrier and t coefficiengain between relation empirical The
0
0
qd
Jn
n
J
R
nnvgvG
G
nng
ng
th
r
th
th
th
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m
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m
Laser Diode Rate Equations
layer. active theof width theis where
(12) )(
generatedpower Optical
medium. in thelight of velocity group ,
by related
are area)unit per power (intensity optical and density Energy
by related are density photon and density Energy
(11) )(0
(10) 1
0
w
JJq
vw
IwdP
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Iu
u
u
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gg
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thm
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Example 5
320
1234
3
389
29
66
104493.2
)10190)106256.6/((83.30)/(densityPhoton
83.30
)103/(7.3102.5/
/102.5
)104101000/()10()/(
ly.respective
microns, 4 and 1000 are area active of thicknessandwidth
3.7, index refractive : Assume density.photon theCalculate
power. of W 10 generates THz 190at operatinglaser GaAsA
m
hfu
J/m
J/mvIu
mW
wdPI
uvI
g
g