optical sources

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


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

E

Eiii

uNBR

E

Eii

sp

st


(6) 1

1)(

is intervalfrequency unit per

density energy radiation the theory,sPlanck' toAccording

J/K.101.38constant sBoltzmann'

(5)

is and

of ratio them,equilibriuunder law, sBoltzmann' Using

(4) )/(

)(

)( )(

/32

30

3

23-

//)(

1

2

12

211221

1122212

12

Tk

B

TkTkEE

B

BB

ec

nu

k

eeN

N

NN

BBNN

Au

uNBuNBAN


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

2

32

30

3

21

1221

RTk

euBN

ANR

BAc

nBA

BBB

B

TkB

: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

the toconfined iselectron an If toscontribute

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

*

*

*

*

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

*

*

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

*

*

*

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

*

*

*

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

int

tot

nrrr

nrrr

rr

tot

rr

R

RR

RR

R

R

R

iciencyuantum effinternal q

*

*

*

Non-radiative recombination

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

5int

int

*

*

*

*

rrnr

nrrr

nrrr

nr

nrnrrrrr

N

NRNR

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

int

intint

int

iciencyuantum effexternal q

qIPP

P

qIRP

R

RRqI

qI

q

qII

ext

extexte

rr

rr

rrtot


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

intexttot

00

tot

2ext

c

c

1cc

qVP

P

V IV P

P efficiency

tumtotal quan

nn

n

/n(

elec

e

elec

e


0totintext

current and power emitted of ratio

theas calledquantity thedefine touseful also isIt

VqI

PR

IP

Rtyresponsivi

e

e

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

qhcIPnrrr

nr

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

2

2ext

I

P

nn

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

dI

SdzuNN

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


(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

0

totmirRRLg

EikLLRRgLE

LRR

n

RR

E


. 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


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

JnG

dt

dn

RGdt

d

r

g

mirmircav

cavcavgph

sp

m

rm

phspm


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

sp

ggmgm

m

gm

m


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

vuvI

Iu

u

u

JJqdqd

JnG

GG

thgph

gg

thph

r

thm

phphm

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

optical sources

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