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Széchenyi István University
Győr
Hungary
General propertiesGeneral propertiesLasersLasers
Szilvia NagySzilvia Nagy
Department of TelecommunicationDepartment of Telecommunicationss
22ESM Sofia 2009ESM Sofia 2009
Outline – General PropertiesOutline – General Properties
Modeling of lightModeling of lightphotonsphotonselectromagnetic waveselectromagnetic wavesgeometrical opticsgeometrical optics
Nonlinear effectsNonlinear effectsBrillouin scatteringBrillouin scatteringself-phase modulationself-phase modulationcross-phase modulationcross-phase modulationfour-wave mixingfour-wave mixingRaman scatteringRaman scattering
33ESM Sofia 2009ESM Sofia 2009
Outline – LasersOutline – Lasers
Operation of lasersOperation of lasersPropertiesProperties
applicationsapplications
Atomic energy levelsAtomic energy levels
Population inversion Population inversion
Energy bands in solid statesEnergy bands in solid states
Heterojunctions in semiconductorsHeterojunctions in semiconductors
Quantum well lasersQuantum well lasers
Vertical cavity surface emitting lasersVertical cavity surface emitting lasers
44ESM Sofia 2009ESM Sofia 2009
Modeling of lightModeling of light
Photon modelPhoton model
particles with energy particles with energy hh, , bosonsbosons
useful inuseful in quantum mechanicsquantum mechanics particle physicsparticle physics telecommunicationstelecommunications
electron excitations: lasers, detectorselectron excitations: lasers, detectors
55ESM Sofia 2009ESM Sofia 2009
Modeling of lightModeling of light
Electromagnetic wave modelElectromagnetic wave model
the Maxwell equations describe the the Maxwell equations describe the behavior behavior
c c = (= (0000))−1/2−1/2 velocity of light in vacuum velocity of light in vacuum
v v = (= ())−1/2 −1/2 velocity of propagation in velocity of propagation in materialsmaterials
refraction index: refraction index: n n = (= (rrrr))−1/2 −1/2
used in optical telecommunicationused in optical telecommunication modeling the fiber as waveguidemodeling the fiber as waveguide
66ESM Sofia 2009ESM Sofia 2009
Modeling of lightModeling of light
Geometrical opticsGeometrical optics
raysrays
Snelius—Descartes lawSnelius—Descartes law
n1 sin = n2 sin
reflection and reflection and transmissiontransmission
n1
n2
n1 < n2
77ESM Sofia 2009ESM Sofia 2009
Nonlinear effectsNonlinear effects
Brillouin scatteringBrillouin scattering
self-phase modulationself-phase modulation
cross-phase modulationcross-phase modulation
four-wave mixingfour-wave mixing
Raman scatteringRaman scattering
Nonlinear effectsNonlinear effects
88ESM Sofia 2009ESM Sofia 2009
Brillouin scattering:Brillouin scattering: acoustic vibrations caused by electro-acoustic vibrations caused by electro-
magnetic fieldmagnetic field(e.g. the light itself, if (e.g. the light itself, if PP>3mW)>3mW)
acoustic waves generate refractive index acoustic waves generate refractive index fluctuationsfluctuations
scattering on the refraction index wavesscattering on the refraction index waves the frequency of the light is shifted the frequency of the light is shifted
slightly slightly direction dependently direction dependently (~11 GHz(~11 GHz backw.backw.))
longer pulses – stronger effectlonger pulses – stronger effect
Nonlinear effects in fibersNonlinear effects in fibers
99ESM Sofia 2009ESM Sofia 2009
Raman scattering:Raman scattering: optical phonons (vibrations) caused by optical phonons (vibrations) caused by
electromagnetic field and the light can electromagnetic field and the light can exchange energy (similar to Brillouin but exchange energy (similar to Brillouin but not acoustical phonons)not acoustical phonons)
Stimulated Raman and Brillouin scattering Stimulated Raman and Brillouin scattering can be used for amplificationcan be used for amplification
Self-phase and cross-phase modulationSelf-phase and cross-phase modulation
Four-wave mixingFour-wave mixing
Nonlinear effects in fibersNonlinear effects in fibers
1010ESM Sofia 2009ESM Sofia 2009
Four-wave mixingFour-wave mixing
Nonlinear effects in fibersNonlinear effects in fibers
1550 1550 + x
Pcrit>10 mW
mixing terms 1550 - x
1550 + 2x
1111ESM Sofia 2009ESM Sofia 2009
((Pockels effect:Pockels effect: refractive index change due to external refractive index change due to external
electronic fieldelectronic field nn ~~ ||EE| - a | - a linear effectlinear effect))
Nonlinear effects in fibersNonlinear effects in fibers
1212ESM Sofia 2009ESM Sofia 2009
Kerr effect:Kerr effect: the refractive index changes in response the refractive index changes in response
to an electromagnetic field to an electromagnetic field n n = = KK ||EE||22
light modulators up to 10 GHzlight modulators up to 10 GHz can cause self-phase modulation, self-can cause self-phase modulation, self-
induced phase and frequency shift, self-induced phase and frequency shift, self-focusing, mode lockingfocusing, mode locking
can produce solitons with the dispersioncan produce solitons with the dispersion
Nonlinear effects in fibersNonlinear effects in fibers
1313ESM Sofia 2009ESM Sofia 2009
Kerr effect:Kerr effect: the polarization vectorthe polarization vector
if if EE==EE cos( cos(tt)), the polarization in first , the polarization in first order isorder is
Nonlinear effects in fibersNonlinear effects in fibers
3
1
3
1
3
1
10
3
1
3
1
20
3
1
10
j kkjijk
j kkjijk
jjiji EEEEEEP
PockelsKerr
t cos231
0 EEP
1414ESM Sofia 2009ESM Sofia 2009
Kerr effect:Kerr effect:
the susceptibilitythe susceptibility
the refractive indexthe refractive index
nn22 is mostly small, large intensity is needed is mostly small, large intensity is needed (silica: (silica: nn22≈10≈10−20−20mm22/W, /W, II ≈10≈1099W/cmW/cm22))
Nonlinear effects in fibersNonlinear effects in fibers
231
43
E
t cos231
0 EEP
Innn
nn 20
23
00 8
3 E
1515ESM Sofia 2009ESM Sofia 2009
Gordon-Haus jitter:Gordon-Haus jitter: a timing jitter originating from a timing jitter originating from
fluctuations of the center frequency of fluctuations of the center frequency of the (soliton) pulsethe (soliton) pulse
noise in fiber optic links caused by noise in fiber optic links caused by periodically spaced amplifiersperiodically spaced amplifiers
the amplifiers introduce quantum noise, the amplifiers introduce quantum noise, this shifts the center frequency of the this shifts the center frequency of the pulsepulse
the behavior of the center frequency the behavior of the center frequency modeled as random walkmodeled as random walk
Nonlinear effects in fibersNonlinear effects in fibers
1616ESM Sofia 2009ESM Sofia 2009
Gordon-Haus jitter:Gordon-Haus jitter: dominant in long-haul data transmissiondominant in long-haul data transmission ~~LL33,, can be suppressed by can be suppressed by
regularly applied optical filtersregularly applied optical filters
amplifiers with limited gain bandwidthamplifiers with limited gain bandwidth can also take place in mode-locked can also take place in mode-locked
laserslasers
Nonlinear effects in fibersNonlinear effects in fibers
1717ESM Sofia 2009ESM Sofia 2009
Outline – LasersOutline – Lasers
Operation of lasersOperation of lasersPropertiesProperties
applicationsapplications
Atomic energy levelsAtomic energy levels
Population inversion Population inversion
Energy bands in solid statesEnergy bands in solid states
Heterojunctions in semiconductorsHeterojunctions in semiconductors
Quantum well lasersQuantum well lasers
Vertical cavity surface emitting lasersVertical cavity surface emitting lasers
1818ESM Sofia 2009ESM Sofia 2009
Properties of lasersProperties of lasers
Monochromatic light – small bandwidthMonochromatic light – small bandwidth
Small divergence – narrow and directed Small divergence – narrow and directed beambeam
Coherent beam – all photons have nearly Coherent beam – all photons have nearly the same phasethe same phase
Usually not too high power, but Usually not too high power, but
High power densityHigh power density
Not an effective energy transformerNot an effective energy transformer
1919ESM Sofia 2009ESM Sofia 2009
Application of the lasersApplication of the lasers
Materials processing – cutting, drilling, Materials processing – cutting, drilling, welding, heat treating, …welding, heat treating, …
Reading optical signs – CD, barcode, …Reading optical signs – CD, barcode, …
Graphics – printers, color separators, Graphics – printers, color separators, printing plate makers, …printing plate makers, …
Laboratory, measurementsLaboratory, measurements
Medicine – bloodless scalpel, tumor Medicine – bloodless scalpel, tumor destroying, …destroying, …
Military – target designators, finders, …Military – target designators, finders, …
TelecommunicationsTelecommunications
2020ESM Sofia 2009ESM Sofia 2009
optical power of the light before reflection: Pafter reflection:(1−1)P
Operation of lasersOperation of lasers
What is needed for laser operationWhat is needed for laser operation
Laser gain – an optical amplifierLaser gain – an optical amplifier
Optical resonator – positive feedbackOptical resonator – positive feedback
reflection
2121ESM Sofia 2009ESM Sofia 2009
Operation of lasersOperation of lasers
What is needed for laser operationWhat is needed for laser operation
Laser gain – an optical amplifierLaser gain – an optical amplifier
Optical resonator – positive feedbackOptical resonator – positive feedback
new photons arisereflection
optical gain in the amplifier: P g∙ℓ∙P
2222ESM Sofia 2009ESM Sofia 2009
Operation of lasersOperation of lasers
What is needed for laser operationWhat is needed for laser operation
Laser gain – an optical amplifierLaser gain – an optical amplifier
Optical resonator – positive feedbackOptical resonator – positive feedback
(1−2)P
2∙P
2323ESM Sofia 2009ESM Sofia 2009
Operation of lasersOperation of lasers
In equilibrium the gain and the losses have In equilibrium the gain and the losses have to be the same: the power of the light to be the same: the power of the light varies asvaries as
ℓ
P
2424ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
The solution of the SchrThe solution of the Schröödinger equationdinger equation
results inresults in - quantized eigenenergies- quantized eigenenergies
- corresponding wave functions- corresponding wave functions
EH
E
ground state
1st excited state
2nd excited state
2525ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
If a photon of energy If a photon of energy
interacts with an atom, an electron can be interacts with an atom, an electron can be excited from energy level excited from energy level EEmm to level to level EEnn
mn EEh
E
nE
mE
ephoton
photon absorption – relative rate:
hffB
r
nmmn
mn
1
2626ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
An excited electron from energy level An excited electron from energy level EEmm can can relax to a lower from energy level relax to a lower from energy level EEnn, , releasing a photon of energyreleasing a photon of energy
mn EEh
E
nE
mE
ephoton – random direction
spontaneous emission – relative rate:
spontaneous lifetime
mnnmnm ffAr 1
2727ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
If a photon corresponding to the energy If a photon corresponding to the energy
interacts with an atom which has an excited interacts with an atom which has an excited electron at energy level electron at energy level EEnn, it can stimulate , it can stimulate the electron to relax to level the electron to relax to level EEnn
mn EEh
E
nE
mE
photon
stimulated emission
2 photons – same direction, same phase
hffBr nmmnmn 1stim
2828ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
Stimulated emission can take place long Stimulated emission can take place long before the spontaneous lifetime.before the spontaneous lifetime.
Stimulated emission:Stimulated emission:
one photon in one photon in two photons outtwo photons out
The The optical amplifieroptical amplifier can be a collection of can be a collection of atoms with lots of electrons excited to the atoms with lots of electrons excited to the same state (with long spontaneous lifetime).same state (with long spontaneous lifetime).
2929ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
LLight ight AAmplification by mplification by SStimulated timulated EEmission mission of of RRadiationadiation
The resonator is usually much longer than The resonator is usually much longer than the wavelength.the wavelength.
E
Upper Laser Level
Lower Laser Level
3030ESM Sofia 2009ESM Sofia 2009
Atomic energy levelsAtomic energy levels
In equilibrium, the relative rates In equilibrium, the relative rates
Thus the photon density at energy Thus the photon density at energy hh
stimnmnmmn rrr
nm
mn
nmmn
nm
Bffff
B
Ah
11
relative occupation probability
3131ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
In thermodynamical equilibrium, the In thermodynamical equilibrium, the population of the states follow Boltzmann’s population of the states follow Boltzmann’s lawlaw
TkE
iB
i
eNN
0
TkEE
B
mn exp
the relative occupation probability is
nmTk
EEmn
nm
BBA
hB
mn exp
thus
3232ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
Comparing the resulting photon density Comparing the resulting photon density with the black body radiationwith the black body radiation
nmmn BB
1 exp
4
2
3
Tkh
c
hh
B
nm
B
mnmn
nm
BTkEE
B
Ah
exp 2
34ch
BA
nm
nm
3333ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
In thermodynamical equilibrium, the In thermodynamical equilibrium, the population of the states follow Boltzmann’s population of the states follow Boltzmann’s lawlaw
TkE
iB
i
eNN
0
iE
iNmE
nE
If Bmn=Bnm, the relative , the relative rate of absorption in rate of absorption in equilibrium is much equilibrium is much higher than that of higher than that of stimulated emissionstimulated emission
3434ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
Somehow the number of electrons in the Somehow the number of electrons in the upper laser level is increasedupper laser level is increased
population inversionpopulation inversion occurs. occurs.
iE
iNmE
nE
The particles are not in thermodynamical equilibrium
3535ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
Population inversion is generated by Population inversion is generated by
exciting the electrons to a exciting the electrons to a level with short spontaneous level with short spontaneous lifetime above the upper lifetime above the upper laser level: laser level: pumpingpumping
from the from the ppumping umping llevel the evel the electrons relax to the electrons relax to the uupper pper llaser aser llevel, which has longer evel, which has longer spontaneous lifetimespontaneous lifetime
electrons accumulate at the upper electrons accumulate at the upper laser levellaser level
E
ULL
LLL
PL
GS
3636ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
Three-level laser Three-level laser Four-level laserFour-level laser
EE
upper laser level
lower laser level =
pumping level
ground state
upper laser level
lower laser level
pumping level
ground state
short spontaneous lifetime
3737ESM Sofia 2009ESM Sofia 2009
Population inversionPopulation inversion
Inverse population can be generated by Inverse population can be generated by
special filtersspecial filters
electrical pumpingelectrical pumping direct electrical dischargedirect electrical discharge
radio frequency fieldradio frequency field
electron beamelectron beam
p-n heterostructurep-n heterostructure
optical pumpingoptical pumping
chemical pumpingchemical pumping
nuclear pumpingnuclear pumping
3838ESM Sofia 2009ESM Sofia 2009
Energy bands in solid statesEnergy bands in solid states
In solids the atomic niveaus broaden In solids the atomic niveaus broaden energy bands are formedenergy bands are formed
vibrations (and rotations) in the crystalvibrations (and rotations) in the crystal momentum dependence of energy levelsmomentum dependence of energy levels splitting of degenerate states, …splitting of degenerate states, …
E
valance band
conduction band
bandgap – no electrons are allowed
3939ESM Sofia 2009ESM Sofia 2009
Energy bands in solid statesEnergy bands in solid states
The Fermi level is the highest energy level The Fermi level is the highest energy level occupied by electrons:occupied by electrons:
Fermi level in the conduction bandFermi level in the conduction band metalmetal
Fermi level in the gap Fermi level in the gap insulator insulatorE E
FE
FE
metal insulator (semiconductor)
4040ESM Sofia 2009ESM Sofia 2009
Energy bands in solid statesEnergy bands in solid states
At non-zero temperature, the Fermi level is At non-zero temperature, the Fermi level is not strict, the occupation probability will not strict, the occupation probability will follow Fermi-Dirac statisticsfollow Fermi-Dirac statistics
E E
FE FE
T = 0 K
T > 0 K
f(E)
TkB
TkEE
B
fEf
exp11
f(E)
4141ESM Sofia 2009ESM Sofia 2009
Energy bands in solid statesEnergy bands in solid states
So if an insulator has a bandgapSo if an insulator has a bandgap
considerable amount of electrons can be considerable amount of electrons can be present in thepresent in the conduction conduction band: band:
E
,roomTkB
E
FE roomTkB
conduction band
conduction bandgap
semiconductor insulator
4242ESM Sofia 2009ESM Sofia 2009
Energy bands in solid statesEnergy bands in solid states
In a crystal the energy levels depend on the In a crystal the energy levels depend on the electron’s wave number electron’s wave number k k (quasi momentum):(quasi momentum):
E
v.b
c.b
indirectgap
k
E
v.b
c.b
direct gap
kmomentum conservation
no photon emissionno momentum to be taken photon emission
4343ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
Charge carriers can be injected to semi-Charge carriers can be injected to semi-conductors by conductors by dopingdoping: :
group V atoms: electrons group V atoms: electrons n-typen-type
group III atoms: holes group III atoms: holes p-typep-type
conduction band
valance band
E
FEp-
type
E
FE
n-type
localized acceptor/donor levels
4444ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
If n-type and p-type doped semiconductorIf n-type and p-type doped semiconductor
layers are brought in contact, layers are brought in contact,
the positive and negative charge carriers the positive and negative charge carriers near the junction can recombine near the junction can recombine
photons can be emittedphotons can be emitted
potential barrier buildspotential barrier builds
barrierUe
no recombination
FE
x
4545ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
If n-type and p-type doped semiconductorIf n-type and p-type doped semiconductor
layers are brought in contact, layers are brought in contact,
the recombination stops, unless external the recombination stops, unless external bias is appliedbias is applied LEDsLEDs
externalUeFpE
FnE
x
recombination possible active region
4646ESM Sofia 2009ESM Sofia 2009
If n-type and p-type doped semiconductorIf n-type and p-type doped semiconductor
layers are brought in contact, layers are brought in contact,
the recombinationthe recombinationstops, unless stops, unless external bias external bias is appliedis appliedLEDsLEDs
1 ns −100 ns1 ns −100 ns
Heterojunctions in Heterojunctions in semiconductorssemiconductors
Popt
I0
t
t
PoptSUPER-LED
ELED
SLED
4747ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
The simple heterojunctions have some The simple heterojunctions have some disadvantagesdisadvantages
due to the relative large spatial dimension, due to the relative large spatial dimension, high current is needed for creating high current is needed for creating sufficient population inversionsufficient population inversion
the heat generated by the current is very the heat generated by the current is very high, destroys the devicehigh, destroys the device
Solution: Solution: restrict the high current density region into restrict the high current density region into small regionsmall region double heterojunctiondouble heterojunction
4848ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
1
active layer
The double heterojunction localizes the population The double heterojunction localizes the population inversion into a small region of space applying inversion into a small region of space applying two different materials with different bandgaps two different materials with different bandgaps 11 and and 22
22
x
4949ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
1n
active layern
The semiconductors of the double hetero-The semiconductors of the double hetero-junction have different refractive indices junction have different refractive indices nn11 and and nn22 (not just different bandgaps (not just different bandgaps 11, , 22))
2n
x
the laser beam is also localized in direction x
5050ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
The double heterojunction localizes the The double heterojunction localizes the population inversion and the laser beam into population inversion and the laser beam into a small region of spacea small region of space less heatless heat
substrate, p-type substrate, p-type dopeddoped
p-type, p-type, 22
n-type, n-type, 22
substrate substrate (n-type/undoped)(n-type/undoped)
electrodeelectrode
electrodeelectrode
x
active layer, active layer, 11
5151ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
Materials grown upon each other should have Materials grown upon each other should have similar grid distance in order not to produce similar grid distance in order not to produce strain or dislocations in the crystal.strain or dislocations in the crystal.
x
p-GaAs, p-InGaAsP,…
p-Ga0,7Al0,3As, p-InP,…Ga0,95Al0,05As, InGaAsP,…n-Ga0,7Al0,3As, n-InP,…n-GaAs, n-InP,…
exampleexampless
5252ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
Thin layers of semiconductors have to be Thin layers of semiconductors have to be grown on each other with very accurate grown on each other with very accurate layer thickness:layer thickness:
metal-organic chemical vapor depositionmetal-organic chemical vapor deposition
molecular beam epitaxymolecular beam epitaxy
5353ESM Sofia 2009ESM Sofia 2009
The mirrors placed parallel to the plane The mirrors placed parallel to the plane plottedplotted the light propagates the light propagates parallel to the layerparallel to the layer
Heterojunctions in Heterojunctions in semiconductorssemiconductors
x
lighlightt
The optical properties The optical properties of the cleaved of the cleaved facelets are not facelets are not controllable during controllable during the fabrication the fabrication processprocess
The cleaved facelets The cleaved facelets of the stripe are of the stripe are usually sufficient usually sufficient reflectors.reflectors.
5454ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
The population inversion can be restricted in The population inversion can be restricted in the other dimension, too:the other dimension, too:
electrodeelectrodestripe electrode stripe electrode restricts the current restricts the current flowflow
x
the population the population inversion takes place inversion takes place in a small stripe in a small stripe inside the active inside the active layerlayer
5555ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
With special geometry the laser beam can With special geometry the laser beam can be localized, as well as the population be localized, as well as the population inversioninversion
x
the n-p junctions do the n-p junctions do not allow current not allow current outside of the stripeoutside of the stripe
n-typen-typen-typen-type
p-typep-typep-typep-type
refractive index refractive index nn<<nn11 the low refractive the low refractive index regions index regions restrict the beam: restrict the beam: the high refractive the high refractive index field is a index field is a waveguidewaveguide
5656ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
With special geometry the laser beam can With special geometry the laser beam can be localized, as well as the population be localized, as well as the population inversioninversion
x
elliptical elliptical beambeam
the thinner the the thinner the layer, the layer, the less less modesmodes can can propagatepropagate
the thinner the the thinner the layer, the layer, the less less currentcurrent is needed is needed for sufficient for sufficient amount of inverse-amount of inverse-population charge population charge carrierscarriers
5757ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
For proper optical confinement single For proper optical confinement single waveguide mode is neededwaveguide mode is needed the the higher order modes have to be cut off.higher order modes have to be cut off.This requires thicknessThis requires thickness
222 cg nnd
or less. For or less. For = the1.3 = the1.3 m, m, dd<0.56 <0.56 m.m.
((nngg and and nncc are reflective indices of are reflective indices of wavewavegguide and the uide and the ccladding)ladding)
5858ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
If the waveguide is too thin, the light spreads out of If the waveguide is too thin, the light spreads out of itit the loss increases.the loss increases.
For confining the population inversion thinner For confining the population inversion thinner layers would be needed.layers would be needed.
Solution: the waveguide and the active layer are Solution: the waveguide and the active layer are not the same – not the same – SSeparate eparate CConfinement onfinement HHeterostructure (SCH)eterostructure (SCH)
active layeractive layer
waveguidewaveguide
5959ESM Sofia 2009ESM Sofia 2009
Heterojunctions in Heterojunctions in semiconductorssemiconductors
If the waveguide is too thin, the light spreads out If the waveguide is too thin, the light spreads out of itof it the loss increases.the loss increases.
For confining the population inversion thinner For confining the population inversion thinner layers would be needed.layers would be needed.
Solution: the waveguide and the active layer are Solution: the waveguide and the active layer are not the same – not the same – GRGRaded aded ININdex SCH (GRINSCH)dex SCH (GRINSCH)
active layeractive layer
waveguidewaveguide
6060ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
If the active region is thin enough, If the active region is thin enough, 10 nm10 nm
only few layers of atoms in the active only few layers of atoms in the active regionregion
quantum wellquantum well is formed is formed
The solution of the Schrödinger equation of The solution of the Schrödinger equation of quantum wells:quantum wells:
I.I. electron in a potential well in the electron in a potential well in the xx directiondirection
II.II. free electron gas solution in the free electron gas solution in the yzyz plane plane
m
kkE zy
2
222
k
6161ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
The solution of the 1D potential well The solution of the 1D potential well problem:problem:
xV
x2/w2/w
x2 x1 x3
6262ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
The solution of the 1D potential well problem:The solution of the 1D potential well problem:
the Schrthe Schröödinger equationdinger equation
2
2
2w
2
2
2
2
33032
2
222
2
11012
2
wxxExVx
xm
xw
xExxm
wxxExVx
xm
6363ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
the boundary conditions:the boundary conditions:
xV
x2/w2/w
22
22
21
21
wx
wx
ww
22
22
32
32
wx
wx
ww
6464ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
The solution of the differential equation The solution of the differential equation system:system:
xkbxkax cossin 222
xAx exp11
xAx exp33
EVm 02
mE
k2
withwith
andand
6565ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.0029 a.u.:For V0=1 a.u., w=40 a.u., E=0.0029 a.u.:
xkbxkax cossin 222
xAx exp11 xAx exp33
6666ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.0115 a.u.:For V0=1 a.u., w=40 a.u., E=0.0115 a.u.:
xAx exp11 xAx exp33
xkbxkax cossin 222
6767ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.0259 a.u.:For V0=1 a.u., w=40 a.u., E=0.0259 a.u.:
xAx exp11 xAx exp33
xkbxkax cossin 222
6868ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.0460 a.u.:For V0=1 a.u., w=40 a.u., E=0.0460 a.u.:
xAx exp11 xAx exp33
xkbxkax cossin 222
6969ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.0718 a.u.:For V0=1 a.u., w=40 a.u., E=0.0718 a.u.:
xAx exp11 xAx exp33
xkbxkax cossin 222
7070ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
For V0=1 a.u., w=40 a.u., E=0.1035 a.u.:For V0=1 a.u., w=40 a.u., E=0.1035 a.u.:
xAx exp11 xAx exp33
xkbxkax cossin 222
7171ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
k
The energy versus quasi momentum The energy versus quasi momentum function:function:
E
7272ESM Sofia 2009ESM Sofia 2009
Quantum well lasersQuantum well lasers
If the free electron gas is restricted to two or If the free electron gas is restricted to two or less dimensions, the density of states less dimensions, the density of states behaves different from the 3D casebehaves different from the 3D case
3D3D
jEEdEdN
Eg
E
Eg
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Quantum well lasersQuantum well lasers
If the free electron gas is restricted to two or If the free electron gas is restricted to two or less dimensions, the density of states less dimensions, the density of states behaves different from the 3D casebehaves different from the 3D case
2D2D
.constdEdN
ED
E
EDpositions adjustable positions adjustable via via d d (well thickness)(well thickness)
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Quantum well lasersQuantum well lasers
If the free electron gas is restricted to two or If the free electron gas is restricted to two or less dimensions, the density of states less dimensions, the density of states behaves different from the 3D casebehaves different from the 3D case
1D1D
jEEdE
dNE
1
E
E
positions adjustable positions adjustable via via d d (well thickness)(well thickness)
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Quantum well lasersQuantum well lasers
The absorption spectrum is also different for The absorption spectrum is also different for 2D electron systems from the bulk case:2D electron systems from the bulk case:
3D:3D:
2D:2D:the absorption spectrum is steplike with the absorption spectrum is steplike with resonances at the frequencies resonances at the frequencies corresponding to the energy differencescorresponding to the energy differences
better absorption spectrum, transparency.better absorption spectrum, transparency.
h
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Quantum well lasersQuantum well lasers
Usually a single quantum well (SQW) is too Usually a single quantum well (SQW) is too thin for confining the lightthin for confining the light
multiple quantum wells (MQW) with barrier multiple quantum wells (MQW) with barrier layers can be applied:layers can be applied:
x x
GRINSCHGRINSCHMQWMQW
SCH-MQWSCH-MQW
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Quantum well lasersQuantum well lasers
The quantum well lasers have higher The quantum well lasers have higher threshold than the bulk lasers, but they threshold than the bulk lasers, but they also have higher gain, better transparency.also have higher gain, better transparency.
Quantum wells based on GaAs perform well, Quantum wells based on GaAs perform well, low loss, high gainlow loss, high gain
Quantum wells based on InP have higher loss Quantum wells based on InP have higher loss (Auger recombination,…)(Auger recombination,…)a a strainstrain in the QW layers improves the in the QW layers improves the performance of QW InGaAsP lasersperformance of QW InGaAsP lasers
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Quantum well lasersQuantum well lasers
k
EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other electron, which other electron, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)
e.g. CCCH e.g. CCCH processprocess
C.B.C.B.
HH.B.HH.B.
LH.B.LH.B.SO.B.SO.B.
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Quantum well lasersQuantum well lasers
k
EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other hole, which other hole, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)
e.g. CHHL e.g. CHHL processprocess
C.B.C.B.
HH.B.HH.B.
LH.B.LH.B.SO.B.SO.B.
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Quantum well lasersQuantum well lasers
k
EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other hole, which other hole, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)
e.g. CHHS e.g. CHHS processprocess
C.B.C.B.
HH.B.HH.B.
LH.B.LH.B.SO.B.SO.B.
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Quantum well lasersQuantum well lasers
k
EQuantum wellsQuantum wells cause splitting in the cause splitting in the conduction band, lift conduction band, lift the degeneracy of the degeneracy of the heavy hole and the heavy hole and light hole bands, and light hole bands, and distort the shapedistort the shape
Similar effective Similar effective mass (curvature) means mass (curvature) means more effective more effective population inversion population inversion (smaller threshold)(smaller threshold) k
C.B.C.B.
HH1HH1
LH.B.LH.B.SO.B.SO.B.HH2HH2
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Quantum well lasersQuantum well lasers
k
EQuantum wells + Quantum wells + tensile straintensile strain lifts the lifts the light hole bandslight hole bands
TM mode TM mode
The split off band is The split off band is also depressed also depressed
less Auger less Auger recombination, recombination, higher carrier higher carrier density is possibledensity is possible
k
C.B.C.B.
HH1HH1
LH.B.LH.B.
SO.B.SO.B. HH2HH2
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Quantum well lasersQuantum well lasers
k
EQuantum wells + Quantum wells + compressive straincompressive strain depresses the light depresses the light hole bands, and hole bands, and further reduce the further reduce the heavy hole band’s heavy hole band’s curvaturecurvature
TE modulation TE modulation and further decrease and further decrease in threshold levelin threshold level
k
C.B.C.B.
HH1HH1
LH.B.LH.B.SO.B.SO.B.
HH2HH2
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VCSELsVCSELs
The high gain of quantum wells make The high gain of quantum wells make possible to place the resonator above and possible to place the resonator above and under the active region:under the active region:
Bragg Bragg reflectorsreflectors(multiple) (multiple) quantum well quantum well structurestructure
electrodeselectrodes
apertureaperture
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VCSELsVCSELs
The confinement of population inversion in The confinement of population inversion in the the yy and and zz dimensions is necessary dimensions is necessary
aperture usually at aperture usually at the bottomthe bottom
n n DBRDBR
p p DBRDBR
etched mesa/air post etched mesa/air post VCSELVCSEL
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VCSELsVCSELs
The confinement of population inversion in The confinement of population inversion in the the yy and and zz dimensions is necessary dimensions is necessary
the etched regions the etched regions are regrown are regrown epitaxiallyepitaxially
(e.g., high index nipi (e.g., high index nipi layers – passive layers – passive antiguide region)antiguide region)
n n DBRDBR
p p DBRDBR
buried regrowth buried regrowth VCSELsVCSELs
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VCSELsVCSELs
Since the reflectors are grown upon the diode Since the reflectors are grown upon the diode structurestructure
the resonator length is much shorter than the resonator length is much shorter than the edge emitting lasers’ cavity (less modes)the edge emitting lasers’ cavity (less modes)
the properties of the reflectors can be the properties of the reflectors can be monitored during the growthmonitored during the growth
very good reflectance can be very good reflectance can be producedproduced
it is easier to couple the VCSEL’s light into it is easier to couple the VCSEL’s light into an optical fiberan optical fiber
laser arrays can be producedlaser arrays can be produced
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Erbium doped fibersErbium doped fibers
The 4f (5f) orbitals of the The 4f (5f) orbitals of the rare earth metalsrare earth metals are special:are special:
the electronic structure is [Xe]4fthe electronic structure is [Xe]4fNN−1−15d5d116s6s22 or [Xe]4for [Xe]4fNN6s6s22
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Erbium doped fibersErbium doped fibers
K Ca Sc
Fr
Ti V Cr Mn Fe Co Mi Cu Zn Ga Ge As Se Br Kr
Rb Sr Y
Ra
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
Cs Ba La
Ac
Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
B C N O F Ne
Al Si P S Cl Ar
Li Be
Na Mg
H He1.
2.
3.
4.
5.
6.
7.
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Erbium doped fibersErbium doped fibers
The 4f (5f) orbitals of the The 4f (5f) orbitals of the rare earth metalsrare earth metals are special:are special:
the electronic structure is [Xe]4fthe electronic structure is [Xe]4fNN−1−15d5d116s6s22 or [Xe]4for [Xe]4fNN6s6s22
they are usually 3+ ionsthey are usually 3+ ions
5s5s225p5p6 6 orbitals have larger radius, than the orbitals have larger radius, than the 4f4f
isolating “sphere”isolating “sphere” atom-atom-like behaviorlike behavior
energy spectrum of very narrow bands if energy spectrum of very narrow bands if insulator is doped by lantanoidsinsulator is doped by lantanoids
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Erbium doped fibersErbium doped fibers
The 4f orbitals of the The 4f orbitals of the rare earth metalsrare earth metals is is split by atomic forces and the crystalline split by atomic forces and the crystalline field field
4f4fNN
spin-orbit spin-orbit coupling, etc.coupling, etc.
Stark Stark splittingsplitting
22SS+1+1LLJJ
degeneracydegeneracy
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Erbium doped fibersErbium doped fibers
The The 44II13/213/2↔↔44II15/215/2(GS) transition in Er(GS) transition in Er3+3+ ions ions belong to photons of wavelength ~1.5 belong to photons of wavelength ~1.5 mm
two main pump regions: 1480 nm and 980 two main pump regions: 1480 nm and 980 nm with significant absorptionnm with significant absorption
large gap between the two lowest level large gap between the two lowest level 44II13/2 13/2 and and 44II11/211/2 large lifetime of the large lifetime of the 44II13/2 13/2 (~10 ms, depending on hosts), mostly (~10 ms, depending on hosts), mostly radiative transitionradiative transition
three-level systemthree-level system
concentration quenchingconcentration quenching shorter shorter lifetimelifetime
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Erbium doped fibersErbium doped fibers
The The 44II13/213/2↔↔44II15/215/2(GS) transition in Er(GS) transition in Er3+3+ ions ions belong to photons of wavelength ~1.5 belong to photons of wavelength ~1.5 mm
1531 nm1480 nm980 nm
44II13/213/2
44II15/215/2
44II11/211/2
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Fiber Optic Handbook, Fiber, Devices, and Systems for Optical Fiber Optic Handbook, Fiber, Devices, and Systems for Optical Communications,Communications,editor: M. Bass, (associate editor: E. W. Van Stryland)editor: M. Bass, (associate editor: E. W. Van Stryland)McGraw-Hill, New York, 2002.McGraw-Hill, New York, 2002.
P. C. Becker, N. A. Olsson, and J. R. Simpson,P. C. Becker, N. A. Olsson, and J. R. Simpson,Erbium-Doped Fiber Amplifiers, Fundamentals and Technology,Erbium-Doped Fiber Amplifiers, Fundamentals and Technology,Academic Press, San Diego, 1999.Academic Press, San Diego, 1999.
J. Singh,J. Singh,Semiconductor Optoelectronics, Physics and Technology,Semiconductor Optoelectronics, Physics and Technology,McGraw-Hill, New York, 1995.McGraw-Hill, New York, 1995.
J. Singh,J. Singh,Optoelectronics, An Introduction to Materials and Devices, Optoelectronics, An Introduction to Materials and Devices, McGraw-Hill, New York, 1996.McGraw-Hill, New York, 1996.
9595ESM Sofia 2009ESM Sofia 2009
J. Hecht,J. Hecht,Understanding fiber Optics (fifth edition),Understanding fiber Optics (fifth edition),Pearson Prentice Hall, Upper Saddle River, New Jersey, Pearson Prentice Hall, Upper Saddle River, New Jersey, Columbus, OhioColumbus, Ohio,, 2006 2006..
C. R. Pollock,C. R. Pollock,Fundamentals of OptoelectronicsFundamentals of OptoelectronicsIrwin, Chicago, 1995.Irwin, Chicago, 1995.
J. L. Miller, and E. Friedman,J. L. Miller, and E. Friedman,Photonics Rules of Thumb, Optics, Electro-Optics, Fiber Optics, Photonics Rules of Thumb, Optics, Electro-Optics, Fiber Optics, and Lasers, and Lasers, McGraw-Hill, New York, 1996.McGraw-Hill, New York, 1996.