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Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Tunable semiconductor lasers
Thesis qualifying exam presentation by
Chuan Peng
B.S. Optoelectronics, Sichuan University(1994)M.S. Physics, University of Houston(2001)M.S. Physics, University of Houston(2001)
Thesis adviser: Dr. Han Le
Submitted to the Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the
Doctor of PhilosophyAt the
University of HoustonOct. 2003
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
1. Introduction and motivation
2. Semiconductor laser physics
3.Tunable laser fundamentals
OutlineOutline
3.Tunable laser fundamentals
4. Technologies for tunable lasers
5. Summary and Conclusion
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Milestones: • 1917 Origin of laser can be traced back to Einstein's treatment of
stimulated emission and Planck’s description of the quantum.
• 1951 Development of the maser by C.H. Townes.
• 1958 Laser was proposed by C.H. Townes and A.L. Schawlow
Introduction: Laser HistoryIntroduction: Laser History
• 1958 Laser was proposed by C.H. Townes and A.L. Schawlow
• 1960 T.H. Maiman at Hughes Laboratories reports the first laser: the
pulsed ruby laser.
• 1961 The first continuous wave laser was reported (the helium neon
laser).
• 1962 First semiconductor laser
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Introduction: Laser types and applicationsIntroduction: Laser types and applications
Compact diskLaser printer Optical disc drives Optical computer Bar code scanner Holograms against forgery Fiber optic communications Free space communications Laser shows Holograms
Common Daily Applications
Scientific Applications
Surgery:•Eyes
Basic Scientific ResearchSpectroscopy Nuclear Fusion Cooling Atoms Short Pulses
Gas Lasers
Liquid Lasers
Free Electron laser (FEL)
X-ray lasersRuby
Nd:YAG
Ti-Sphire
Alexandrite
Semiconductor lasers
NAsSbLead-salt
30µµµµm 10µµµµm 3µµµµm 1µµµµm 300nm 100nm 30nm 10nm
λλλλEnergy
InfaredFar infared Visible Ultraviolet Soft x-rays
Holograms Kinetic sculptures
Military Applications
Medical Applications
Industrial ApplicationsSpecial
Applications
Laser range-finderTarget designationLaser weapons Laser blinding
•Eyes•General•Dentistry•Dermatology
Diagnostic fluorescenceSoft lasers
MeasurementsStraight Lines Material Processing Spectral Analysis
Energy Transport Laser Gyroscope Fiber Lasers
He-Ne
He-NeHe-Cd
CO2
N2HFFIR lasers
Ar+Kr+
Cu vapor
Ag (Gold) vapor
Organic Dye
Liquid Lasers
Special Lasers
Solid Lasers
Alexandrite
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Introduction: Semiconductor LaserIntroduction: Semiconductor Laser
• Small physical size• Electrical pumping • High efficiency in converting electric power to light • High speed direct modulation (high-data-rate optical communication systems)
What made the semiconductor lasers the most popular light sources ?
systems) • Possibility of monolithic integration with electronic and optical components to form OEICs (optoelectronic integrated circuits)• Optical fiber compatibility• Mass production using the mature semiconductor-based manufacturing technology.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
• Spectroscopy- Single frequency mode, tunable
• Environmental sensing and pollution monitoring- Lidar- Requires Ruggedness, Correct Wavelength
• Industrial Process Monitoring
MotivationsMotivations
Application interests in tunable mid-IR semiconductor lasers:
• Industrial Process Monitoring- Requirements similar to Environmental Monitoring
• Medical Diagnostics- Breath analysis; Non-invasive Glucose monitoring, Cancer Detection, etc.
• Military and law enforcement • Optical communication
A key requirement:A key requirement:Broad, continuous wavelength tunabilityBroad, continuous wavelength tunability
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
OutlineOutline
1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Conclusion
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Laser physicsLaser physics
G, αi
L
MirrorActive medium
Laser output
Partially transmitting mirror
R2R1
G, αi
L
MirrorActive medium
Laser output
Partially transmitting mirror
R2R1
1)(~
22/121 =LieRR β
Oscillation condition is reached when
L mirrorL mirror
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν =c/2 µ gL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
µLmcm 2/=νLoop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν =c/2 µ gL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν=c/2nL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
Loop gain
Gain curve
Laserthreshold
Longitudinalmodes
Laser output power
Frequency (v)
Linewidth
GL∆ν∆ν∆ν∆ν =c/2 µ gL
ννννo
ννννm-1ννννm-2 νννν ννννm+1ννννm+2
µLmcm 2/=ν µLmcm 2/=ν
====−
,..)3,2,1(,22
1)(
0
)(2/121
mmLk
eRR Lg i
πµ
αReal part: Threshold condition
Imaginary part: wavelength condition
2/0
~
αµβ ik −=
|1
|ln2
1
21RRLg ith += α
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor laser physicsSemiconductor laser physics
• Threshold: carrier density, cavity loss
• Wavelength: bandgap physics, or intraband energy level (QC)
• Tunability: gain bandwidth:
for interband D.H. and quantum well laser: Fermi Distributionfor interband D.H. and quantum well laser: Fermi Distribution
for quantum cascade laser: energy level linewidth
• Power and efficiency
• Operating temperature
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor laser band diagramSemiconductor laser band diagram
N-GaAlAs P-AlGaAsp-GaAs
∆∆∆∆Ec
Ev
Ec
Ef
(a) Equilibrium band structure
-1
0
1
2
3
Ene
rgy
(eV
)
Probability of occupancy
f(E)
E F
n(E)
p(E)
ρc (E)
ρv (E)
Energy band diagrams for a double hetero-structure laser (a) unbiased, (b) forward biased
N-GaAlAs P-AlGaAs
∆∆∆∆Ec Ec
Efv
Ev
Ec
Efc
(b) Forward biased
∫
∫
+−=
+−=
vFVv
vv
cFCc
cc
dEKTEE
Ep
dEKTEE
En
1]/)exp[(
)(
1]/)exp[(
)(
ρ
ρCarrier concentration in each band:
-2
0.0E+00 1.0E+21 2.0E+21 3.0E+21 4.0E+21
Density (cm-3eV-1)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Threshold current densityThreshold current density
Carrier density rate equation:
nrA nonradiative process 2Bn
)()( 2 nRqd
JnD
t
n −+∇=∂∂
At steady state, 0=∂∂
t
n
phstnr NRCnBnnAnR
qd
JnR
+++=
=
32)(
)(
)()(
n
nnR
eτ=
)( the
thth n
qdnJ
τ=
Rst stimulated recombination that leads to emission of light and it is proportional to the photon density Nph.
2Bn spontaneous radiative rate 3Cn nonradiative Auger recombination
Below or near threshold:
So, the threshold current density is
So:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Power and efficiency of semiconductor lasersPower and efficiency of semiconductor lasers
phthgth NgqdvJJ +=
If the current is above threshold, this leads to stimulated emission
Optical output power P vs. injection current is determined by
)( thim
miphmgout II
q
hhVNvP −
+==
αααηννα
Optical output power Pout vs. injection current is determined by
)/1ln(
)/1ln(
/
/
RL
R
q
dIdP
iii
im
moute +
=+
==α
ηηαα
αω
ηh
External quantum efficiency is defined as:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Quantum Well lasersQuantum Well lasers
)(2
),,( 22*
2
yxn
nyx kkm
EkknE ++= h
Energy eigenvalues for a particle confined in the quantum well are:
Intersubband transition QC
Inerband transition
Quantum wells are important in semiconductor lasers because they allow some degree of freedom in the design of the emitted wavelength through adjustment of the energy levels within the well by careful consideration of the well width.
z
cici L
m2
hπρ =>>>
Density of states:
2/12/32
)2
(4)( Eh
mE c
c πρ =
Compare with Heterostructure:
Inerband transition
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Advantages:
• It doesn’t depends on material
system bandgap making it easy to
make long wavelength lasers.
• In a QCL, each electron can take
Quantum cascade lasersQuantum cascade lasers
23 EE −=ωh
• In a QCL, each electron can take
participate in stimulated emission
many times.
• QC lasers in mid-IR region have
now been demonstrated with CW
operations at room temperature.
• It could be used as THz sources.
Quantum cascade laser is unipolar intersubband device
The QC laser relies on only one type of carrier, making electronic transition between conduction band states arising from size quantization.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
OutlineOutline
1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Conclusion
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Existing Tunable Laser technologiesExisting Tunable Laser technologies
•Distributed Feedback Bragg Grating (DFB)
•Sampled grating Distributed Bragg Reflectors (DBR)
•MEM-VCSEL
•Grating coupled external cavity (ECLD)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Existing Tunable Laser Structures (DFB)Existing Tunable Laser Structures (DFB)
DFB laser structure. The grating is etched onto one of the cladding layers. Grating
Cross section
4.420 4.440 4.460 4.480 4.500 4.520wavelength (um)
Inte
nsity
4.420 4.440 4.460 4.480 4.500 4.520
wavelength (um)
Inte
nsity
Wavelength (um)
DFB laser structure. The grating is etched onto one of the cladding layers. Grating period is determined by ΛΛΛΛ=mλλλλ/2. λλλλ is the wavelength inside the medium.
Tunable DFB laser arrays (a) Serial (b) Parallel (c) Mem mirror
QDI Fujitsu Santur
Wire bond
DFB Array MEMs tilt
mirror
Optical fiber
Laser stripes
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Existing Tunable Laser Structures (DBR)Existing Tunable Laser Structures (DBR)
EAM Amplifier Front mirror Gain Phase Rear mirror
SG-DBR laser
MQW active region Q waveguide
Light output
Agility
λB
λ
RFP(λ)
λ
R1(λ)
λ
R2(λ)
λ
R(λ)
� Fabry-Perot cavity: • Modes with FP spacing
� Sampled Bragg Reflectors:• Spectra with wider spacing and broader profile • Filters out 1 Bragg mode• Increasing Idbr shifts filter profile to shorter λ� Phase Section: Fine tuning Lasing mode
Rear mirror
Front mirror
Longitudinal modes
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Existing Tunable Laser Structures (MemExisting Tunable Laser Structures (Mem--VCSEL)VCSEL)
• MEM-VCSEL
Active region
OutputTop curved mirror
Membranepost
Schematic of micromechanically tunable VCSEL from Coretek / Nortel Networks.The upper membrane is moved electrostically to modify the cavity length and tune the lasing wavelength of the vertical cavity laser.
Bottom mirrorPump injection
Substrate
Coretek
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Existing Tunable Laser Structures (ECLD)Existing Tunable Laser Structures (ECLD)
Schematic representations of the Littman Cavities.of the Littman Cavities.
Photograph and schematic of Iolon’s MEMs based external cavity laser configuration.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Grating coupled external cavity tunable laser fundamentalsGrating coupled external cavity tunable laser fundamentals
Collimating lens
λλλλ1
λλλλ2
Outputλλλλ1 λλλλ2 λλλλ3
Blazed grating
θθθθ
λλλλ
Collimating lens
λλλλ1
λλλλ2
Outputλλλλ1 λλλλ2 λλλλ3
Blazed grating
θθθθ
λλλλ
Example
1st orderFeed back
Laser chipλλλλ3
λλλλ2λλλλ1 λλλλ2 λλλλ3..
Zeroth order output2dsinθθθθ = mλλλλ
θθθθ
Grating equation:
d
1st orderFeed back
Laser chipλλλλ3
λλλλ2λλλλ1 λλλλ2 λλλλ3..
Zeroth order output2dsinθθθθ = mλλλλ
θθθθ
Grating equation:
d
Grating coupled external cavity tunable laser struc ture.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
External cavity laser modelingExternal cavity laser modeling
λλλλS4
(+)(-)n−= 1
r−=
2n+
=t m +n−= 1
r−= n−= 1
r−=
2n+
=t m +2n+
=t m +
−
−=
mm
m
m
p
m
pmp
tt
rt
r
t
rrt
S
11
1
1
1
1
111
11
−
−=
mm
m
m
p
m
pmp
tt
rt
r
t
rrt
S
22
2
2
2
2
222
13
= − lik
lik
sem
sem
e
eS
0
02
1st order Feed back
Laser chip
λλλλ1
λλλλ3
λλλλ2
S1
S4
S5
S6
S3S2n
1
2+
=n
t p +
1n
+=
n
1r
+=
p
11
+−=
n
nr
+−=
m
1+=
nt m +
n
1
2+
=n
t p +1
2+
=n
t p +
1n
+=
n
1r
+=
p 1n
+=
n
1r
+=
p
11
+−=
n
nr
+−=
m 11
+−=
n
nr
+−=
m
1+=
nt m +1+
=n
t m +
= − Lik
Lik
air
air
e
eS
0
04
−
−=
GmGm
Gm
Gm
Gp
Gm
GpGmGp
tt
rt
r
t
rrt
S1
5
=
closs
clossS 1
0
06
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Grating coupled external cavity tunable LaserGrating coupled external cavity tunable Laser
An example: Cavity mode loss curve with longitudina l modes.
Cav
ity m
ode
loss
(cm
-1)
20
25
Laser oscillation condition
pefft
illg
rree semith
1
2)( 1=− βα
|1
|ln1
1peffth rrl
g +=α
πφβ ml sem 22 =+
φieffeff err ||=
Frequency (THz)
Cav
ity m
ode
loss
(cm
5
10
15
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Fujitsu*, Santur, QDI , Princeton Lightwave, < 5 nm40 mW*DFB
Agility*(SGDBR), Bookham(Marconi)(DSDBR) ,NTT/NEL(SSGDBR), Multiplex, Intel(Sparkolor), (Altitun(GCSRDBR)),
> 40 nm30 mW*DBR
CompaniesTuning range
PowerLaser type
DFBAdvantages:• Cost comparable to fixed lasers• High power• Wavelength stability
External cavity lasersAdvantages:• Wide tuning range• High output power• High spectral purity• Low RIN• Continuous tuning
MEM VCSELAdvantages:Low costLow power consumptionGood mode stabilityWide tuning rangeWafer level testing
DBRAdvantages:Wide tuning range Fast switching speedGood side mode suppressionModerate output powerLow power consumption
Current tunable laser developmentCurrent tunable laser development
Intel(new focus)*, Iolon, Blue Sky Research, Princeton Optronics,
>100 nm30 mW*External cavity
Bandwith9*, Novalux, Beamexpress, (Coretek) ~ 40 nm<2 mW*VCSEL
Fujitsu*, Santur, QDI , Princeton Lightwave, Excelight, Alcatel, Intel, Nortel,Triquint(Agere), JDSU, , etc.
< 5 nmper λ
40 mW*DFB • Proven technologyDisadvantages:• Limited tuning range (5nm per laser)• Slow tuning speed (~ few ms)• Reproducibility in manufacturing
• Continuous tuning• Plug-in module for different wavelengthDisadvantages:• High cost• Bulky• Slow switching• Shock/vibration sensitivity
Wafer level testingDisadvantages:Low output powerSlow switching1550 nm technology still in development
Low power consumptionIntegrated functions (Modulators, optical amplifiers)Disadvantages:YieldWavelength stabilityRelatively broad linewidthComplex softwarePower
Companies in brackets no longer exist, but honorable
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
OutlineOutline
1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Proposed research and summary
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Theoretical calculations and modeling in order to g et single mode and continuous long tuning rangeDesign and construct the E.C. laser testing apparat us and programsPerform testing to qualify lasers for more in depth testing
Key points of the Proposed ResearchKey points of the Proposed Research
Perform testing to qualify lasers for more in depth testing
Laser spectroscopy of some real samplesDesign compact and robust EC laser source
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
- For basic research, breadboard systems
- Study of basic properties: thermo-optic behavior, gain property, power, efficiency, noise model developed
- Overcome challenges: λλλλ-scaling issue, facet coating problem, non-optimum optics
- Single-mode or nearly so (pulse operation),
Recent performance of tunable MidRecent performance of tunable Mid--IR lasersIR lasers
- Single-mode or nearly so (pulse operation), 7-12-dB side mode suppression ratio
- Linewidth dominated by thermo-optics (~500 MHz; theoretical model projects near transform-limited for < 20-ns pulse)
- Wavelength bands: 4.6, 5.2, 7.1, 9 µµµµm- Tuning range ~ 2-2.5% of center wavelength, limited by the gain band
- Power ~1 – 40 mW peak (up to 5% d.c.)
- Turn-key, high stability
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Thermal fine phase control of tunable laserThermal fine phase control of tunable laser
- Substantial thermal-induced phase tuning and grating tuning provide continuous and broad tuning even without AR coating
Use the coupled-cavity effect to advantage
Peng et al., Appl. Optics (8/20/03)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Peng et al., Appl. Optics (8/20/03)
Ammonia
Tuning performance of tunable MidTuning performance of tunable Mid--IR lasersIR lasers
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Phase tuning is needed: 2-segment laser
• Use only thermo-optic effect
• No need of specialized phase-segment in monolithic device
• A key test of the miniature module design
Approach for miniature tunable moduleApproach for miniature tunable module
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 1000 2000 3000 4000
Time (ns)
Cur
rent
(A
)
Phase: Gain 50ns:
∆∆∆∆tVariable
I phase
T=1 µµµµs
0.1
1
10
100
0 2 4 6 8 10 12 14 16 18 20Delay (µµµµs)
∆∆ ∆∆f(G
Hz)
Iphase=800mA, 600mA, 400mA, 300mA, 200mA
Thermal decay time ~ 3 µs
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
0.4
0.6
0.2
0.8
1.0
288 GHz
0.0
CO gas absorption spectroscopyCO gas absorption spectroscopy
4.86 4.87 4.88 4.89 4.900.0
Wavelength ( µµµµm)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Summary and ConclusionSummary and Conclusion
• Various types of semiconductor lasers were investigated and studied.
• Most common used tunable laser structures were introduced and evaluated. One example of tuning principle introduced and evaluated. One example of tuning principle was explained.
• Dissertation research topics will be novel mid-IR tunable semiconductor laser concept and demonstration.
• Research strategy and recent results were presented.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Thank you !Thank you !
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Additional readingsAdditional readingsAdditional readingsAdditional readings
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser Physics: Semiconductor Laser Physics: Density of states calculationDensity of states calculation
dE
dkk
L
dE
dk
dk
dN
dE
dN 23)( ××== ππ
Where
2/12/322
2/12/3223
2
)2
(1
)2
(1
)2(
4)2(
Em
Em
dE
dkk
vv
cc
h
h
πρ
πππρ
=
==
33
3
4)(
8
12 k
LN ×××××= π
π
dE
dkk
dE
dkk
dE
dN
LE
2
2
3
2
3 )2(
42
1)(
πππρ ===
Where
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
1EE
fc −=
Semiconductor Laser Physics:Semiconductor Laser Physics:Occupation factors for both bands Occupation factors for both bands
Occupation factor for each band by Fermi-Dirac distribution function
)exp(1
1
)exp(1
KT
EEf
KT
EEf
FVvv
FCcc
−+=
−+=
Probability of occupancy versus energy of the Fermi-Dirac, the Bose-Einstein and the Maxwell-Boltzmann distribution
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser Physics:Semiconductor Laser Physics:Carrier concentration calculationCarrier concentration calculation
Electron concentration n and hole concentration p are given by
∫
∫
+−=
+−=
vvv
vv
ccc
cc
dEKTFE
Ep
dEKTFE
En
1]/)exp[(
)(
1]/)exp[(
)(
ρ
ρ
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser Physics: Semiconductor Laser Physics: Fermi energy and occupation factor calculationFermi energy and occupation factor calculation
∫∫ +−=
+−= v
vv
vvc
cc
cc dEKTFE
EpdE
KTFE
En
1]/)exp[(
)(,
1]/)exp[(
)( ρρ
Fermi energy, occupation probability can be approxi mately derived from above equations, which is often referred as Bo ltzmann from above equations, which is often referred as Bo ltzmann approximation.
)ln(C
FC N
nKTE =
)exp()(KT
E
N
nEf
Cc
−≅
2/32)/2(2 hKTmN cC π=
For valence band:
)ln(V
FV N
pKTE =
)exp()(KT
E
N
pEf
Vv
−≅
For conduction band:
where
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser Physics: Semiconductor Laser Physics: Stimulated emission rate and gain calculationStimulated emission rate and gain calculation
Net stimulated emission rate per unit volume per unit energy interval at photon energy hνννν:
Bernard and Duraffourg condition for stimulated emission
cc
vvccvcccstim dEffhEEVhEBhPhR 1
21 )1)()(()(),()()( −+∞
∞−
+−−= ∫ ρρνρρννν
interval at photon energy hνννν:
)exp()exp(kT
EE
kT
EhE FCcFVc −>−− ν νhEE FVFC >−Or
cc
vvccvccc
ggstim dEffhEEVEB
ccRhg 1)1)()(()()()()( −
+∞
∞−
+−−Γ
=Γ= ∫ ρρνρρ
µµν
Gain per unit length can be derived as
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Quantum well lasersQuantum well lasers
Another innovation, now nearly ubiquitous, was the use of a Quantum Well (QW) active region where the gain region thickness is reduced until Vgain region thickness is reduced until the electronic states are quantised in one dimension. The quantisation allows the density of states to be engineered, and the tiny active volume reduces greatly the injection current required to achieve transparency.
V
z
Lz 0
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
)( 222
kkE += h
Along the x, y direction, the energy levels form a continuum of states given by
V
Quantum well lasers: Quantum well lasers: Energy levels calculations by Schrodinger equationEnergy levels calculations by Schrodinger equation
)(2
22yx kk
mE +=
The energy levels in z direction can be solved by Schrodinger equation for one dimensional potential well:
z
Lz0
ψψψ
ψψ
Vdz
d
mE
dz
d
mE
+−=
−=
2
22
2
22
2
2
h
h inside the well(0<z<Lz)
outside the well(z>Lz, z<0)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Boundary conditions are that ψ and dψ/dz are continuum at z=0 and z=Lz, The solution is:
≤≤+≤
=zzkA 0)exp( 1
δψ2/1
21 ])(2
[EVm
k−=
Quantum well lasers:Quantum well lasers:Solution in finite quantum wellSolution in finite quantum well
≥−≤≤+=
z
z
LzzkC
LzzkB
)exp(
0)sin(
1
2 δψ2/1
22
21
)2
(
][
h
h
mEk
k
=
=where
212 /)tan( kkLk z =The eigenvalue equation is:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Conduction band
E3c
E2c
∆∆∆∆Ec
Conduction band
E3c
E2c
∆∆∆∆Ec
)(2
),,( 22*
2
yxn
nyx kkm
EkknE ++= h
Energy eigenvalues for a particle confined in the quantum well are:
Quantum well lasers:Quantum well lasers:Energy quantization in quantum wellEnergy quantization in quantum well
Valenceband
E1hh
E2hh
E3hh
E1lh
E2lh
E1c
∆∆∆∆Ev
Eg ����ωωωω=Eg+E1c+E1hh
����ωωωω
LzValenceband
E1hh
E2hh
E3hh
E1lh
E2lh
E1c
∆∆∆∆Ev
Eg ����ωωωω=Eg+E1c+E1hh
����ωωωω
Lz
The confined energy levels En are denoted by E1c, E2c, E3c, for electrons, … heavy holes and light holes. They can be calculated by the solution above.
En is the nth confined particle energy level for carrier motion normal to the well and m* is the effective mass for this level.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Density of states: The number of electron states per unit area in the x-y plane for the ith subband, within an energy interval dE is given by:
22
2
2
2,
)2(2)(
h
π cii
m
m
kE
kddEED
=>>>
==
Quantum well lasers:Quantum well lasers:Density of sates calculationDensity of sates calculation
z
ci
z
ici L
m
L
D2
hπρ ==>>>
2hπ
cii
mD =>>>
2/12/32
)2
(4)( Eh
mE c
c πρ =Compare with Heterostructure:
Density of states per unit volume:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Calculated number of electrons in the conduction band
iici E
ci dEEfnio
)(∑ ∫∞
= ρ
Quantum well lasersQuantum well lasersCarrier concentration calculationCarrier concentration calculation
where]/)exp[(1
1)(
TkEEEf
Bfciic −+
=
)exp()]exp(1ln[Tk
EN
Tk
EETkn
B
fcc
B
iofc
iciB =
−+= ∑ ρ
TkN Bcic ρ=
It is easy to obtain
where
Similar solutions hold for holes in the valence ban d.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
104
105
106
120K 140K 160K 180K
Electrical properties of semiconductor lasersElectrical properties of semiconductor lasersCarrier density derivation from photoluminanceCarrier density derivation from photoluminance
wde
R
dzewdRL
LGspon
L
z
zGsponF
n
n
]1
)[(
)()(
)(
0
)(
ωω
ωωω
ω
ω
hh
hhh
h
h
−=
= ∫=
The light spectrum taken from facet is the amplified spontaneous emission,
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.6010-4
10-3
10-2
10-1
100
101
102
103
10
CO2 Absorption
180K 200K 220K 240K
Inte
nsity
Energy (eV)
Threshold photoluminescence spectra at different temperatures. Experimental data are shown in square symbols. Solid lines show the calculations.
wdG
eR
n
spon ])(
1)[(
ωωω
hhh
−=
ingG αω −Γ=)(hwhere is net gain.
By fitting the gain curve of the device, the carrier density can be derived at different current. The threshold carrier density will increase with increasing temperature.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
• Temperature dependence of threshold current )/exp( 00 TTII th =T0 is characteristic temperature. A lower T0 value implies that the threshold current increases more rapidly with increasing temperature.
• Temperature dependence of carrier lifetimeIt decreases with increasing temperature.
ththth qdnJ τ/=
Temperature dependence of electrical properties of Temperature dependence of electrical properties of semiconductor laserssemiconductor lasers
• Leakage current
Caused by diffusion and drift of electrons and holes from the edges of the active region to the cladding layers.
It is higher at higher temperatureIt increases when the barrier height decreases.It increases with the decreases in cladding layer doping.
• Temperature dependence of optical gain
It increases with increasing temperature.
• Temperature dependence of differential quantum effi ciency
It decreases with increasing temperature.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Optical properties of semiconductor lasers: Optical properties of semiconductor lasers: Gaussian beam profileGaussian beam profile
The expression for a real laser beam’s electric field is given by:
])(2)(
exp[)(
)](exp[),,(
22
2
22
zR
yxik
zw
yx
zw
ziikzzyxE
+−+−−−∝ ψ
)/arctan()(
/)(
)/(1)(2
20
R
R
R
zzz
zzzzR
zzwzw
=+=
+=
ψ
Expression for spot size, radius of curvature, and phase shift:
Where ZR is the Rayleigh Range, it is given by
λπ /20wzR =
The beam divergence half angle is given by
0
00/1
)(
wz
w
zz
zw
z
zw
RRe π
λθ ====
field is given by:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Optical properties of semiconductor lasers: AstigmatismOptical properties of semiconductor lasers: Astigmatism
L>wθθθθL< θθθθw
w
θθθθL
θθθθw
λλλλ/l λλλλ/w
w l
λλλλ/w λλλλ/L
L W
An edge emitting laser has astigmatism, the divergent angles are: L
w
L
w
πλθ
πλθ
=
=
L
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser gain dynamicsSemiconductor Laser gain dynamics
pggain
i gNvN
eV
I
dt
dN −−=τ
η
Consider two coupled aspects. We therefore consider two simple “rate equations” – first order differential equations that are coupled to one another.
Number of carriers added per unit volume per unit time
Number of undesired carrier recombination per unit volume per unit timegain
p
ppg
p NgNv
dt
dN
τ−Γ=
0000 pg
gain
i gNvN
eV
I −−=τ
η
p
popog
NNgv
τ−Γ= 00
At steady state, the carrier and photon density are stable, so
per unit volume per unit time
Number of stimulated carrier recombination per unit volume per unit time
Number of photons added per unit cavity volume per unit time
Number of photons lost from the cavity per unit cavity volume per unit time
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser gain dynamicsSemiconductor Laser gain dynamics
Suppose there is small variation at steady condition.
NaNvNN
eV
I
dt
Ndpog
p
p
gain
i δτ
δτ
δδηδ −Γ
−−=
NaNvNd p δ
δΓ= NaNv
dt pogp δΓ=
dt
Id
eVN
aNv
dt
NdaNv
dt
Nd
gain
i
p
pogpog
δηδτ
δτ
δ =+++ )()1
(2
2
Solving them:
p
pogR
aNv
τω =Relaxation oscillation frequency:
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Semiconductor Laser gain dynamicsSemiconductor Laser gain dynamics
General form of the frequency response
)1
(1
1
)0(
)(
2
2
pRRRR
iP
P
τωτωω
ωωωδ
ωδ
++−=
Note that 1. there is an intrinsic limit to
the modulation speed 2. the modulation speed tend
to rise with the square root of the differential gain,
3. the modulation speed tends to rise as the square root of the laser output power.
Frequency response of the output powermodulation of a laser diode as the frequency of electrical drive is increased.
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Noise arises from the spontaneous emission process and carrier-generation-recombination process, can be modeled by adding Langevin noise source.
Noise properties of semiconductor lasersNoise properties of semiconductor lasers
Modified rate equations with added noise
)()(2
1)(
)(/
)()(
0 tFG
tFGPNqIN
tFRPGP
cth
Ne
psp
φγβωωφ
γ
γ
+−+−−=
+−−=
++−=
•
•
•
Fp and Fφ are from spontaneous emission, FN has its origin in the discrete nature of carrier generation and recombination processes (shot noise)
Photonic Device and System LaboratoriesDepartment of Electrical and Computer Engineering
Intensity noise, RIN
RIN decreases with increasing power (P3>P2>P1). It shows maximum at the relaxation-oscillation peak.
Phase noise
Electrical and optical properties of semiconductor lasersElectrical and optical properties of semiconductor lasers
RIN
(d
B/H
z)
P1
P2
P3
RIN
(d
B/H
z)
P1
P2
P3
Phase noise
Phase fluctuation comes from spontaneous emission, change in optical gain and refractive index induced by carrier population, linewidth enhancement factor (huge for semiconductor laser).
)1(4
2c
sp
P
Rβ
πδν +=
Frequancy (GHz)R
IN (
dB
/Hz)
Frequancy (GHz)R
IN (
dB
/Hz)
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