Tunable semiconductor lasers - University of Houstoncourses.egr.uh.edu/ECE/ECE6323/Class...

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


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


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


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


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.


• 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


OutlineOutline



3. Tunable laser fundamentals

4. Technologies of tunable lasers

5. Conclusion


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


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth

GL∆ν∆ν∆ν∆ν =c/2 µ gL

ννννo


µLmcm 2/=νLoop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


Loop gain

Gain curve

Laserthreshold

Longitudinalmodes

Laser output power

Frequency (v)

Linewidth


ννννo


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


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


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)


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:


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:


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


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.


OutlineOutline





5. Conclusion


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)


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


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


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


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.


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.


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


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


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


OutlineOutline





5. Proposed research and summary


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


- 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


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)


Peng et al., Appl. Optics (8/20/03)

Ammonia

Tuning performance of tunable MidTuning performance of tunable Mid--IR lasersIR lasers


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


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)


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.


Thank you !Thank you !


Additional readingsAdditional readingsAdditional readingsAdditional readings


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


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


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


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


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


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


)( 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)


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:


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.


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:


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.


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.


• 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.


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:


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


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



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:



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.


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)


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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