[PPT] - Tunable semiconductor lasers Thesis qualifying exam presentation by PowerPoint Presentation

SLIDE 1

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 Philosophy At the University of Houston

Oct. 2003

SLIDE 2

1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals

Outline Outline

3. Tunable laser fundamentals
4. Technologies for tunable lasers
5. Summary and Conclusion

SLIDE 3

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 History Introduction: 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

SLIDE 4

Introduction: Laser types and applications

Introduction: Laser types and applications

Compact disk Laser 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 Research Spectroscopy Nuclear Fusion Cooling Atoms Short Pulses

Gas Lasers Liquid Lasers

Free Electron laser (FEL) X-ray lasers Ruby Nd:YAG Ti-Sphire Alexandrite Semiconductor lasers N As Sb Lead-salt

30µ µ µ µm 10µ µ µ µm 3µ µ µ µm 1µ µ µ µm 300nm 100nm 30nm 10nm

λ λ λ λ Energy

Infared Far infared Visible Ultraviolet Soft x-rays Holograms Kinetic sculptures

Military Applications Medical Applications Industrial Applications Special Applications

Laser range-finder Target designation Laser weapons Laser blinding

Eyes
General
Dentistry
Dermatology

Diagnostic fluorescence Soft lasers Measurements Straight Lines Material Processing Spectral Analysis Energy Transport Laser Gyroscope Fiber Lasers

He-Ne He-Ne He-Cd CO2 N2 HF FIR lasers Ar+ Kr+ Cu vapor Ag (Gold) vapor Organic Dye

Liquid Lasers Special Lasers Solid Lasers

Alexandrite

SLIDE 5

Introduction: Semiconductor Laser

Introduction: 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.

SLIDE 6

Spectroscopy
Single frequency mode, tunable
Environmental sensing and pollution monitoring
Lidar
Requires Ruggedness, Correct Wavelength
Industrial Process Monitoring

Motivations Motivations

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 tunability Broad, continuous wavelength tunability

SLIDE 7

Outline

Outline

1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Conclusion

SLIDE 8

Laser physics

Laser physics

G, αi L Mirror Active medium Laser output Partially transmitting mirror R2 R1 G, αi L Mirror Active medium Laser output Partially transmitting mirror R2 R1

1 ) (

~

2 2 / 1 2 1

=

L i

e R R

β

Oscillation condition is reached when

L mirror L mirror

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν =c/2 µ gL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

µL mc

m

2 / = ν

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν =c/2 µ gL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν=c/2nL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

Loop gain Gain curve Laser threshold Longitudinal modes Laser

utput

power Frequency (v) Linewidth

GL

∆ν ∆ν ∆ν ∆ν =c/2 µ gL

ν ν ν νo ν ν ν νm-1 ν ν ν νm-2 ν ν ν ν ν ν ν νm+1ν ν ν νm+2

µL mc

m

2 / = ν µL mc

m

2 / = ν

   == = =

−

,..) 3 , 2 , 1 ( , 2 2 1 ) (

) ( 2 / 1 2 1

m m L k e R R

L g

i

π µ

α

Real part: Threshold condition Imaginary part: wavelength condition

2 /

~

α µ β i k − =

| 1 | ln 2 1

2 1R

R L g

i th

+ =α

SLIDE 9

Semiconductor laser physics

Semiconductor 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 Distribution for interband D.H. and quantum well laser: Fermi Distribution for quantum cascade laser: energy level linewidth

Power and efficiency
Operating temperature

SLIDE 10

Semiconductor laser band diagram

Semiconductor laser band diagram

N-GaAlAs P-AlGaAs p-GaAs ∆ ∆ ∆ ∆Ec Ev Ec Ef (a) Equilibrium band structure

1

1 2 3

Energy (eV) Probability of occupancy

f(E) E F n(E) p(E) ρc (E) ρv (E)

Energy band diagrams for a double heterostructure laser (a) unbiased, (b) forward biased

N-GaAlAs P-AlGaAs ∆ ∆ ∆ ∆Ec Ec Efv Ev Ec Efc (b) Forward biased

∫ ∫

+ − = + − =

v FV v v v c FC c c c

dE KT E E E p dE KT E E E n 1 ] / ) exp[( ) ( 1 ] / ) exp[( ) ( ρ ρ

Carrier concentration in each band:

2

0.0E+00 1.0E+21 2.0E+21 3.0E+21 4.0E+21

Density (cm-3eV-1)

SLIDE 11

Threshold current density

Threshold current density

Carrier density rate equation:

nr

A

nonradiative process

2

Bn

) ( ) (

2

n R qd J n D t n − + ∇ = ∂ ∂ At steady state, = ∂ ∂ t n

ph st nr

N R Cn Bn n A n R qd J n R + + + = =

3 2

) ( ) (

) ( ) ( n n n R

e

τ =

) (

th e th th

n qdn J τ =

Rst stimulated recombination that leads to emission of light and it is proportional to the photon density Nph.

2

Bn

spontaneous radiative rate

3

Cn

nonradiative Auger recombination

Below or near threshold: So, the threshold current density is So:

SLIDE 12

Power and efficiency of semiconductor lasers

Power and efficiency of semiconductor lasers

ph th g th

N g qdv J J + =

If the current is above threshold, this leads to stimulated emission Optical output power P

vs. injection current is determined by

) (

th i m m i ph m g

ut

I I q h h VN v P − + = = α α α η ν ν α

Optical output power Pout vs. injection current is determined by

) / 1 ln( ) / 1 ln( / / R L R q dI dP

i i i i m m

ut

e

+ = + = = α η η α α α ω η

External quantum efficiency is defined as:

SLIDE 13

Quantum Well lasers

Quantum Well lasers

) ( 2 ) , , (

2 2 * 2 y x n n y x

k k m E k k n E + + =

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 ci ci

L m

2

π

ρ = >>>

Density of states:

2 / 1 2 / 3 2 )

2 ( 4 ) ( E h m E

c c

π ρ = Compare with Heterostructure:

Inerband transition

SLIDE 14

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 lasers Quantum cascade lasers

2 3

E E − = ω

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

perations 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.

SLIDE 15

Outline

Outline

1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Conclusion

SLIDE 16

Existing Tunable Laser technologies

Existing Tunable Laser technologies

Distributed Feedback Bragg Grating (DFB)
Sampled grating Distributed Bragg Reflectors (DBR)
MEM-VCSEL
Grating coupled external cavity (ECLD)

SLIDE 17

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 4.520 wavelength (um) In te n s ity 4.420 4.440 4.460 4.480 4.500 4.520

wavelength (um) In te n s ity

Wavelength (um)

DFB laser structure. The grating is etched onto one of the cladding layers. Grating period is determined by Λ Λ Λ Λ=mλ λ λ λ/2. λ λ λ λ 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

SLIDE 18

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

SLIDE 19

Existing Tunable Laser Structures (Mem

Existing Tunable Laser Structures (Mem-VCSEL) VCSEL)

MEM-VCSEL

Active region Output Top curved mirror Membrane post

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 mirror Pump injection Substrate Coretek

SLIDE 20

Existing Tunable Laser Structures (ECLD)

Existing Tunable Laser Structures (ECLD)

Schematic representations

f the Littman Cavities.
f the Littman Cavities.

Photograph and schematic of Iolon’s MEMs based external cavity laser configuration.

SLIDE 21

Grating coupled external cavity tunable laser fundamentals

Grating coupled external cavity tunable laser fundamentals

Collimating lens λ λ λ λ1 λ λ λ λ2 Output λ λ λ λ1 λ λ λ λ2 λ λ λ λ3 Blazed grating θ θ θ θ λ λ λ λ Collimating lens λ λ λ λ1 λ λ λ λ2 Output λ λ λ λ1 λ λ λ λ2 λ λ λ λ3 Blazed grating θ θ θ θ λ λ λ λ

Example

1st order Feed back Laser chip λ λ λ λ3 λ λ λ λ2 λ λ λ λ1 λ λ λ λ2 λ λ λ λ3 .. Zeroth order output

2dsinθ θ θ θ = mλ λ λ λ

θ θ θ θ Grating equation: d 1st order Feed back Laser chip λ λ λ λ3 λ λ λ λ2 λ λ λ λ1 λ λ λ λ2 λ λ λ λ3 .. Zeroth order output

2dsinθ θ θ θ = mλ λ λ λ

θ θ θ θ Grating equation: d

Grating coupled external cavity tunable laser structure.

SLIDE 22

External cavity laser modeling

External cavity laser modeling

λ λ λ λ S4

(+) (-)

n− = 1 r − = 2n + = t m + n− = 1 r − = n− = 1 r − = 2n + = t m + 2n + = t m +

            − − =

m m m m p m p m p

t t r t r t r r t S

1 1 1 1 1 1 1 1 1

1 1

            − − =

m m m m p m p m p

t t r t r t r r t S

2 2 2 2 2 2 2 2 2

1 3

        =

− l ik l ik

sem sem

e e S 2

1st order Feed back Laser chip

λ λ λ λ1 λ λ λ λ3 λ λ λ λ2 S1 S4 S5 S6 S3 S2

n

1 2 + = n t p + 1 n + = n 1 r + =

p

1 1 + − = n n r + − =

m

1 + = n t m +

n

1 2 + = n t p +1 2 + = n t p + 1 n + = n 1 r + =

p

1 n + = n 1 r + =

p

1 1 + − = n n r + − =

m

1 1 + − = n n r + − =

m

1 + = n t m +1 + = n t m +

        =

− L ik L ik

air air

e e S 4

            − − =

Gm Gm Gm Gm Gp Gm Gp Gm Gp

t t r t r t r r t S 1 5

        = closs closs S 1 6

SLIDE 23

Grating coupled external cavity tunable Laser

Grating coupled external cavity tunable Laser

An example: Cavity mode loss curve with longitudinal modes.

s (cm-1)

20 25

Laser oscillation condition

p efft il l g

r r e e

sem i th

1 2 ) (

1 =

− β α

| 1 | ln 1

1p eff th

r r l g + =α

π φ β m l

sem

2 2 = +

φ i eff eff

e r r | | =

Frequency (THz) Cavity mode loss (

5 10 15

SLIDE 24

Fujitsu*, Santur, QDI, Princeton Lightwave,

< 5 nm 40 mW* DFB

Agility*(SGDBR), Bookham(Marconi)(DSDBR) , NTT/NEL(SSGDBR), Multiplex, Intel(Sparkolor), (Altitun(GCSRDBR)),

> 40 nm 30 mW* DBR Companies Tuning range Power Laser type

DFB Advantages:

Cost comparable to fixed lasers
High power
Wavelength stability

External cavity lasers Advantages:

Wide tuning range
High output power
High spectral purity
Low RIN
Continuous tuning

MEM VCSEL Advantages: Low cost Low power consumption Good mode stability Wide tuning range Wafer level testing DBR Advantages: Wide tuning range Fast switching speed Good side mode suppression Moderate output power Low power consumption

Current tunable laser development Current tunable laser development

Intel(new focus)*, Iolon, Blue Sky Research, Princeton Optronics,

>100 nm 30 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 nm per λ 40 mW* DFB

Proven technology

Disadvantages:

Limited tuning range (5nm per laser)
Slow tuning speed (~ few ms)
Reproducibility in manufacturing
Continuous tuning
Plug-in module for different wavelength

Disadvantages:

High cost
Bulky
Slow switching
Shock/vibration sensitivity

Wafer level testing Disadvantages: Low output power Slow switching 1550 nm technology still in development Low power consumption Integrated functions (Modulators, optical amplifiers) Disadvantages: Yield Wavelength stability Relatively broad linewidth Complex software Power

Companies in brackets no longer exist, but honorable

SLIDE 25

Outline

Outline

1. Introduction and motivation
2. Semiconductor laser physics
3. Tunable laser fundamentals
4. Technologies of tunable lasers
5. Proposed research and summary

SLIDE 26

Theoretical calculations and modeling in order to get single

mode and continuous long tuning range Design and construct the E.C. laser testing apparatus and programs Perform testing to qualify lasers for more in depth testing

Key points of the Proposed Research Key points of the Proposed Research

Perform testing to qualify lasers for more in depth testing Laser spectroscopy of some real samples Design compact and robust EC laser source

SLIDE 27

λ

λ λ λ

Recent performance of tunable Mid

Recent performance of tunable Mid-IR lasers IR lasers

!" # $%&&'()*+ ,!&

./0%/!/ 1µ

µ µ µ 2$!!/%3

4$ 5 .&-6%3//

26

SLIDE 28

Thermal fine phase control of tunable laser

Thermal fine phase control of tunable laser

78

Use the coupled- cavity effect to advantage

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

SLIDE 29

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

Ammonia

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

SLIDE 30

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 module Approach for miniature tunable module

0.1

0.1 0.2 0.3 0.4 0.5 1000 2000 3000 4000 Time (ns)

Current (A)

Phase: Gain 50ns: ∆ ∆ ∆ ∆t Variable

Iphase

T=1 µ µ µ µs

0.1 1 10 100 2 4 6 8 10 12 14 16 18 20

Delay (µ µ µ µs) ∆ ∆ ∆ ∆f (GHz) Iphase=800mA, 600mA, 400mA, 300mA, 200mA Thermal decay time ~ 3 µs

SLIDE 31

0.4

0.6 0.2 0.8 1.0 288 GHz 0.0

CO gas absorption spectroscopy CO gas absorption spectroscopy

4.86 4.87 4.88 4.89 4.90 0.0 Wavelength (µ µ µ µm)

SLIDE 32

Summary and Conclusion

Summary 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.

SLIDE 33

Thank you !

Thank you !

SLIDE 34

Additional readings

Additional readings Additional readings Additional readings

SLIDE 35

Semiconductor Laser Physics:

Semiconductor Laser Physics: Density of states calculation Density of states calculation

dE dk k L dE dk dk dN dE dN

2 3

) ( × × = = π π

Where

2 / 1 2 / 3 2 2 2 / 1 2 / 3 2 2 3 2

) 2 ( 1 ) 2 ( 1 ) 2 ( 4 ) 2 ( E m E m dE dk k

v v c c

π

ρ π π π ρ = = =

3 3

3 4 ) ( 8 1 2 k L N × × × × × = π π dE dk k dE dk k dE dN L E

2 2 3 2 3

) 2 ( 4 2 1 ) ( π π π ρ = = =

Where

SLIDE 36

1

E E 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 E E f KT E E f

FV v v FC c c

− + = − + =

Probability of occupancy versus energy of the Fermi-Dirac, the Bose-Einstein and the Maxwell-Boltzmann distribution

SLIDE 37

Semiconductor Laser Physics:

Semiconductor Laser Physics: Carrier concentration calculation Carrier concentration calculation

Electron concentration n and hole concentration p are given by

∫ ∫

+ − = + − =

v v v v v c c c c c

dE KT F E E p dE KT F E E n 1 ] / ) exp[( ) ( 1 ] / ) exp[( ) ( ρ ρ

SLIDE 38

Semiconductor Laser Physics:

Semiconductor Laser Physics: Fermi energy and occupation factor calculation Fermi energy and occupation factor calculation

∫ ∫

+ − = + − =

v v v v v c c c c c

dE KT F E E p dE KT F E E n 1 ] / ) exp[( ) ( , 1 ] / ) exp[( ) ( ρ ρ

Fermi energy, occupation probability can be approximately derived from above equations, which is often referred as Boltzmann from above equations, which is often referred as Boltzmann approximation.

) ln(

C FC

N n KT E = ) exp( ) ( KT E N n E f

C c

− ≅

2 / 3 2)

/ 2 ( 2 h KT m N

c C

π =

For valence band:

) ln(

V FV

N p KT E = ) exp( ) ( KT E N p E f

V v

− ≅

For conduction band: where

SLIDE 39

Semiconductor Laser Physics:

Semiconductor Laser Physics: Stimulated emission rate and gain calculation Stimulated emission rate and gain calculation

Net stimulated emission rate per unit volume per unit energy interval at photon energy hν ν ν ν: Bernard and Duraffourg condition for stimulated emission

c c v v c c v c c c stim

dE f f h E E V h E B h P h R

1 21

) 1 )( )( ( ) ( ) , ( ) ( ) (

− +∞ ∞ −

+ − − =

∫

ρ ρ ν ρ ρ ν ν ν

interval at photon energy hν ν ν ν:

) exp( ) exp( kT E E kT E h E

FC c FV c

− > − − ν

ν h E E

FV FC

> −

Or

c c v v c c v c c c g g stim

dE f f h E E V E B c c R h g

1

) 1 )( )( ( ) ( ) ( ) ( ) (

− +∞ ∞ −

+ − − Γ = Γ =

∫

ρ ρ ν ρ ρ µ µ ν

Gain per unit length can be derived as

SLIDE 40

Quantum well lasers

Quantum 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

V

gain region thickness is reduced until the electronic states are quantised in

ne 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

SLIDE 41

)

(

2 2 2

k k E + =

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 equation Energy levels calculations by Schrodinger equation

) ( 2

2 2 y x

k k m E + =

The energy levels in z direction can be solved by Schrodinger equation for one dimensional potential well: z Lz

ψ ψ ψ ψ ψ V dz d m E dz d m E + − = − =

2 2 2 2 2 2

2 2

inside the well

(0<z<Lz)

utside the well

(z>Lz, z<0)

SLIDE 42

Boundary conditions are that ψ and dψ/dz are continuum

at z=0 and z=Lz, The solution is:

  ≤ ≤ + ≤ = z z k A ) exp( 1 δ ψ

2 / 1 2 1

] ) ( 2 [ E V m k − =

Quantum well lasers: Quantum well lasers: Solution in finite quantum well Solution in finite quantum well

    ≥ − ≤ ≤ + =

z z

L z z k C L z z k B ) exp( ) sin(

1 2

δ ψ

2 / 1 2 2 2 1

) 2 ( ] [

mE

k k = =

where

2 1 2

/ ) tan( k k L k

z =

The eigenvalue equation is:

SLIDE 43

Conduction

band E3c E2c ∆ ∆ ∆ ∆Ec Conduction band E3c E2c ∆ ∆ ∆ ∆Ec

) ( 2 ) , , (

2 2 * 2 y x n n y x

k k m E k k n E + + =

Energy eigenvalues for a particle

confined in the quantum well are:

Quantum well lasers: Quantum well lasers: Energy quantization in quantum well Energy quantization in quantum well

Valence band E1hh E2hh E3hh E1lh E2lh E1c ∆ ∆ ∆ ∆Ev Eg

ω

ω ω ω=Eg+E1c+E1hh

ω

ω ω ω Lz Valence band E1hh E2hh E3hh E1lh E2lh E1c ∆ ∆ ∆ ∆Ev Eg

ω

ω ω ω=Eg+E1c+E1hh

ω

ω ω ω 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.

SLIDE 44

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:

2 2 2 2

2 , ) 2 ( 2 ) (

π

ci i

m m k E k d dE E D = >>> = =

Quantum well lasers: Quantum well lasers: Density of sates calculation Density of sates calculation

z ci z i ci

L m L D

2

π

ρ = = >>>

2

π

ci i

m D = >>>

2 / 1 2 / 3 2 )

2 ( 4 ) ( E h m E

c c

π ρ =

Compare with Heterostructure: Density of states per unit volume:

SLIDE 45

Calculated number of electrons in the conduction band

i i c i E ci

dE E f n

io

) (

∑ ∫

∞

= ρ

Quantum well lasers Quantum well lasers Carrier concentration calculation Carrier concentration calculation

where ] / ) exp[( 1 1 ) ( T k E E E f

B fc i i c

− + =

) exp( )] exp( 1 ln[ T k E N T k E E T k n

B fc c B io fc i ci B

= − + =

∑ ρ

T k N

B ci c

ρ = It is easy to obtain

where Similar solutions hold for holes in the valence band.

SLIDE 46

10

4

10

5

10

6

120K 140K 160K 180K

Electrical properties of semiconductor lasers Electrical properties of semiconductor lasers Carrier density derivation from photoluminance Carrier density derivation from photoluminance

wd e R dz e wdR L

L G spon L z z G spon F

n n

] 1 )[ ( ) ( ) (

) ( ) (

ω ω ω ω ω

ω ω

−

= =

∫

=

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 0.60 10

4

10

3

10

2

10

1

10 10

1

10

2

10

3

10

CO2 Absorption 180K 200K 220K 240K

Intensity Energy (eV)

Threshold photoluminescence spectra at different temperatures. Experimental data are shown in square symbols. Solid lines show the calculations.

wd G e R

n spon

] ) ( 1 )[ ( ω ω ω

−

=

i n

g G α ω − Γ = ) (

where 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.

SLIDE 47

Temperature dependence of threshold current

) / exp( T T I Ith =

T0 is characteristic temperature. A lower T0 value implies that the threshold current increases more rapidly with increasing temperature.

Temperature dependence of carrier lifetime

It decreases with increasing temperature.

th th th

qdn J τ / =

Temperature dependence of electrical properties of Temperature dependence of electrical properties of semiconductor lasers semiconductor lasers

Leakage current

Caused by diffusion and drift

f electrons and holes from

the edges of the active region to the cladding layers. It is higher at higher temperature It 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 efficiency

It decreases with increasing temperature.

SLIDE 48

Optical properties of semiconductor lasers:

Optical properties of semiconductor lasers: Gaussian beam profile Gaussian beam profile

The expression for a real laser beam’s electric field is given by:

] ) ( 2 ) ( exp[ ) ( )] ( exp[ ) , , (

2 2 2 2 2

z R y x ik z w y x z w z i ikz z y x E + − + − − − ∝ ψ

) / arctan( ) ( / ) ( ) / ( 1 ) (

2 2 R R R

z z z z z z z R z z w z w = + = + = ψ

Expression for spot size, radius of curvature, and phase shift: Where ZR is the Rayleigh Range, it is given by

λ π /

2

w zR =

The beam divergence half angle is given by

/ 1

) ( w z w z z z w z z w

R R e

π λ θ = = = =

field is given by:

SLIDE 49

Optical properties of semiconductor lasers: Astigmatism

Optical properties of semiconductor lasers: Astigmatism

L>w θ θ θ θL< θ θ θ θw w θ θ θ θL θ θ θ θw

λ λ λ λ/l λ λ λ λ/w w l λ λ λ λ/w λ λ λ λ/L L W

An edge emitting laser has astigmatism, the divergent angles are:

L w

π λ θ π λ θ = =

L

SLIDE 50

Semiconductor Laser gain dynamics

Semiconductor Laser gain dynamics

p g gain i

gN v N 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 time

gain p p p g p

N gN v dt dN τ − Γ =

p g gain i

gN v N eV I − − = τ η

p po po g

N N g v τ − Γ =

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

SLIDE 51

Semiconductor Laser gain dynamics

Semiconductor Laser gain dynamics

Suppose there is small variation at steady condition.

N aN v N N eV I dt N d

po g p p gain i

δ τ δ τ δ δ η δ − Γ − − = N aN v N d

p

δ δ Γ = N aN v dt

po g p

δ Γ = dt I d eV N aN v dt N d aN v dt N d

gain i p po g po g

δ η δ τ δ τ δ = + + + ) ( ) 1 (

2 2

Solving them:

p po g R

aN v τ ω =

Relaxation oscillation frequency:

SLIDE 52

Semiconductor Laser gain dynamics

Semiconductor Laser gain dynamics

General form of the frequency response

) 1 ( 1 1 ) ( ) (

2 2 p R R R R

i P P τ ω τ ω ω ω ω ω δ ω δ + + − =

Note that 1. there is an intrinsic limit to the modulation speed 2. the modulation speed tend to rise with the square root

f the differential gain,

3. the modulation speed tends to rise as the square root of the laser output power.

Frequency response of the output power modulation of a laser diode as the frequency

f electrical drive is increased.

SLIDE 53

Noise arises from the spontaneous emission process and carrier-

generation-recombination process, can be modeled by adding Langevin noise source.

Noise properties of semiconductor lasers Noise properties of semiconductor lasers

Modified rate equations with added noise

) ( ) ( 2 1 ) ( ) ( / ) ( ) ( t F G t F GP N q I N t F R P G P

c th N e p sp φ

γ β ω ω φ 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)

SLIDE 54

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 lasers Electrical and optical properties of semiconductor lasers

RIN (dB/Hz) P1 P2 P3 RIN (dB/Hz) P1 P2 P3

Phase noise Phase fluctuation comes from spontaneous emission, change in

ptical gain and refractive index

induced by carrier population, linewidth enhancement factor (huge for semiconductor laser).

) 1 ( 4

2 c sp

P R β π δν + =

Frequancy (GHz) R Frequancy (GHz) R