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ELEC425/6261 Dr. M. Z. Kabir 1
Stimulated emission Devices: Lasers
ELEC425/6261 Dr. M. Z. Kabir 2
Laser operation
Laser: Light amplification by stimulated emission of radiation
Photons collide with
electrons and drop
them to lower state.
ELEC425/6261 Dr. M. Z. Kabir 3
Absorption and emission
Absorption rate, 1211212 NBR
Emission rate, 1222122121 NBNAR
Under thermal equilibrium,
2112 RR And
kT
h
kT
EE
N
N 1212
1
2 expexp
ELEC425/6261 Dr. M. Z. Kabir 4
Absorption and emission
Radiation from the atoms must give rise to an equilibrium photon energy
density, eq(h), that is given by Planck’s black body radiation distribution
law,
Under thermal equilibrium,
Or,
1exp
8
3
33
Tk
hc
hnh
B
eq
2112 RR
eqeq NBNANB 221221112
212112
21
/ BNNB
Aeq
Photon energy per unit vol.
per unit frequency
ELEC425/6261 Dr. M. Z. Kabir 5
In order that this holds, the conclusion is that,
2112 BB
2112
21
3
33
exp1exp
8
BTk
hB
A
Tk
hc
hn
BB
And 3
33
21
21 8
c
hn
B
A
12
21
21
221
12221
21
21
)(
)(
A
B
NA
NB
sponR
stimR
During laser operation,
1
2
112
221
12
21
)(
)(
N
N
NB
NB
absorpR
stimR
Einstein relation
ELEC425/6261 Dr. M. Z. Kabir 6
(1) Population Inversion, N2 N1. Needs external means, e.g., optical
pumping, forward biasing for Laser diodes.
(2) Large photon concentration. Needs optical resonant cavity to contain a
large value of photons by internal reflections and to sustain the coherent
emission.
Absorption and emission (contd.)
1221
21
21
21
)(
)(
A
B
sponR
stimR
1
2
12
21
)(
)(
N
N
absorpR
stimR
Two important conditions for Laser
ELEC425/6261 Dr. M. Z. Kabir 7
dE
dkkEg D 3
2
32
42
3-D density of states:
n
kcEand
c
nk
21
33
221
3
213
8
ch
EnEg D
33
221
3
213
8
ch
hEnEg D
States/modes per vol. per unit frequency
1exp
8
1exp
8
3
33
3
23
Tk
hc
hn
Tk
h
h
c
nh
BB
States/modes per vol. per unit energy
Average energy per mode
1exp
Tk
h
h
B
(quantum) or kT (classical)
(Black body
radiation)
Extra slide
ELEC425/6261 Dr. M. Z. Kabir 8
Energy of the Er3+ ion
in the glass fiber
E10
1.27 eV
0.80 eV E2
E3
1550 nm 1550 nm
InOut
980 nm
Non-radiative decayPump
Optical fiber amplifier
Based on Er3+ doped fiber amplifier (EDFA). SiO3-GeO2 core region is doped.
Electrons rapidly decays to long-lived (10 ms) level E2.
The net optical gain,
12 NNKGop
The energy levels E1,
E2, and E3 are closely
spaced collection of
several levels.
Therefore, transition
from E2 to E1 emits
photons of about 1.525
– 1.565 nm.
ELEC425/6261 Dr. M. Z. Kabir 9
EDFA:
If EDFA is not pumped at any time it will act as an attenuator as 1.55 m photons
will be absorbed by Er ions.
Signal in Signal outSplice
Er3+-doped
fiber (10 - 20 m)
Wavelength-selective
coupler
Pump laser diode
Splice
l = 1550 nm l = 1550 nm
l = 980 nm
Termination
Optical
isolator
Optical
isolator
Optical isolators only allow the optical signals at 1.55 m to pass in one direction
and prevent 0.98 m light propagation. There is usually a photodetector system is
coupled to monitor the pump power or the EDFA output power.
Gain efficiency is 8-10 dB/mW at 0.98 m pumping.
ELEC425/6261 Dr. M. Z. Kabir 10
Optical resonant cavity
The reflecting mirrors reflect the photons
back and forth, which allows the photon
energy density to build up.
One or both the mirrors are partially
transmitting so that a fraction of the light
will leak out. This transmitted light is the
output of the laser.
For coherent light build up and stimulated
emission,
;2
0
n
mL
l
m is an integer and n is
refractive index
L
MirrorMirror
R1 R2
Spontaneous emission will initially occur.
For lasing, the optical gain in photons per
pass must be larger than the total loss.
Fabry-Perot optical resonator or etalon
rn
ELEC425/6261 Dr. M. Z. Kabir 11
(c)
l
Relative intensity
l
Emission Intensity
(a)
l
Allowed Cavity
Oscillations
(b)
n(l/2) = L
l
Doppler
broadening
Laser cavity modes: Only standing electromagnetic waves, or modes, of certain
wavelengths are allowed to exist within the optical cavity L. If m is an
integer, the allowed wavelength l0 is
2
0lmL
Modes that exist along the cavity axis are called axial or longitudinal
modes.
The spectral width is due to the acoustic or thermal fluctuation of cavity length
and the partially reflected mirrors.
Optica
l gain
ELEC425/6261 Dr. M. Z. Kabir 12
Example 1:
The He-Ne Laser A particular He-Ne laser operating at 632.8 nm has a tube that is 50
cm long. The operating temperature is 130 C.
The linewidth of the gain curve is 0.002 nm. What is the mode number m of the center
wavelength, the wavelength and frequency separation between two consecutive modes,
and how many modes do you expect within the bandwidth of the optical gain curve?
m
Lm
2l
L
mcm
2
Lm
2
2
0ll
L
cm
2
No of allowed modes
ml
l
2/1
ELEC425/6261 Dr. M. Z. Kabir 13
Laser oscillation conditions: Threshold gain
L
PiPf
R1R2
Steady state EM oscillations
Reflectingsurface
Reflectingsurface
Cavity axis x12
Ef Ei
For steady state oscillation, 1/ ifop PPG
After one round trip of path length 2L
LgLRRPP if 2exp2exp21
For steady state oscillation,
1/ if PP
21
1ln
2
1
RRLgg th and
Optical gain coefficient, g
ELEC425/6261 Dr. M. Z. Kabir 14
Threshold gain
This corresponds to a threshold population inversion or thNN 12
21
1ln
2
1
RRLgth
Considering confinement factor,
Lasing threshold is the point at which the optical gain is equal to the total
loss t
;endtthg
21
1ln
2
1
RRLend
end corresponds to the lasing output from the end.
corresponds to the actual loss in the cavity.
For lasing operation,thgg
ELEC425/6261 Dr. M. Z. Kabir 15
Pump rate
Threshold pump rate
(N2N1)th
N2N1
Threshold population
inversion
Po = Lasing output power
(N2N1) and Po
ELEC425/6261 Dr. M. Z. Kabir 16
Wave fronts
Spherical
mirror
Optical cavity
TEM00 TEM10
TEM01TEM11
TEM00 TEM10
TEM01TEM11
(b)
(c) (d)
Laser Modes (a) An off-axis transverse mode is able to self-replicate after one roundtrip. (b) Wavefronts in a self-replicating wave (c) Four low order transverse cavitymodes and their fields. (d) Intensity patterns in the modes of (c).
(a)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Allowed modes are designated based on the spatial field patterns in both
longitudinal and transverse (like in waveguide) directions. These modal field
paterns at a reflector is described by three integers p, q, and m and designated
by TEMpqm.
Laser modes:
ELEC425/6261 Dr. M. Z. Kabir 17
Principle of the Laser diodes
p+ n+
EFn
(a)
Eg
Ev
Ec
Ev
Holes in VBElectrons in CB
Junction
ElectronsEc
p+
Eg
V
n+
(b)
EFn
eV
EFp
Inversionregion
EFp
EcEc
eVo
gEV 0
gEVV 0
SCL is no longer depleted and more electrons in the conduction band
than in the valence band near Ev.
Population Inversion between Ec and Ev Injection pumping
Incoming photons with energy (Ec – Ev) can not excite an electron from Ev to Ec
but stimulates an electron to fall down from Ec to Ev. This gives optical gain.
Injection pumping
ELEC425/6261 Dr. M. Z. Kabir 18
h
Eg
Optical gainE
F n E
F p
Optical absorption
0
Energy
Ec
Ev
CB
VB
(a) The density of states and energy distribution of electrons and holes inthe conduction and valence bands respectively at T 0 in the SCLunder forward bias such that EFn EFp > Eg. Holes in the VB are emptystates. (b) Gain vs. photon energy.
Density of states
Electrons
in CB
Holes in VB
= Empty states
EF n
EF p
eV
At T > 0
At T = 0
(a) (b)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Population inversion in Laser diodes
Lasing condition
FpFng EEhE
ELEC425/6261 Dr. M. Z. Kabir 19
Optical cavity in Laser diodes
LElectrode
Current
GaAs
GaAsn+
p+
Cleaved surface mirror
Electrode
Active region(stimulated emission region)
A schematic illustration of a GaAs homojunction laserdiode. The cleaved surfaces act as reflecting mirrors.
L
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Two planes are cleaved or
polished.
Two remaining sides are
roughened to eliminate lasing.
nmL
2
0l
Lasing radiation is only possible when the optical gain can overcome the
photon losses from the cavity.
ELEC425/6261 Dr. M. Z. Kabir 20
Typical output optical power vs. diode current (I) characteristics and the correspondingoutput spectrum of a laser diode.
l
Laser
l
LaserOptical Power
Optical Power
I0
l
LEDOptical Power
Ith
Spontaneous
emission
Stimulated
emission
Optical Power
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Optical power vs. diode current
To reduce threshold current, heterostructure is used.
ELEC425/6261 Dr. M. Z. Kabir 21
In DH structure,
Carriers are confined
Optical field is
confined within the
active region by the
abrupt change of
refractive index
Confinement reduces
the Ith.
Confinement factor,
ndC exp1
ELEC425/6261 Dr. M. Z. Kabir 22
Schematic illustration of the the structure of a double heterojunction stripecontact laser diode
Oxide insulator
Stripe electrode
SubstrateElectrode
Active region where J > Jth.
(Emission region)
p-GaAs (Contacting layer)
n-GaAs (Substrate)
p-GaAs (Active layer)
Current
paths
L
W
Cleaved reflecting surfaceElliptical
laser
beam
p-AlxGa
1-xAs (Confining layer)
n-AlxGa
1-xAs (Confining layer)
12 3
Cleaved reflecting surface
Substrate
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Stripe Geometry:
Reduced contact area reduces Ith.
Reduced emission area makes easy
coupling to optical fiber
Optical gain is highest where
the current density is
greatest- Gain guided laser.
ELEC425/6261 Dr. M. Z. Kabir 23
Oxide insulation
n-AlGaAs
p+-AlGaAs (Contacting layer)
n-GaAs (Substrate)
p-GaAs (Active layer)
n-AlGaAs (Confining layer)
p-AlGaAs (Confining layer)
Schematic illustration of the cross sectional structure of a buriedheterostructure laser diode.
Electrode
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Buried double heterostructure:
Index guided laser- Can have
single mode by narrowing the
lateral dimensions.
ELEC425/6261 Dr. M. Z. Kabir 24
Diode characteristics (index guided laser)
Height, dWidth W
Length, L
Fabry-Perot cavity
Dielectric mirror
Diffractionlimited laserbeam
778 780 782
Po = 1 mW
Po = 5 mW
Relative optical power
l (nm)
Po = 3 mW
0 20 40 60 800
2
4
6
8
10
Po (mW)
I (mA)
0 C25 C
50 C
JWLI
Threshold current increases
with temperature
ELEC425/6261 Dr. M. Z. Kabir 25
0/exp TTIth
T0 is 120 to 190 K for GaAs devices.
Mode hopping: At new operating temperature, another mode fulfils
the laser oscillation condition. Thermoelectric cooler can stabilize its
wavelength.
ELEC425/6261 Dr. M. Z. Kabir 26
Example 3: Laser output wavelength variation
Consider the refractive index of GaAs is 3.7 and it has a temperature dependence
dn/dT 1.5 10-4 K-1. Estimate the change in emitted wave length per degree
change in temperature for the peak radiation of 870 nm.
ELEC425/6261 Dr. M. Z. Kabir 27
Steady-state rate equation (in laser diode)
ph
phph
ph NBnN
dt
dN
t
rph
c
n
Rate of electron injection by current
Rate of spontaneous emissions
Rate of stimulated eissions
phsp
BnNn
ed
J
dt
dn
Under steady-state:
21
1ln
2
1
RRLt
Nph is the coherent photon concentration in the active layer
ph Is the average lifetime of photon due to transmission and the total losses
Rate equations govern the interaction of photons and electrons in the active
region.,
Rate of stimulated emission
– Rate of coherent photon loss in the cavity
0dt
dN ph 0dt
dnand
(nr refractive index)
ELEC425/6261 Dr. M. Z. Kabir 28
Steady-state rate equation
Under steady-state lasing:
For lasing, J has to increase to Jth. At this case, n is clamped to nth. Up
to the threshold point, Nph 0. Right at the threshold,
)(sp
thth n
ed
J
0ph
phphth
NNBn
0 phthsp
th NBnn
ed
J
Or,
Adding these two equations:0
ph
ph
sp
thNn
ed
J
0ph
phthN
ed
J
ed
J
Thus, th
phph JJ
edN
sp
thth n
ed
J
0ph
sp
BnNn
ed
J
dt
dn
ELEC425/6261 Dr. M. Z. Kabir 29
For J Jth, n clamped at nth and the excess carriers above nth take part in
stimulated recombination process. The rate of stimulated recombination
increases with J (J Ith) and so does the carrier injection.
Power generated by stimulated emission
e
hIIP ithst
21
21
21
21
/1ln2
/1ln
/1ln2/1
/1ln2/1
RRL
RR
e
hII
RRL
RRLPP
ith
stout
Output Power
Overall efficiency or powerefficiency ,
app
out
IV
P
nrr
ri
RR
R
thth gJ
For a strongly confined structure,
Gain factor is a constant appropriate to specific devices
ELEC425/6261 Dr. M. Z. Kabir 30
The external differential efficiency,
eIId
hPd
th
outex
/
/
21
21
/1ln2
/1ln
RRL
RRi
In practice, eVapp = 1.4 Eg and h Eg
This discrepancy is due to the series resistance of the Laser diode.
This gives a measure of the rate of change of the optical power with current.
Hence it is also referred to as the slope quantum efficiency.
ththresholdabove
slopeII
P
I
P oo
Slope efficiency:
ELEC425/6261 Dr. M. Z. Kabir 31
External Quantum Efficiency:
IE
eP
eI
hP
g
outout /
/EQE
Internal Quantum Efficiency:
nrr
r
/1/1
/1IQE
Extraction efficiency:
= (Loss from the exit cavity end) / (Total loss)
EE = (1/2L)ln(1/R1R2) / t
ELEC425/6261 Dr. M. Z. Kabir 32
Optical Gain Curve
ELEC425/6261 Dr. M. Z. Kabir 33
Example 4:
Consider a GaAs-AlGaAs DH laser operating at 1310 nm. L = 60 m, W = 10 m
and d = 0.25 m, the refractive index is 3.5 and the loss coefficient, = 10 cm-1.
1. Find the total loss coefficient in the cavity, t and ph.
2. If Jth = 500 A/cm2, and sp = 10 ps, what is the threshold electron concentration?
3. Calculate the lasing optical power when the current is 5 mA.
R
n 1
n 1
2
3.51
3.51
2
ELEC425/6261 Dr. M. Z. Kabir 34
Single frequency solid state lasers
Using distributed Bragg reflector
Corrugated
dielectric structure
Distributed Bragg
reflector
(a) (b)
A
B
L
q(lB/2n) = L
Active layer
Reflected waves A and B interfere constructively when,
L 2n
q Blq = 1, 2, 3, …
Only a particular Fabry-Perot cavity mode, within the optical gain curve, that is
close to lB can lase and exist in the output.
ELEC425/6261 Dr. M. Z. Kabir 35
A quantum well (QW) device. (a) Schematic illustrat ion of a quantum well (QW) structure in which athin layer of GaAs is sandwiched between two wider bandgap semiconductors (AlGaAs). (b) Theconduction electrons in the GaAs layer are confined (by ² Ec) in the x-direction to a small length d so
that their energy is quantized. (c) The density of stat es of a two-dimensional QW. The density of statesis constant at each quantized energy level.
AlGaAs AlGaAs
GaAs
y
z
x
d
Ec
Ev
d
E1
E2
E3
g(E)Density of states
E
BulkQW
n = 1
Eg2Eg1
E n = 2² Ec
BulkQW
² Ev
(a) (b) (c)
Dy
Dz
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Quantum Well Devices:
ELEC425/6261 Dr. M. Z. Kabir 36
Ec
Ev
E1
E1
h = E1 – E
1
E
In single quantum well (SQW) lasers electrons areinjected by the forward current into the thin GaAslayer which serves as the active layer. Populationinversion between E1 and E1 is reached even with a
small forward current which results in stimulatedemissions.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Single Quantum Well (SQW)
Reduced threshold current
Reduced linewidth
2*
22
8 dm
nhEn
ELEC425/6261 Dr. M. Z. Kabir 37
Example 5:
Consider a GaAs quamtum well of thickness d = 10 nm. The effective masses of
electrons and holes are 0.07me and 0.5 me. What is the change in the
emission wavelength with respect to bulk GaAs that has an energy bandgap of
1.42 eV.