Stimulated emission Devices: Lasers - Concordia …kabir/ELEC425/Chapter4_s.pdf · ELEC425/6261 Dr. M. Z. Kabir 2 Laser operation Laser: Light amplification by stimulated emission

ELEC425/6261 Dr. M. Z. Kabir 1

Stimulated emission Devices: Lasers


Laser operation

Laser: Light amplification by stimulated emission of radiation

Photons collide with

electrons and drop

them to lower state.


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


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


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


(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


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


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.


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.


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


(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


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


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


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


Pump rate

Threshold pump rate

(N2N1)th

N2N1

Threshold population

inversion

Po = Lasing output power

(N2N1) and Po


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:


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


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)


Population inversion in Laser diodes

Lasing condition

FpFng EEhE


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


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.


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


Optical power vs. diode current

To reduce threshold current, heterostructure is used.


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


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


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.


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


Buried double heterostructure:

Index guided laser- Can have

single mode by narrowing the

lateral dimensions.


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


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.


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.


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)


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


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


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:


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


Optical Gain Curve


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


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.


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


Quantum Well Devices:


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.


Single Quantum Well (SQW)

Reduced threshold current

Reduced linewidth

2*

22

8 dm

nhEn


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.

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Stimulated emission Devices: Lasers - Concordia …kabir/ELEC425/Chapter4_s.pdf · ELEC425/6261 Dr. M. Z. Kabir 2 Laser operation Laser: Light amplification by stimulated emission