Lasers
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Prof. Wei-I Lee
Stimulated Emission and Photon Amplification
Stimulated Emission and Photon Amplification
Light Amplification by Stimulated Emission or Radiation, Laser
3 features of stimulated emission :
(1) 1 photon in, 2 photons out Æ light amplification
(2) emitted photon in the same direction as the incoming photon
(3) emitted photon in phase ( coherent ) with the incoming photon
besides stimulated emission, need two more conditions to make lasers :
(1) population inversion
(2) metastable state ( long-lived state ) – a higher energy state in which ecan stay for a much longer time than in an ordinary excited state (10-3
sec vs. 10-8 sec )
a two-level system
can not sustain laser
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Prof. Wei-I Lee
Stimulated Emission and Photon Amplification
Principle of Ruby Laser
E1, E2, and E3 : energy levels of Cr+3 ion in Al2O3 crystal
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Prof. Wei-I Lee
Stimulated Emission and Photon Amplification
Characteristics of Laser
characteristics of a laser :
(1) unidirectional
(2) high intensity
( Ex : He-Ne laser : ~ 100 W/m2
which is ~ 4000 x sunlight )
(3) nearly monochromatic
(4) coherent
T.H. Maiman
holding the first laser ( 1960 )
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Prof. Wei-I Lee
Stimulated Emission and Photon Amplification
Einstein Coefficients
B12, A21, and B21 : Einstein coefficients
(ρ : photon energy density per unit freq.)
at thermal equilibrium :
ratio of stimulated emission to spontaneous emission :
ratio of stimulated emission to absorption :
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Prof. Wei-I Lee
Stimulated Emission and Photon Amplification
Lasing Requirements
ratio of stimulated emission to spontaneous emission :
Î need large ρ(hυ) Î need optical cavity to contain photons
ratio of stimulated emission to absorption :
Î need to achieve N2 > N1 Î population inversion
from Boltzmann statistics (@T.E.) :
N2 > N1 Î negative T (K)
Î laser based on non-T.E.
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Prof. Wei-I Lee
Optical Fiber Amplifiers
Erbium Doped Fiber Amplifier ( EDFA )
Er3+ ions doped into the core region of an optical fiber
to achieve light amplification Î need (stimulated emission > absorption)
Î population inversion required ( N2 > N1 )
optical gain, Gop = K ( N2 – N1 )
K : a constant depends on pumping intensity
Er-doped fiber is usually
inserted into the fiber
communication line by
splicing
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t
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Prof. Wei-I Lee
Optical Fiber Amplifiers
Erbium Doped Fiber Amplifier ( EDFA )
Er-doped fiber usually inserted into fiber communication line by splicing
gain efficiency : 8-10 dB/mW
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Prof. Wei-I Lee
Gas Lasers : He-Ne Laser
He-Ne Laser
a gaseous mixture of He and Ne atoms ( 5:1 ) in a gas discharge tube
stimulated emission from Ne atoms ( ground state : 1s22s22p6 )
He atoms ( ground state : 1s2 ) excite Ne atoms by atomic collisions
He + e- Æ He* + eHe* : 1s12s1 w. parallel spin
selection rule : Δl = ±1 for
photon emission/absorption
Î He* a metastable state
Î He* build up
He* + Ne Æ He + Ne*
Ne* : 1s22s22p55s1
Î population inversion
1s22s22p55s1 Î ~ 2p53p1
: laser emission @ 632.8 nm
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Prof. Wei-I Lee
Gas Lasers : He-Ne Laser
More About He-Ne Laser
~2p55s1 : 4 closely spaced levels, ~2p53p1 : ten closely spaced levels
Î lasing emissions contain a variety of λ
there are also other levels which can generate lasing emissions ( e.g. in
the infrared range )
reflecting mirrors can be made λ selective to suppress unwanted λ
1s22s22p53s1 Î 1s22s22p6 requires change in e- spin, which can not
be achieved by photon radiation Î 1s22s22p53s1 : a metastable level
Î needs collision w. the tube wall to return to the ground state
Î thin tube required
tube length ↑ Î emission intensity ( optical gain ) ↑
typical characteristics :
Gaussian beam
0.5-1 mm beam diameter
1 milliradians divergence
a few mW power
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Prof. Wei-I Lee
Output Spectrum of Gas Laser
Doppler Broadening
gas atoms are in random motion with an average K.E. = 3/2 kBT
assume these gas atoms emit radiation of freq. υo , due to Dopper effect :
atom moving away from observer Î observer detects
atom moving towards observer Î observer detects
( vx : relative v of atom along the laser tube w.r.t. the observer )
Î gas laser has an approximate “linewidth” Δυ = υ2 – υ1
Î Doppler broadened linewidth of a laser radiation
gas atom velocity obeys Maxwell distribution
Î stimulated emission λ exhibit distribution about a central λo= c/υo
Î optical gain ( or photon gain ) shows
similar distribution ( optical gain lineshape )
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Prof. Wei-I Lee
Output Spectrum of Gas Laser
Optical Gain and Cavity Modes
from Doppler broadening : optical gain lineshape Æ ~ Gaussian function
with typical spread in frequency of 2-5 GHz
FWHM of the optical gain vs. freq. spectrum (assuming Maxwell
velocity distribution) :
Î applied nearly to all gas lasers
( solid state lasers have different broadening mechanisms )
for Fabry-Perot optical resonator or etalon : only certain cavity modes
with specified λ can be
maintained as standing
waves in the cavity
m : mode number
( longitudinal axial modes )
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Prof. Wei-I Lee
Output Spectrum of Gas Laser
Laser Output Spectrum
laser output : (optical gain curve) x (allowed cavity modes)
Î peaks at certain λ corresponding to various cavity modes with the
envelop of optical gain curve due to Doppler broadening ( which is a
Gaussian distribution )
the intensity spikes have finite width ( ~ 1kHz – 1 MHz ) due to
nonidealities of the optical cavity ( e.g. thermal fluctuation of cavity
length, nonideal mirrors etc. )
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Prof. Wei-I Lee
Laser Oscillation Conditions
Optical Gain Coefficient
if light intensity decreases along x due to absorption
Î light intensity ∝ exp(-αx) , α : absorption coef.
if light intensity increases along x:
Î light intensity ∝ exp(g x)
g : optical gain coefficient
( optical gain per unit length )
,(
)
( ρ : photon energy density per unit freq. )
Î
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Prof. Wei-I Lee
Laser Oscillation Conditions
Threshold Gain
assuming reached a steady state lasing emission in an optical cavity
Î net round-trip optical gain, Gop = Pf / Pi = 1
exp( gx ) includes : stimulated emission and counter absorptions
exp(- γx) includes : losses in cavity/wall acting against stimulated
emission gain, e.g. light scattering at defects, absorption by impurities/
free carriers etc. ( γ : attenuation or loss coefficient of the medium )
( R1, R2 : reflectance at reflecting surface )
Pf = Pi
Î threshold gain gth :
Î threshold population
inversion :
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Prof. Wei-I Lee
Laser Oscillation Conditions
Pump Rate and Output Power
round-trip optical gain = 1
Î threshold gain gth :
Î threshold population inversion :
simplified description of (N2 – N1) and Po vs. pump rate under steady
state continuous waver operation
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Prof. Wei-I Lee
Laser Oscillation Conditions
Phase Condition
round trip phase change :
assume constant n and neglect phase changes at the mirrors
Î only k values that satisfy the following phase condition can exist
Î
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( longitudinal axial modes )
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Prof. Wei-I Lee
Laser Oscillation Conditions
Laser Modes
simplified ideal analysis : plane wave & perfectly parallel mirrors assumed
all practical laser cavities have finite transverse size and not all cavities
have flat reflectors at the ends
off-axis self-replicating rays can exist Î non-axial modes
greater transverse size Î more off-axis modes
a mode : a particular spatial electric field pattern at one reflector that can
replicate itself after one round trip through the cavity
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Prof. Wei-I Lee
Laser Oscillation Conditions
Laser Modes - TEMpqm
All modes can be represented by fields ( E & B ) that are nearly normal to
the cavity axis Î transverse electric and magnetic (TEMpqm) modes
p , q Î # of nodes in the field distribution along y and z ( transverse to the
cavity axis x )
m ( longitudinal mode number ) Î # of nodes along the x-axis, usually
very large ( ~ 106 in gas laser )and not written
TEM00 :
• lowest order mode
• radially symmetric
• lowest divergence
• requires restrictions in transverse
size of the cavity
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Prof. Wei-I Lee
Principle of Laser Diode
Population Inversion in Homojunction Laser Diode
degenerately doped direct bandgap
p-n junction diode
Î EFn > Ec , EFp < Ev
forward bias with eV > Eg
Î population inversion at the junction
incoming phonon hυ = Eg in active region
Î more likely to cause stimulated emission
than being absorbed Î optical gain
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Prof. Wei-I Lee
Principle of Laser Diode
Formation of Cavity in Laser Diode
reflectors formed by cleaved surfaces ( ~ 30% reflecting )
mode of the cavity :
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, ( n : refractive index )
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Prof. Wei-I Lee
Principle of Laser Diode
Threshold Current
pumping mechanism : forward diode current
at I = Itrans ( transparency current )
Î stimulated emission balances counter absorption
at I > Ith ( threshold current ) Î optical gain g reached gth
Î optical gain overcome photon losses from the cavity
Î optical gain reached gth Î lasing emission
Jth in homojunction laser diode is too high for practical uses ( can operate
only at very low temp. )
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Prof. Wei-I Lee
Heterostructure Laser Diodes
Heterostructure Laser Diodes
to reduce Ith Î need better (1) carrier confinement (2) photon confinement
improved carrier confinement in DH structure
Î easier to achieve population
inversion in narrow Eg active layer
Î Ith ↓
narrow Eg semiconductor usually
has higher refractive index
Î better photon confinement in
narrow Eg active region
Î photon conc. ↑
Î stimulated emission rate ↑
Î Ith ↓
advantage of the AlGaAs DH laser
Î lattice matched to substrate
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Prof. Wei-I Lee
Heterostructure Laser Diodes
Gain Guided Laser Diode
Ex. stripe geometrical AlGaAs/GaAs/AlGaAs DH laser diode
current flow confined to between path 2 & 3
J at path 1 > path 2 & 3 , region where J > Jth defines active region
width of the active region decided by J and hence the optical gain
Î gain guided laser
advantages of stripe geometry :
1. reduced contact area
Î Ith ↓
2. reduced emission area
Î easier coupling to
optical fibers
typical W ~ a few μm
Î Ith ~ tens of mA
poor lateral optical
confinement of photons
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Prof. Wei-I Lee
Heterostructure Laser Diodes
Index Guided Laser Diode
Ex. buried double heterostructure laser diode
good lateral optical confinement by lower refractive index material
Î stimulated emission rate ↑
active region confined to the waveguide defined by the refractive index
variation Î index guided laser diode
buried DH with right dimensions compared with the λ of radiation
Î only fundamental
mode can exist
Î single mode laser
diode
DH AlGaAs/GaAs LD
Î ~ 900 nm LD
DH InGaAsP/InP LD
Î 1.3/1.55 μm LD
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Prof. Wei-I Lee
Elementary Laser Diode Characteristics
Output Modes of LD
output spectrum depends on
1. optical gain curve of the active medium
2. nature of the optical resonator
L decides longitudinal mode separation
W & H decides lateral mode separation
with sufficiently small W & H
Î only TEM00 lateral mode will exist
( from Kasap Ex. 4.5.1 : Number of laser modes
depends on how the cavity modes intersect the
optical gain curve. )
( longitudinal modes depends on L )
diffraction at the cavity ends
Î laser beam divergence
( aperture ↓ Î diffraction ↑)
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Prof. Wei-I Lee
Elementary Laser Diode Characteristics
Current Dependence of Power Spectrum
output spectrum depends on
(1) optical gain curve of the active medium, and
(2) nature of the optical resonator
output spectrum depends on pumping current level
Ex. output spectrum from an index guided LD
low current Æ multimode
high current Æ single mode
spectrum of most gain guided LD
remain multimode even at high
diode current
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Prof. Wei-I Lee
Elementary Laser Diode Characteristics
Temperature Dependence of Ith and λ
Tj ↑Î Ith ↑
Tj ↑ Î Eg ↓ , n ↑ , cavity length ↑ Î λ0 ↑
in single mode LD :
when shift of peak gain causes mode
change to an adjacent longer λ mode
Î mode hopping
to restrict mode hopping Î design the
device structure to keep modes sufficiently separated
Tj depends on
(1) ambient
temperature
(2) operation
current
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Prof. Wei-I Lee
Elementary Laser Diode Characteristics
Slope Efficiency
slope efficiency ηslope :
typical ηslope < 1 W/A
Po = ηslope ( I – Ith )
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Prof. Wei-I Lee
Steady State Semiconductor Rate Equations
Rate Equations and Laser Diode Equation I
Po = ? x ( J – Jth )
( Δt = nL/c )
Nph = ? x ( J – Jth )
at steady state :
( neglecting nonradiative recombinations )
at I = Ith , n = nth, Nph ≈ 0
Î
Î nth = Ithτsp / edLW Î
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Prof. Wei-I Lee
Steady State Semiconductor Rate Equations
Rate Equations and Laser Diode Equation II
at steady state :
( τph : average time for a photon to be
lost due to transmission through the
end-faces, scattering and absorption )
Î nth = 1 / C τph
Î
Î
( laser diode equation )
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Prof. Wei-I Lee
Light Emitters For Optical Fiber Communications
Light Emitters for Optical Fiber Communications
LED adv. : simpler to drive,
more economic,
longer lifetime
disadv.
: wider output spectrum,
less power
Î usually used with multimode
graded index fibers for short haul appl.
LD adv. : narrow linewidth, high output power
Î wide bandwidth long haul appl.
rise time : the time
for light output to
rise from 10% to
90% of the final
value ( with a step
input )
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Prof. Wei-I Lee
Single Frequency Solid State Lasers
Distributed Bragg Reflector Laser Diode
typical Δλ of single frequency ( single mode ) lasers < 0.1 nm
one way to achieve single mode operation Î freq. selective mirrors
, λB : Bragg wavelength , q : diffraction order
Î in-phase interference
Î only particular Fabry-Perot cavity mode within the optical gain curve
that is close to λB can lase and exist in the output
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Prof. Wei-I Lee
Single Frequency Solid State Lasers
Distributed Feedback Laser Diode I.
radiation fed from active layer into guiding layer in the whole cavity length
corrugated grating Îperiodic refractive index change Î partially reflected
waves
oppositely traveling waves can only coherently coupled to set up a
standing wave, a mode, if their frequency is related to the corrugation
periodictiy Λ
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Prof. Wei-I Lee
Single Frequency Solid State Lasers
Distributed Feedback Laser Diode II.
allowed DFB modes with λm :
, m = 0, 1, 2 …, L : effective length of diffraction grating
relative threshold gain for higher mode is high
Î only m = 0 mode can effectively lase
asymmetry introduced by fabrication process or on purpose
Î only one mode appear
L >> Λ Î ( λm Æ λB )
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Prof. Wei-I Lee
Single Frequency Solid State Lasers
Cleaved-Coupled-Cavity Laser
couple two different laser optical cavities
only waves that can exist as modes in both cavities are allowed
Î restriction in modes and increase separation between modes
Î single mode operation more easily
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Prof. Wei-I Lee
Quantum Well Devices
Single Quantum Well Structure
very thin ( < 50 nm ) narrow Eg active region sandwiched between wider Eg
semiconductors ( Ex. GaAs/AlGaAs SQW : ΔEc > ΔEv )
Î two-dimensional electron gas confined in the x-direction
, d << Dy , Dz
density of electronic states changes in a steplike fashion
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Prof. Wei-I Lee
Quantum Well Devices
SQW and MQW Lasers
advantages of QW lasers to DH lasers :
1. lower threshold current
2. narrower linewidth in λ
advantages of SQW can be extended
by using MQW
MQW design can be combined with
a distributed feedback structure to
obtain a single mode operation
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Prof. Wei-I Lee
Vertical Cavity Surface Emitting Lasers (VCSELs)
Vertical Cavity Surface Emitting Laser
optical cavity along current flow direction
distributed Bragg reflectors as mirrors with high reflectance at λ :
λ chosen to coincide with the optical gain of the active layer
very short cavity length ( a few μm ) :
1. need high reflectance end mirrors (~99%)
2. large separation between longitudinal
modes Æ single mode more probable
unwanted voltage drop thru DBR mirrors
usually circular cross section
matrix emitters possible Î applications in
optical interconnect, optical computing ,
and higher optical power
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Prof. Wei-I Lee
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Prof. Wei-I Lee
Optical Laser Amplifiers
Optical Laser Amplifiers
traveling wave semiconductor laser amplifier :
1. incoming light with λ within optical gain bandwidth of the laser structure
Î stimulated emission and light amplification
2. AR coating at ends to suppress cavity oscillation
3. noise induced by spontaneous emission can be overcome by optical
filter at the output
Fabry-Perot laser amplifier :
1. operated below threshold current to suppress optical gain
2. presence of optical resonator Î λ around cavity resonant wavelength
experience higher gain
Î higher gain,
but less stable
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Prof. Wei-I Lee