36
Principles of Lasers
Cheng Wang
Phone: 20685263 Office: SEM 318
The course
4 credits, 64 credit hours, 16 weeks, 32 lectures
70% exame, 30% project including lab
Reference:
O. Svelto, Principles of Lasers, Springer, 2010 (main)
B. Saleh and M. Teich, Fundamentals of Photonics, Wiley, 2007
William T. Silfvast, Laser Fundamentals, Cambridge, 2004
2
Electromagnetic spectrum 3
Electromagnetic spectrum 4
Ref: Wikipedia
5 Photons
A photon is an elementary particle, the quantum of all forms of
electromagnetic radiation including light.
1. Photons exhibit wave-particle duality, both waves and particles
2. Photon has zero rest mass
3. Photon energy
4. Photon momentum wave number
5. Photon has 2 possible polarization states
6. Photons obey the Bose-Einstein statistics, rather than the Fermi Dirac statistics (electrons, neutron, proton>> Pauli exclusion principle: two identical fermions cannot occupy the same quantum sate simultaneously)
http://actu.epfl.ch/news/the-first-ever-photograph-of-light-as-both-a-parti/
/E hv hc
p k 2 /k
LASER:
6
Light Amplification of Stimulated Emission of Radiation
Lasers in our life
https://youtu.be/D0DbgNju2wE
7
Approaches 8
Classical Appr. Semi-classical Appr. Quantum Appr. Approach Classical thoery Semi-classical theory Quantum theory (Quantum Electrodynamics)
Matter Classical, Newtonian mechanics
Quantized, Quantum mechanics
Quantized, Quantum mechanics
Light Classical, Maxwell’s equations
Classical, Maxwell’s equations
Quantized, Quantum field thoery
Complexity Simple middle complex
Chapter 1 Introduction_L1
Laser history
Laser concept
Laser properties
9
Discovery of stimulated emission in 1917 10
Ref: S. Domsch, Basics of Laser Physics, at Univeritaetsmedizin Mannheim
Maser in 1950s 11
Charles Hard Townes Jim Gordon
First Laser in 1960 (Ruby) 12
@694 nm https://www.youtube.com/watch?v=h5ZgJBuq4XY
Nobel prize in physics in 1964 13
14
11
• January 1962: observations of superlumenscences in GaAs p-n junctions
(Ioffe Institute, USSR).
• Sept.-Dec. 1962: laser action in GaAs and GaAsP p-n junctions
(General Electric , IBM (USA); Lebedev Institute (USSR).
Condition of optical gain: EnF – Ep
F > Eg
Lasers andLasers and LEDsLEDs onon pp––n junctionsn junctions
Wavelength
Lig
ht
inte
nsity
“+”
“–”Cleaved mirror
p
nGaAs
EnF
EpF
EgL
pD
LnD
h
Ref: Z. Alferov, Semiconductor Revolution in the 20th Century, St Petersburg Academic University
15
1717
The Nobel Prize in Physics 2000The Nobel Prize in Physics 2000
"for basic work on information and communication technology"
Zhores I.
Alferovb. 1930
Herbert
Kroemerb. 1928
Jack S.
Kilby1923–2005
“for his part in the
invention of the
integrated circuit”
“for developing semiconductor
heterostructures used in high-speed- and
opto-electronics”
Laser-related Nobel prizes in Physics 16
17 Laser-related Nobel prizes in Physics
18 Laser-related Nobel prizes in Physics
Charles H. Townes, How the Laser Happened, Oxford, 1999
International Year of Light 19
In proclaiming an International Year focusing on the topic of light science and its applications, the UN has recognized the importance of raising global awareness about how light-based technologies promote sustainable development and provide solutions to global challenges in energy, education, agriculture and health. Light plays a vital role in our daily lives and is an imperative cross-cutting discipline of science in the 21st century. It has revolutionized medicine, opened up international communication via the Internet, and continues to be central to linking cultural, economic and political aspects of the global society.
Chapter 1 Introduction_L1
Laser history
Laser concept
Laser properties
20
Absorption of light 21
When light passes through materials it is usually absorbed.
In certain circumstances light may be amplified. This was called “gain” (negative absorption) It is the basis of laser action
Interaction of light and an atom 22
E2
E1
hv
hv=E2-E1
Absorption
E2
E1
hv
hv=E2-E1
Spontaneous emission
E2
E1
hv
hv=E2-E1
Stimulated emission Stimulated emission produces
photons in the same phase and
direction, different to spontaneous
emission
Non-radiative decay…
Probability of the processes 23
Spontaneous emission
2 2
sp sp
dN N
dt
Non-radiative decay (no photon)
2 2
nr nr
dN N
dt
Stimulated emission
221 2s
st
dNF N
dt
Absorption
112 1s
a
dNF N
dt
Cross section relation
2 21 1 12g g
21
12
: Carrier population (number)
: Photon flux (number)
: Spontaneous emission lifetime
: Nonradiative decay lifetime
: Cross section of stimulated emission
: Cross section of absorption
: D
X
s
sp
nr
X
N
F
g
egeneracy of the energy level
1
sp
A
21 21 sW F
12 12 sW F
Rates relation
2 21 1 12g W g W
Population vs. time 24
/
2 2( ) (0) spt
spN t N e
N(0)e-1
sp
Po
pu
lati
on
N2
Time t
N(0)
Carrier decay due to spontaneous emission
Boltzman distribution 25
Thermal equilibrium: A system is said to be in thermal equilibrium if the temperature within the system is spatially and temporally uniform (constant), where the motion of atoms reach a steady state, and the atom fluctuations are, on average, invariant to time.
2 2 2 1
1 1
( ) exp( / )
exp
mm m
NP E E kT
N
N g E E
N g kT
kT = 25.7 meV @298 K
Population inversion (non-equilibrium)
22 1
1
gN N
g
Under thermal equilibrium
22 1
1
gN N
g
Ref: B. Saleh and M. Teich, Fundamentals of Photonics, Wiley, 2007
Amplification or absorption of light 26
dz
FS FS+dFS
Photon generation
21 2 12 1
221 2 1
1
S S S
S
dF F N F N dz
gF N N dz
g
Amplifier 0g
Absorber g 0
Gain coefficient: the material capability of amplifing light
s 221 2 1
1
1g
s
dF gN N
F dz g
( ) (0) gz
S SF z F e
Ph
oto
n F
s
Length z
The way to laser 27
Population inversion
Active material, gain medium
Amplifier
Oscillator
Laser (Maser)
2( )
1 2(2 ) (0) ig L
S SF L F e R R
1 Si
s
dF
F dz
Loss coefficient
Threshold condition
2( )
1 2
1 2
(2 ) (0)
1
ln( ) / 2
i
S S
g L
th i
F L F
e R R
g R R L
Active medium Mirror R1 Mirror R2
Length L
Pump
Laser components:
Active medium
Resonant Cavity (mirrors)
Pump source
Pump 28
Two-level system
Three-level laser system Four-level laser system
Pump is the process to lift atoms from a low state to a high state.
It can be realized by intense light source or electrical source.
Two-level system is impossible to lase. (Best is N2=N1)
Three-level system can lase due to the long lifetime of level 2,
but still needs strong pump. (Threshold N2=N1, Ruby laser, pulsed)
Four-level system can lase easily, due to the quasi-empty level 2.
Chapter 1 Introduction_L1
Laser history
Laser concept
Laser properties
29
Laser fundamental properties 30
Monochromaticity
Coherence (phase correlation)
Directionality
Brightness
1. Monochromaticity--- optical linewidth olv
2. Temporal coherence --- coherence length Lc
/c c olL c c v
3. Spatial coherence --- coherence area Dc
4. Directionality--- beam divergence
cD
dD
Difraction limit
D is the mirror diameter
Laser
2 410 ~10 (0.57 ~ 0.0057 )rad
1.22 for plane wave
Note: Wave optics 31
In the framework of wave optics, Wavefront is the collection of points characterized by propagation of position of the same phase: a propagation of a line in 1d, a curve in 2d or a surface for a wave in 3d.
The wavefronts of a plane wave are planes.
The wavefronts of a spherical wave are planes.
A lens can be used to change the shape of wavefronts. Here, plane wavefronts become spherical after going through the lens.
Note: Huygens’ principle 32
Huygens principle: Each point at the wavefront becomes a source for the secondary
spherical wave. At any subsequent time, the wavefront can be determined by the sum
of these secondary waves.
Brightness of laser 33
Brightness: The light power per unit projected surface area of the light source per unit solid angle.
2 unit: W/
cos
dPB cm sr
dS d
2 2
2
sin
/ 2
PB
S
P
R
P
D
2
2dB P
Difraction limit
D
Laser
Normal to the emission surface
Note: Solid angle 34
Ref: A. V. Arecchin, T. Messadi; R. J. Koshe, Field Guide to Illuminatin, SPIE, 2007
Types of lasers 35
Physical state: solid state, liquid, and gas lasers. (free electron lasers)
Wavelength: infrared, visible, UV, and X-ray lasers. (1 mm---1 nm)
Power: CW laser from nW to a few MW; Pulsed laser peak power up to PW (1015 W)
Pulse duration: from ms down to fs (10-15 s)
Cavity length: from nm up to km
Homework 36
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