basics of lasers · laser wavelength 1.064 1.05-1.06 µm laser upper lifetime σfor stimulated...
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Basics of lasers Slide: 1 - 1
Basics of lasers
Nathalie VermeulenBrussels Photonics Team (B-PHOT)
Vrije Universiteit Brussel
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Basics of lasers Slide: 1 - 2
Some examples of laser applications
telecom
optical data storage
cutting steel cleaning and restoring art
laser projectors
laser medicine
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Basics of lasers Slide: 1 - 3
Light
Amplification
by Stimulated
Emission
of Radiation
All special properties of laser light find their origin in this stimulated emission.
Introduction
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Basics of lasers Slide: 1 - 4
Interaction between light and matter
Model = “thermodynamic” model of Einstein:
• atom = two-level system, energy difference ∆E (≈ eV)
• light = either a wave or a collection of photons
Interaction only possible when ∆E = h f0
Three different kinds of interaction between light and matter:
• absorption
• emission spontaneous
stimulated
f0
E2
E1
f0
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Basics of lasers Slide: 1 - 5
General description of absorption
Each absorbing atom in energy level #1 is represented by a circular disc of area σ,
its “cross section”.
The incident light is measured by the photon flux density F.
F = number of incident photons per second and per square meter
f0
E2
E1
N2
N1
Assume we have a box with two-level atoms in it.
There are N1 atoms per m3 in lower energy level #1 and N2
atoms per m3 in upper level #2.
dzF
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Basics of lasers Slide: 1 - 6
Absorption and transmission through matter
Lambert-Beer law for absorption
F(z) = F (0) e−σ N
1 z
F
z
dzF
dN1
dt= − F σ N1
Rate equation for absorption
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Basics of lasers Slide: 1 - 7
Rate of change:
Spontaneous emission
E2
E1
f0
N2
N1
2 22 21 2
212 2
(1 10)
(1 11)
( ) (0) A t
dN dNN A N
dt dt
N t N e
−
−−
∝ ⇒ = −
⇒ =t
N2(0)
N2
1e
τsp=A21-10
= “life time”
Consider an atom that has been excited to level 2.
⇒ spontaneous decay to level 1 with the emission of light
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Basics of lasers Slide: 1 - 8
Light is emitted
- in all directions
- in a broad spectral emission line
- no phase relation (= no coherence)
Example: High pressure lamp
Properties of spontaneous emission
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Basics of lasers Slide: 1 - 9
Photon incident on excited atom:
no absorption possible, but instead the photon forces
the atom to jump to its lower level, with emission of a
new photon
⇒ stimulated emission
General description of stimulated emission
E2
E1
f0
N2
N1
The new wave has
- the same direction
- the same frequency/wavelength ⇒ the light is amplified
- the same phase (coherent)
This is the basis of laser action.
⇒ LASER = Light Amplification by Stimulated Emission of Radiation
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Basics of lasers Slide: 1 - 10
Calculation of stimulated emission
The reasoning is completely analogous to the reasoning for absorption.
The cross section for absorption is identical to the one for stimulated emission.
⇒
Rate equation for stimulated emission
dN2
dt= − F σ N2
dz
E2
E1
f0
N2
N1
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Basics of lasers Slide: 1 - 11
Total rate equation:
spontaneous stimulated absorption emission emission N1+N2=const ⇒ dN1= - dN2
Total rate equation and laser action
dN1
dt= A21N2 + σF(N2 − N1) (1 − 13)
In thermal equilibrium: ⇒ N2 ≈ 0 ⇒ absorption dominates
For realizing emission, the atom should be excited: N2 ≠ 0.
As long as N2 < N1, net emission is spontaneous.
Stimulated emission will be dominant only when N2 > N1 .
⇒ Amplification is only possible when this “population inversion” (N2 >>>> N1) is obtained.
N2
N1
= e−
∆E
kT ≈ 0 (1 − 14 )
E2
E1
N2
N1
(1-15)
(1-16)
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Basics of lasers Slide: 1 - 12
Amplification of light
Lambert-Beer law for amplification
F(z) = F (0) eσ (N
2− N
1) z
(1 − 17)
F
z
dzF
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Basics of lasers Slide: 1 - 13
Basic laser set up
Two mirrors provide feedback; they form the resonator.
One mirror (here the rear mirror at the right) is a little bit
transparent to couple part of the beam out of the resonator.
Pump: energy input
creates the population
inversion
useful
laser beam
Amplifying medium (gas, liquid,
solid-state, semiconductor) with
population inversion
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Basics of lasers Slide: 1 - 14
First laser: ruby laser realized by T. Maiman (1960)
Mirror
(polished crystal
facet with silver
coating)
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Basics of lasers Slide: 1 - 15
A few examples of lasers nowadays
Solid-state laser Dye laser
Fiber laser Semiconductor laser
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Basics of lasers Slide: 1 - 16
Modes in a laser resonator: a simple picture
Light bounces back and forth in the resonator
⇒ standing waves are created; they are called
modes.
[ ](1 22)
2
cf N
L−⇒ =
[ ][ ]( ) (1 23)300 for 0.5
2
cf MHz L m
L−∆ = ≈ =
[ ] 6(1 21)2 ( 10 ) N L Nλ −= ≈
etc etc
f
Wave picture: two distinct modes
with a different wavelength
L
λ
2
NN+1
with : optical path length
: longitudinal mode number[ ]L
N
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Basics of lasers Slide: 1 - 17
Frequency dependence of gain: line broadening
f0f
FWHM
σ(f)
f0f
gain
Small-signal gain g0(f)Saturated gain g(f)
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Basics of lasers Slide: 1 - 18
Lasing modes
The modes in a resonator without amplifying
medium form an infinite comb of
frequencies.
In a laser setup, i.e. a resonator with
amplifying medium, modes are only excited
if their frequencies are situated within the
gain bandwidth of the amplifying medium.
Moreover their gain should exceed the losses
of the laser.
As a result, only a limited number of
modes/frequencies will actually experience
lasing action.
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Basics of lasers Slide: 1 - 19
Line broadening in different types of lasers
The shape and width of the gain curve (and hence the number of modes) strongly depends on
the type of amplifying medium.
Some examples
Solid-state laser (ruby):
∆f ≈ 30 GHz
⇒ ∆λ ≈ 50 pm
(many modes)
Gas laser: ∆f ≈ 1GHz Semiconductor laser: ∆f ≈ 1500 GHz
⇒ ∆λ ≈ 3 pm ⇒ ∆λ ≈ 5 nm (few modes) (many modes)
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Basics of lasers Slide: 1 - 20
All unusual properties of laser light are a consequence of the properties of stimulated
emission.
In theory one would expect laser light to be
- monochromatic (one frequency or one wavelength)
- collimated (one direction)
- coherent (one phase)
In practice laser beams are not that perfect…
Basic properties of laser light
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Basics of lasers Slide: 1 - 21
In theory only light rays parallel to the optical axis are amplified by stimulated emission
⇒ the laser beam should be perfectly parallel
In reality light is a wave ⇒ diffraction occurs and the laser beam diverges
Typical value: θ ≈ 10-3 rad (=1mm at a distance of 1 m)
⇒ not perfectly parallel, but better than any other light source
D
θ
laser
One direction = collimated
θ ≈ λ
D
wavelength
opening (1-32)
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Basics of lasers Slide: 1 - 22
In theory: one frequency In reality: line broadening ⇒ multiple modes
gas laser
semiconductor laser
⇒ not perfectly monochromatic, but better than any other light source
P
λ(nm)400 800
One frequency = monochromatic
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Basics of lasers Slide: 1 - 23
⇒ not perfectly coherent, but better than any other light source
1
cohcoh
c fτ
π= =
∆
l
One phase = coherent
In theory all waves are in phase, so laser light
should be completely coherent…
… as opposed to completely incoherent light of
other light sources.
In reality laser light is only coherent over a
limited length (coherence length lcoh) or a
limited time (coherence time τcoh)
⇒ the smaller the laser linewidth Δf,
the larger lcoh and τcoh
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Basics of lasers Slide: 1 - 24
The total power P of a laser beam is (usually) rather small,
but the intensity I is extremely high.
Intensity = power per unit solid angle
Example (orders of magnitude)
P I
light bulb 10 W 1 W/sr
low power laser 1 mW 103 W/sr
ΩP
I =P
Ω (
W
sr)
Laser light is intense
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Basics of lasers Slide: 1 - 25
The need for more than two energy levels
It is not possible to obtain population inversion in a
system with only two energy levels.
Reason: since σ12=σ21, the transition probability 1→2
equals the transition probability 2→1, and one obtains
at most population saturation, i.e. N1=N2 .
To obtain population inversion, one needs a 3-level or, even better, a 4-level system.
N2
N1
level 2
level 1
level 3 N3 ≈ 0
N2
N1 ≈ 0
level 0 N0
pump
fast
laser
fast
N2
N1
level 3 N3 ≈ 0
pumpfast
laser
laserpump
Three-level scheme
Four-level scheme
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Basics of lasers Slide: 1 - 26
CO2 laser as an example of a gas laser
CO2 laser is an electrically-pumped four-level gas laser with far-infrared laser emission
bending
symmetric stretching asymmetric stretching
Properties
Infrared radiation
Multiple vib-rot energy levels leading
to a range of emission lines
Very high power (up to multi-kW)
(001)
(100)
Wavelength (µm)
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Basics of lasers Slide: 1 - 27
Applications of CO2 laser: material processing
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Basics of lasers Slide: 1 - 28
Nd laser as an example of a solid-state laser
Property Nd:YAG Nd:glass units
Laser wavelength 1.064 1.05-1.06 µm
Laser upper lifetime
σ for stimulated emission
230
28
300
3
µs
10-24 m2
Spontaneous emission linewidth
Operation regime
0.45
CW+pulsed
18-28
pulsed
nm
Power levels CW: up to
several kW
Pulsed: up
to several J
up to
several J
Nd:YAG
Nd laser is an optically-pumped four-level solid-state laser with near-infrared laser emission
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Basics of lasers Slide: 1 - 29
Applications of Nd laser: in multiple domains
1 kW CW Nd:YAG laser
pumped with flashlamp
used for material processing
50W CW diode-pumped Nd:YAG laser
used for medical applications and
for pumping other lasers
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Basics of lasers Slide: 1 - 30
Er:glass laser as an example of a fiber laser
Er fiber laser is an optically-pumped three-level fiber laser with near-infrared laser emission
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Basics of lasers Slide: 1 - 31
Applications of Er fiber laser: in telecom
Erbium fiber lasers and amplifiers are used in
telecom applications, e.g. EDFAs in undersea
fiber communication links.
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Basics of lasers Slide: 1 - 32
Transients in a gas laser
time
pump
Wp
time
S
Po
wer
(a.u
.)
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Basics of lasers Slide: 1 - 33
Transients in a solid-state laser
time
pump
Wp
time
S
S0
10 µs
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Basics of lasers Slide: 1 - 34
Pulsed operation
Modulator
⇒ Easiest approach: simply “cut” a pulse
out of a cw laser beam using a modulator
outside the cavity
⇒ Best approach: put a modulator
inside the cavity
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Basics of lasers Slide: 1 - 35
Pulsed operation: Q-switching
1. The laser is pumped with a closed shutter.
Hence no laser action is possible, but
population inversion does build up.
2. Suddenly the shutter opens very quickly.
3. The stored energy is immediately released
and the population inversion drops to its
steady-state value.
4. This is accompanied by the creation of a
giant laser pulse.
laser amplifier
shutter
time
shutter
time
Wp
time
N2
time
P
open
closedclosed
1
2
3
4
pumppump
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Basics of lasers Slide: 1 - 36
Pulsed operation: modelocking (1)
Calculated time evolution of the output power of a solid-state laser with 50 modes featuring a random phase;
∆ν is the frequency difference between adjacent modes; ∆νL is the total oscillation bandwidth
• When Φl(t) is not stochastic, the total field shows a regular time pattern ⇒ mode-locking
Most lasers oscillate in many (longitudinal) modes. The total field is then
E(t) = Σ E0,l expj(ωlt+Φl(t)
• Usually Φl(t) is stochastic ⇒ all those modes behave independently from each other (they are “mutually incoherent”) ⇒ fluctuating output
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Basics of lasers Slide: 1 - 37
Pulsed operation: modelocking (2)
∆t
∆τ
∆τ
Ppeak
Paverage
Train of pulses of a mode-locked fiber laser
16 ps
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Basics of lasers Slide: 1 - 38
Conclusion
• Lasing action requires a laser-active medium with at least 3 energy
levels, a resonator, and pumping for establishing population inversion
in the medium.
• Only lasers generate monochromatic, coherent and highly directional
light.
• Possible danger of laser light is not in its power but in its intensity.
• Gas, solid-state, and semiconductor lasers have totally different
properties regarding lasing wavelengths, output powers, pumping
mechanisms, transient behavior, applications, …
• Pulsed operation through e.g. Q-switching or modelocking can be
obtained using an intra-cavity ‘shutter.’