generation of short pulses jörgen larsson, fysiska instutionen lunds tekniska högskola
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Generation of short pulses
Jörgen Larsson,
Fysiska Instutionen
Lunds Tekniska Högskola
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Generation of short pulses• Cavity modes• Locked cavity modes• Time-bandwidth product• Active mode-locking• Acousto-optic modulation• Passive modelocking• Hybrid modelocking techniques• Kerr lens modelocking• SESAM • Synchrnously pumped dye lasers• Distributed feedback lasers• Fiber lasers• Short-pulse accelerator sources• Group velocity dispersion• Group velocity dispersion compensation• Prism compressor• Chirped mirrors
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Representation of short pulsesGaussian pulses
tjat eeEt 02
*)( 0E
CarrierEnvelopeAmplitudeFrequency
2220
020
2)(
2atrr eE
ct
cI(t)
E
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Representing ”chirp”)(
0
20
2
*)( bttjat eeEt E
btdt
btt
dtt 2
)()( 0
20
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Group velocity dispersion
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Modes in a cavity
Gain profile
(Gain) bandwidth
Mode spacing
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Single Mode
Inte
nsi
ty
40
50
30
20
10
0
(a)
Two Modes
40
50
30
20
10
0
(b)
8 ModesRandom Phases
40
50
30
20
10
0
(c)
8 modesPhases=0 @ t=0
40
50
30
20
10
(d)
Inte
nsi
tyIn
ten
sity
Inte
nsi
ty
0
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Fresnel diagrams
(c)
t= m
2
m
m (c)
m
2
1
t=0
(a) (b)
(d)
m
2
1
t=T=
E 2E mE
E 2E mE
t=t
m
2
1
t
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Time-bandwidth product
time
Frequency
T=2L/c
t
FOURIER TRANSFORM LIMITED
1/T
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Time-bandwidth product- How short pulses can we get?
tjat eeEt 02
*)( 0E
2220
020
2)(
2atrr eE
ct
cI(t)
E
FWHM of the intensity in the temporal domain
2
12212 at
e
atatat
2
2ln2ln2
2
1ln2 21
221
221
atFWHM 2
2ln2
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Time-bandwidth product- How short pulses can we get?
atjat eEeeEt 4
)(
0
20
02
)*))(
F(F(E
aeE)I( 4
)(22
0
)(~
E
FWHM of the intensity in the spectral domain
Next we determine the width in the spectral plane
)2ln(2)(2
1ln
4
)(2
2
1021
20214
)(2
2021
aa
e a
)2ln(22 aFWHM )2ln(2a
vFWHM
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Time-bandwidth product- How short pulses can we get?
Now lets calculate the time-bandwidth product for a gaussian (unchirped) pulse
441.0)2ln(2
2
2ln2
)2ln(2
a
avt FWHMFWHM
If the pulse is chirped it is wider in the temporal domain
441.0FWHMFWHMvt
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Time-bandwidth product- How short pulses can we get?
Task for the interested student:
A Ti:Sapphire laser operating at 800 nm has a 120 nm FWHM spectrum. What is the shortest pulse we can get from this laser?
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Classes of methods for modelockingActive modelocking:
From an active component in the cavity (typically an optic modulator driven by an RF-frequency)
Passive Modelocking
From a passive component in the cavity (Saturable absorber, kerr lens ......)
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Active modelocking Acousto-optic modulation
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Active modelocking Acousto-optic modulation
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Active modelocking Acousto-optic modulationGeneration of sidebands in an AOM
• Optical wave
• Acoustic wave• Optical wave in presence of acoustic wave
)sin()(0
KztiakxtieEE
)sin(0 KztPP
)(0
kxtieEE
nl
a
2
ln
Kztnikkxtidxztkikxti
eEeEEl )sin(
)(
0
),(')(
00
)})sin(2
{)(
0
ln
Kztnnikxti
eE
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Generation of sidebands in an AOM (travelling wave)
)sin()(0
Kztiakxti eeEE
If a<<1
}){2
1( )()()(0
KztiKztikxti eei
iaeEE
Euler’s formulae
))sin(1()(0 KztiaeEE kxti
)22
{ )}({)}({)(0
KzkxtiKzkxtikxti ea
ea
eEE
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Generation of sidebands in an AOM (travelling wave-strong Rf- field)
)sin()(0
Kztiakxti eeEE
m
Kztmim
kxti eaJeEE )()(0 )(
))sin(1()(0 KztiaeEE kxti
m
mKzkxitmm eaJEE )()(
0 )(
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Generation of sidebands in an AOM (standing wave)
)cos()sin()(0
Kztiakxti eeEE
If a<<1
}){2
1}{
21( ))()())()()(
0KziKzititikxti eeee
i
iaeEE
Euler’s formulae
))cos()sin(1()(0 KztiaeEE kxti
}{4
}{4
}{4
}{4
))}({))}({))}({))}({)(0
KzkxtiKzkxtiKzkxtiKzkxtikxti ea
ea
ea
ea
eEE
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Active modelocking
Fig 3.7
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Active modelocking
Fig 3.8
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Passive modelockingSaturable absorber
Fig 3.12
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Passive modelockingSaturable absorber
Fig 3.13
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Gain vs intensity
Fig 3.14
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Passive modelocking
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Passive modelocking-saturable absorber
Fig 3.17
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Passive modelockingSaturable absorber
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Passive modelockingKerr lens
High intensitysmall losses
Low intensitieslarge losses
n=n1+n2I
The beams spatial profile creates the "Kerr lens"
I
x
Titanium sapphirecrystal
Laser beam
Aperture
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Passive modelocking - Saturable semiconductor mirror (SESAM)
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Synchronous pumping
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Frequency filtering
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Passive modelocking-saturable absorber
Fig 3.19
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Hybrid modelocking
Fig 3.20
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Hybrid modelocking
Fig 3.21
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Titanium Sapphire energy level diagram
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Passive modelocking-Kerr lens (early design)
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Modern Titanium Sapphire laser
P1P2
C MCM2
CM1OC
P1,P2 prismsCM1, CM2 curved mirror, krökt spegel(these are transparent for the pump radiation)M mirror, spegelC crystal, kristallOC output coupler utkopplingsspegelL lens for the pump laser
Lpump from Nd-laser