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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Transcript of Generation of short pulses Jörgen Larsson, Fysiska Instutionen Lunds Tekniska Högskola.
Generation of short pulses
Jörgen Larsson,
Fysiska Instutionen
Lunds Tekniska Högskola
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
Representation of short pulsesGaussian pulses
tjat eeEt 02
*)( 0E
CarrierEnvelopeAmplitudeFrequency
2220
020
2)(
2atrr eE
ct
cI(t)
E
Representing ”chirp”)(
0
20
2
*)( bttjat eeEt E
btdt
btt
dtt 2
)()( 0
20
Group velocity dispersion
Modes in a cavity
Gain profile
(Gain) bandwidth
Mode spacing
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
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
Time-bandwidth product
time
Frequency
T=2L/c
t
FOURIER TRANSFORM LIMITED
1/T
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
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
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
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?
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 ......)
Active modelocking Acousto-optic modulation
Active modelocking Acousto-optic modulation
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
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
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 )(
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
Active modelocking
Fig 3.7
Active modelocking
Fig 3.8
Passive modelockingSaturable absorber
Fig 3.12
Passive modelockingSaturable absorber
Fig 3.13
Gain vs intensity
Fig 3.14
Passive modelocking
Passive modelocking-saturable absorber
Fig 3.17
Passive modelockingSaturable absorber
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
Passive modelocking - Saturable semiconductor mirror (SESAM)
Synchronous pumping
Frequency filtering
Passive modelocking-saturable absorber
Fig 3.19
Hybrid modelocking
Fig 3.20
Hybrid modelocking
Fig 3.21
Titanium Sapphire energy level diagram
Passive modelocking-Kerr lens (early design)
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
