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