femtosecond pulse generationreseau-femto.cnrs.fr/img/pdf/femtouphanna2017.pdfsteady state condition...

Femtosecond pulse generation

Marc Hanna

Laboratoire Charles Fabry

Institut d’Optique, CNRS, Université Paris-Saclay

Outline

Introduction

1 Fundamentals of modelocking

2 Femtosecond oscillator technology

3 The carrier-envelope phase

Conclusion

Why ultrafast pulses?

MPQ

Laser matter interaction

- Multiphoton microscopy- Micromachining- XUV HHG sources

Shortest manmade events

- Ultrafast dynamics- Frequency metrology- Attophysics

MPQ GarchingLasik

t

EPpeak

Ultrashort pulses

t

I(t)

ω

I(ω)

ΔtΔω

Time – Bandwidth Product Kt

FourierTransform

Short pulses imply broad spectra

Ultrashort pulses

0.1

1

10

100

1000S

pectr

al B

andw

idth

(nm

)

2500200015001000500

Center wavelength

10 fs20 fs

50 fs100 fs

1 ps

20 fs @ 0.8 µm wavelength → 34 nm

100 fs @ 1 µm wavelength → 12 nm

Ultrafast sources are complex

Apollon project diagram

OscillatorStretchersAmplifiersNonlinear stages PostcompressionContrastOPA

Pulse shapingBeam shapingCompressor

Outline

Introduction

1 Fundamentals of modelocking

2 Femtosecond oscillator technology

3 The carrier-envelope phase

Conclusion

Longitudinal modes in a laser

cav

kL

ck

Lcav

Gain

Longitudinal modes in a laser

Lopt

Gain

Consider N modes that oscillate simultaneously

If the φn are all equal

Lcav/c0

Longitudinal modes in a laser

50 modes oscillating

In-phase modesRandom phase modes

For a 100 fs pulse, spectrum should be broader than 1500 GHz, typical free spectral range is 100 MHz → thousands of modes!

Modelocked laser

Gain Sat.Abs.

To operate in modelocked regime, we must favour pulsed mode vs CW mode i.e. favor large intensities: saturable absorption

Propagation effects: GVD

Propagating broadband pulses experience dispersion

PropagationMaterial n(λ)

Group velocity Group-velocity dispersion (GVD)

Propagation in a dispersive medium

• Field at the input of the medium : sum of monochromaticwaves

13

Propagation over z

Dispersion: Phase accumulates over distance z according to a different propagation constant for each frequency component

The field at z is given by

Phase velocityCEP

Group velocityPulse broadening

Frequency chirp

For a Gaussian pulse

with

Linear evolution of instantaneousfrequency

tt

pinst

Spectrogram : similar to music sheet

The spectrogram

Propagation effects: GVD

Effect of GVD on the spectrogram

Time (fs)

Fré

quency

(TH

z)

2nd order dispersion

Time (fs)

Fré

quency

(TH

z)

Spectrum

Temporal

profile

Fourier-transform limited

pulse

GVD Engineering

Materials – positive (normal, red ahead) GVD in visible and near IR

Negative GVD – prism pairs, grating pairs, chirped mirrors, GTI mirrors

The longer wavelengths traverse more glass

Propagation effects: SPM

Propagating intense pulses experience self-phase modulation

0 ck n(t)l

0 2n(t) n n I(t)

t

I

tinst

Propagation effects: SPM

Effect of SPM on the spectrogram

Temps (fs)

Fré

quence (

TH

z)

Self-phase modulation

Time (fs)

Fré

quency

(TH

z)

Spectrum Temporal

profile

Fourier-transform limited

pulse

20

Propagation effects: filtering

Even if no filter are inserted in the cavity, the gain medium has a finitebandwidth that limits spectral extension

Increasing gain

λ

Optical pow

er

Spectrum

Gain narrowing

Modelocked laser ingredients

Gain Sat.Abs.

β2 SPM

output

Predicting output pulse involves finding the stationary solution

Analytically – Master Equation of Mode Locking

Numerically – Solving propagation equation over large # roundtrips

Filter

Soliton modelocking

Small changes per roundtrip (low loss low gain)

Balance between anomalous GVD and SPM

Often used in bulk oscillators

Sat.Abs.

β2<0 SPM

Time (fs)

Fré

quency

(TH

z)

Soliton modelocking

Intensity profile

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

t/ t

Inte

nsity p

rofile

(a

. u

.)

Soliton area theorem

with γ given by

)/(sech)( 2

0 tPtP

22E

effAc

n20 → Determines the achievable pulse

energy

The bestiary of stable pulse regimes

Intracavity pulse shaping mechanisms depend on: dispersion, SPM, spectral filtering, saturable gain / losses, and their locations and magnitude in the cavity

Andy Chong, William H. Renninger, and Frank W. Wise, "Properties of normal-dispersion femtosecond fiber lasers," J. Opt. Soc. Am. B 25, 140-148 (2008)

Pulse shaping mechanisms

Gain Sat.Abs.

β2 SPM

output

Filter

Example: ANDi lasers

All-normal dispersion lasers

Andy Chong, William H. Renninger, and Frank W. Wise, "Properties of normal-dispersion femtosecond fiber lasers," J. Opt. Soc. Am. B 25, 140-148 (2008)

Output

→ allow larger nonlinear phase shifts per roundtrip and energy scaling

Outline

Introduction

1 Fundamentals of modelocking

2 Femtosecond oscillator technology

3 The carrier-envelope phase

Conclusion

Gain media

1 Ti:Sapphire oscillators

2 Yb:bulk oscillators

3 RE:fiber oscillators

Ti:Sa is the best

absorption

émission

Inte

nsi

té (

u.a

.)

Longueur d’onde (nm)

absorption

émission

Inte

nsi

té (

u.a

.)

Longueur d’onde (nm)

Extremely broad gain bandwidth (5 fs @ 800 nm)

Large emission cross section (41×10-20 m2 @ 780 nm)

Fluorescence lifetime 3 µs

Thermal conductivity 35 W K-1 m-1

A standard Ti:Sa cavity

HR mirror

Tuning slit

Green pump laser

Ti:Sa crystal

Outputcoupler

KLM slit

Prisms for GVD control

Typical performances: 10 – 30 nJ pulse energy at 80 MHz (1 - 2 W) tunable from 700 to 1000 nm sub-100 fs pulses (down to 6 fs!)

Kerr lens saturable absorber

0 2n(x) n n I(x)

Usually requires additional perturbance to start modelocking

→ vibrating mirror

Commercial Ti:Sa oscillators

The Ti:Sa problem

Must be pumped in the green spectral region

Nd laser SHG

Large quantum defect, inefficient, complex, large footprint, expensive…

… but still used in many applications because of its extraordinaryproperties (extreme tunability and short pulsewidth)

Gain media

1 Ti:Sapphire oscillators

2 Yb:bulk oscillators

3 RE:fiber oscillators

Yb:bulk oscillators

Moderatly broad gain bandwidth (host-dependent)

Low emission cross section (host-dependent)

Fluorescence lifetime few 100s µs – few ms

Thermal conductivity 1 - 10 W K-1 m-1

Low quantum defect

Diode pumping @ 980 nm !

Yb-doped materials

Most used material Yb:YAG

But limited gain bandwidth: work on CaF2, CALGO, KYW

Properties are very host-dependent

σ

10-24 m2

∆λ

nm

τfluo

ms

κ

W/m/K

Yb:YAG 2.2 5 0.95 11

Yb:glass 0.05 40 1 0.8

Yb:KYW 3 10 0.7 3.3

Yb:CALGO 0.75 60 0.4 6.5

Yb:CaF2 0.25 30 2.5 9

A standard Yb:bulk cavity

Saturable absorption is usually implemented using a SESAM (SEmiconductor Saturable Absorber Mirror)

Crystal

Dichroic mirror

Prism

Laser diode

PrismSESAM

Typical performances: 10 – 30 nJ pulse energy at 50 MHz (1 - 2 W) at 1030 nm 300 fs pulses

SESAM

Design parameters:

modulation depthsaturation fluence recovery time nonsaturable losses

Often self-starting

Commercial Yb:bulk oscillators

Smaller footprint, less expensive thanTi:Sa…

… but longer pulses

Gain media

1 Ti:Sapphire oscillators

2 Yb:bulk oscillators

3 RE:fiber oscillators

RE:fiber oscillators

Large and broad gain bandwdith (~ 100 fs pulsewidth)

Monolithic integration, robutness, no spatial stability considerations

Large design freedom (nonlinearity dispersion etc)

Yb Er Th

Example of a modelocked oscillator

Erbium 50 pJ 50 MHz (2.5 mW) 1550 nm 150 fs

Ytterbium 100 pJ 50 MHz (5 mW) 1030 nm 150 fs

Thulium 100 pJ 10 MHz (1 mW) 2000 nm 500 fs

Nonlinear Amplifier Loop Mirror

Unbalanced Sagnac interferometer

Relative phase depends on pulse intensity

Commercial RE:fiber oscillators

Even smaller footprint, even lessexpensive than bulk

… but lower energies

Current research

1 Ti:Sapphire oscillators

2 Yb:bulk oscillators

3 RE:fiber oscillators

Selected current research – Ti:Sa

Selected current research – Ti:Sa

500 mW 50 fs @ 400 MHz

Both SESAM and KLM

« Low cost » Ti:Sa

48

Selected current research – Yb:bulk

242 W 1 ps 80 µJ 3 MHz soliton modelocking

HHG demonstrated with additional nonlinear compression

Selected current research – Yb:bulk

Selected current research – Yb:fiber

Selected current research – Yb:fiber

Step like saturable absorber, must be injected to start

Outline

Introduction

1 Fundamentals of modelocking

2 Femtosecond oscillator technology

3 The carrier-envelope phase

Conclusion

The carrier-envelope phase

• Influence of a constant phase term φCEP for a very short pulse

-20 -15 -10 -5 0 5 10 15 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (fs)

Ele

ctr

ic f

ield

(a.u

.)

)(

2

0

2

0

)(

2exp)( CEPpti

et

tEtE

0CEP

The carrier-envelope phase

• Influence of a constant phase term φCEP for a very short pulse

-20 -15 -10 -5 0 5 10 15 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (fs)

Ele

ctr

ic f

ield

(a.u

.)

)(

2

0

2

0

)(

2exp)( CEPpti

et

tEtE

2/ CEP

The carrier-envelope phase

• Influence of a constant phase term φCEP for a very short pulse

-20 -15 -10 -5 0 5 10 15 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (fs)

Ele

ctr

ic f

ield

(a.u

.)

)(

2

0

2

0

)(

2exp)( CEPpti

et

tEtE

CEP

The carrier-envelope phase

• Influence of a constant phase term φCEP for a very short pulse

-20 -15 -10 -5 0 5 10 15 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (fs)

Ele

ctr

ic f

ield

(a.u

.)

)(

2

0

2

0

)(

2exp)( CEPpti

et

tEtE

2/3 CEP

The carrier-envelope phase

• Influence of a constant phase term φCEP for a very short pulse

-20 -15 -10 -5 0 5 10 15 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (fs)

Ele

ctr

ic f

ield

(a.u

.)

)(

2

0

2

0

)(

2exp)( CEPpti

et

tEtE

0CEP

CEP vs propagation

Field after propagation in a dispersive material

02

After propagation over z, maximum of the envelope for tmax=z/vg

At this point the phase is equal to

CEP

p

g

p

CEPL

zzk

v

zz

2)(

nnL

g

CEP

CEP vs propagation

CEP phase is accumulated upon propagation due to differencebetween phase and group velocity

CEP

p

g

p

CEPL

zzk

v

zz

2)(

nnL

g

CEP

Fused silica Air

Consequence of CEP evolution in a cavity?

Gain Sat.Abs.

β2 SPM

output

Filter

Steady state condition for a mode-locked laser

• For a mode-locked laser with repetition rate equal to T, the steady state condition is on the pulse shape, not on the roundtrip phase like in CW

• Stationnary if R(ω)=1, leading to perfectly regular frequencycomb spacing

CEP phase slip

The angular frequency ωCEO represents the rate at which the CEP phase drifts at the output of a mode-locked laser

Fourier

Transform

CEP: summary

CEP: Carrier-envelope phase

Phase of the carrier at the pulse maximum

CEO: Carrier-envelope offset

Frequency shift of the comb, induces a continuous drift of the CEP for successive pulses

Outline

Introduction

1 Fundamentals of modelocking

2 Femtosecond oscillator technology

3 The carrier-envelope phase

Conclusion

Conclusion

Femtosecond oscillators – large variety concepts, technologies, and performance, almost exclusively based on modelocking

Often used as a subsystem in a larger source setup (MOPA, OPCPA) so that few characteristics are retained at the end

Some properties e. g. repetition rate stability are carried over

Ti:Sa oscillators are still widely used for some applications (high field physics, nonlinear microscopy), but are not predominant anymore

66

Bonus: Non modelocked fs sources

67

Bonus: Non modelocked fs sources

140 fs 2.4 µJ pulses @ 1030 nm… without modelocking!

Thank you

Other gain media

Other notable gain media at different wavelengths

Nd:glass (1053 nm)

Cr:LiCAF, Cr:LiSAF (800 nm)

Cr:ZnSe (2.4 µm)

Cr:fosterite (1.25 µm)

Ho:YAG (2 µm)

70

NPE SA