Femtosecond Pulse Generation

Femto-UP 2020-21 School Femtosecond Pulse Generation

Adeline Bonvalet Laboratoire d’Optique et Biosciences CNRS, INSERM, Ecole Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

1 Definitions

Electric field of a 10-fs 800-nm pulse nano 10-9 sec pico 10-12 femto 10-15 2,7 fs atto 10-18 10 fs

time

2 Many properties

Electric field of a 10-fs 800-nm pulse High peaki power (Energy /Duration)

Ultrashorti Duration

Spectral Properties i (Frequency Comb) time

3 Time-resolved spectroscopy

Electric field of a 10-fs 800-nm pulse Ultrashorti Duration

Time-resolved spectroscopy Direct observation of ultrafast motions

time Ahmed Zewail, Nobel Prize in chemistry 1999, femtochemistry 4 Imaging

Electric field of a 10-fs 800-nm pulse High peaki power (Energy /Duration)

Nonlinear microscopy

time

5 Material processing

Electric field of a 10-fs 800-nm pulse High peaki power (Energy /Duration)

Laser matter interaction Drilling, cutting, etching,…

time

Areas of applications : aeronautics, electronics, medical,6 optics… Light matter interaction

Electric field of a 10-fs 800-nm pulse High peaki power (Energy /Duration)

Ability to reach extreme conditions (amplified system) Applications : Sources of intense particles beams, X-rays, high energy density science, laboratory astroprophysics …

time

7 Metrology

Electric field of a 10-fs 800-nm pulse Spectral Properties i (Frequency Comb)

Nobel Prize 2005 "for their contributions to the development of laser-based time precision spectroscopy, including the optical frequency

comb technique." 8 Outline

Introduction

1. Description of ultrashort light pulses

2. Generation of femtosecond laser pulses via mode locking

3. Femtosecond oscillator technology

9 Introduction

Ultrashort pulse = broad spectrum

What makes the difference between white light and femtosecond pulses ?  Manuel Joffre

10 Definitions : Electric fields Real electric field

Ultrashort pulse

Fourier = Transfom sum of monochromatic waves

 d E(t)   E()exp(it)  TFE()   2

 E()   E(t) exp(it)dt TF 1E(t)  

11 Definitions : Complex electric fields

Real electric field

TF-1

Complex spectral field

 ()   () exp(i()) Spectral phase TF Complex temporal field

 (t)   (t) exp(i(t))

12 Temporal phase 12 Definitions : Complex electric fields

Real electric field

TF-1

Complex spectral field

 ()   () exp(i())

TF  (t )  TF ( ( )) Complex temporal field

 (t)   (t) exp(i(t))

13 13 Definitions : Intensity

Temporal Intensity Time width

2 t  t  t0  ε c 2 I(t)  n 0  (t) 2 Spectral width Spectral Intensity 2     0   c 2 I()  n 0  () 2

1 t  i 2 Short pulse = broad spectrum 14 Gaussian pulse

Temporal field

Gaussian Carrier Temporalfield envelope wave

FT-1

Spectral field Spectral field Gaussian envelope centered on the carrier frequency 15 Gaussian pulse

Temporal intensity RMS width

Spectral intensity

16 Gaussian pulse

Temporal intensity RMS width

Spectral intensity

17 Gaussian pulse

Temporal intensity RMS width

The uncertainty limit is only reached for Gaussian pulses

i i

Spectral intensity for a given spectral width, the Gaussian pulse has the shortest possible duration

18 Gaussian pulse

Temporal intensity FWHM Full Width at Half Maximum

i Spectral intensity

For l=1 mm Pulse duration = 100 fs / Spectral bandwidth = 14,6 nm 19 Temporal profile and spectral phase Spectral amplitude Spectral amplitude

 ( )   ( ) exp( i ( )) Temporalamplitude Temporalamplitude

20 Temporal profile and spectral phase Spectral amplitude Spectral amplitude FT-1 FT-1 Temporalamplitude Temporalamplitude

21 Effects of the spectral Phase

i Group delay = relative delay of a spectral component

22 Effects of the spectral Phase

The first two terms have no Constanti impact on the temporal shape

Temporal translation i of the envelope

23 Effects of the spectral Phase

Constanti

Temporal translation i of the envelope t 24 Effects of the spectral Phase

The group delay varies linearly with the frequency

t 25 Parabolic spectral phase

Spectral Phase

Group delay

Temporal field

up-chirpedFT limited down-chirped 26 Propagation effects

Spectral phase accumulated by propagation :

27 Propagation effects

Spectral phase accumulated by propagation :

Constanti delay

Group velocity (velocity of the envelope) Propagation effects

Spectral phase accumulated by propagation :

Group Delayi Dispersion Constanti delay (GDD)

Group velocity The pulse is chirped (velocity of the envelope) 29 Quizz

What is the output pulse after propagation in a material with k’’>0?

Back of the pulse Front of the pulse 30 Quizz

The high frequency components present a higher group delay, they are at the back of the pulse

31 Duration after propagation in a dispersive material Materials transparent in the visible : k’’>0

of Fused silica uainatrpropagation (fs) after Duration

Duration before propagation (fs)

Dispersive effects higher for shorter pulses

32 Summary 1

 ()   () exp(i())

1  Short Pulse = broad spectrum t  2  The spectral phase governs the temporal shape

 Non linear spectral phase = group velocity dispersion

 Propagation in transparent material = up chirped pulse

33 Outline

Introduction

1. Description of ultrashort light pulses

2. Generation of femtosecond laser pulses via mode locking

3. Femtosecond oscillator technology

34 Fundamental of mode locking

Gain medium

Dispersion Mode locking

Compensation Gain medium Non linear effect of the dispersion • Gain for mode locking • • Wavelength • Prismsi i AOM i • Gratings • Pulse duration •Kerr-lens • Chirped mirrors • Pumping • Saturable absorber

35 Gain medium

End mirror Output coupler Gain medium

Longitudinal modes in the frequency domain

36 Longitudinal modes

in time domain

Example :

N modes >100 000 …

… Random phase modes

In-phase modes :

37 Mode locking

time domain frequency domain FT

Mode locking = phases locked Train pulses separated by the round trip time Spectral width increases with N Duration decreases with N

38 Mode locking

Idea :to favor pulsed regime over continous one

Loss modulation

Active modelocking Acousto-optic modulator Electro-optic modulator Passive modelocking KLM SESAM

Figure from book chapter Ultrafast solid-state lasers, Ursula Keller39 Active modelocking

Acousto-optic (or electro-optic) modulator synchronized with the resonator round trip

Piezo + RF modulator Ω =π c/L

Diffracted and frequency shift beam

Generation of a grating that turns ON and OFF at a frequency 2Ω = c /2L

40 Passive modelocking

Self amplitude modulation of the light by fast loss saturation

Shorter pulse Starting with noise fluctuations

• Kerr Lens • Saturable absorber Cavity round-trip time

41 Kerr lens modelocking

Kerr effect: Nonlinear change in refractive index Fast (few fs) and broadband

KLM = Kerr Lens Modelocking

Self focusing + hard or « soft » aperture

Not self starting : vibrating mirror or saturable absorber

42 Saturable absorber Saturable absorber : component with losses reduced by high intensities SESAM : Semiconductor Saturable Absorber Mirror InGaAs quantum well absorber on a Bragg mirror

1.0 Nonsaturable loss Modulation

asSubstrate GaAs depth 0.9 Reflectivity GaAs/AlAs Bragg mirror Saturation fluence 0.8

Fluence 43 Dispersion management

How to compensate for the dispersion in the cavity?

DVG >0 in the visible

Prisms Gratings Chirped mirrors

44 Dispersion management with prisms

Prism sequence for adjustable group delay dispersion. angular dispersion + GDD -

recollimation

spatial chirpback front

45 Dispersion management with prisms

Prism sequence for adjustable group delay dispersion.

+ GDD - z

back front

GDD lp distance between prisms L mean glass pass

TOD 46 Dispersion management with prisms

2-prism sequence in double pass

GDD - Mirror for + double pass

47 Dispersion management with gratings

Retroreflector for double pass

p diffraction order d grating pitch L I angle of incidence angle of the reflected wavelength

back front

48 Dispersion management with gratings

Retroreflector for double pass

L negative group delay Distance between gratings Gratings pitch 4 gratings or 2 gratings in double pass

back front much more dispersive than prisms but introduces higher losses

49 Dispersion management with chirped mirror

Bragg mirror with variable layer thickness values

Compact Layered structure High reflectivity

Can compensate for higher Substrate orders

l/2n l/2n l/2n Fixed GDD -> multiple reflections

50 Quizz

The repetition rate of a femtosecond oscillator is related to:

• The acousto-optic modulator

• The length of the cavity

• the pulse width

51 Quizz

The repetition rate of a femtosecond oscillator is related to:

• The length of the cavity

52 Summary 2

Gain medium

Dispersion Mode locking

Mode locking is a balance between dispersion and NL effects. It allows exact adjustment of the phase of the modes.

53 Frequency comb

t T Time

FT FT

Frequency 1/t

1/T

Discrete and perfectly equally spaced frequency lines

frequency etalon 54 The carrier enveloppe phase

Repetition rate 100MHz-GHz

Carrier Enveloppe Offset (CEO)

For very short pulse, difference between phase and group velocities matters

55 Frequency comb for optical clock

and are Microwave frequencies (100MHz-GHz) linked to optical frequencies (THz)

https://www.nist.gov/programs-projects/femtosecond-laser- Optical clock frequency-combs-optical-clocks 56 A revolution in the measure of time/frequency

Replaced by a laser

57 Frequency comb evolutionary tree

fs oscillator = « comb generator »

Diddams SA. 2008. Direct frequency comb spectroscopy. Advances in Atomic, Molecular, and Optical Physics. 55:1–6

58 Outline

Introduction

1. Description of ultrashort light pulses

2. Generation of femtosecond laser pulses via mode locking

3. Femtosecond oscillator technology

59 Femtosecond oscillator technology

Ti:Sapphire oscillators

Yb:bulk oscillators

Fiber-based oscillators  LCF

60 Laser specifications

Energy Energy per pulse Joule Average power Energy per unit time Watt Peak power Maximum power Watt Intensity (irradiance) Peak power per unit area Watt/cm2

Optical power Peak power Energy

t time 61 Quizz

Pulse width 10 fs Energy 10 nJ Repetition rate 100 MHz Average power? Peak power?

62 Quizz

Pulse width 10 fs Energy 10 nJ Repetition rate 100 MHz Average power? 1 W = 10 nJ x 100 MHz Peak power? 1 MW = 10 nJ / 10fs Energy

Optical power Peak power

Average power

t 63 Ti:Sapphire oscillator

Sapphire crystals doped with ions Ti3+ Ti:Sa emission and absorption spectra

Good thermal conductivity Very broad gain bandwidth from 650 nm to 1100 nm Large emission cross section (41. 10-20 m2 @ 780 nm) Extreme tunability and short duration 64 Ti:Sapphire oscillator

Large quantum defect (energy difference Ti:Sa emission and absorption spectra between pump and laser photons)

Pump : green CW laser (DPSS :frequency doubled diode-pumped laser)

diodes YVO4 SHG

Energetically inefficient, complex and expensive

65 Ti :Sapphire cavity

Ti:Sa Crystal CW DPSS Pump laser

Prisms for GVD HR Mirror Control KLM Output Coupler Prisms or chirped mirrors Pulse width : 15 fs Aperture for KLM Repetition rate : 80 MHz or tunability vibrating mirror or AO or Energy : 10 nJ SESAM 66 Pulses in the two-cycle regime

Interferometric autocorrelation

Pulse duration 5fs

D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, "Semiconductor saturable-absorber mirror–assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime," Opt. Lett. 24, 631-633 (1999) 67 Ti:Sapphire commercial lasers

0,6 W, 800nm, <8fs 0,7 W, 700-1080 nm, <100fs

Ti:Sa today : Expensive and not very effective but reliable, tunable, and very short pulsewidth Many applications : bio-imaging, ultrafast spectroscopy, high field physics, amplifier seeding,… 2,5 W, 690nm- 1020 nm, 140fs

68 Repetition rate : 80MHz Ytterbium : bulk oscilllator Cross section

Many different hosts for Ytterbium ions : YAG, glass, KYW, CaF2, … Low quantum defect : high power efficiency, reduced thermal effects Great advantage : diode pumping at 980 nm

69 Ytterbium : bulk oscilllator

CW Laser Diode Yb:bulk

Chirped mirrors for GVD control

HR Mirror Output SESAM Coupler

Pulse width : 300 fs SESAM Repetition rate : 50 MHz Energy : a few 100s nJ Prisms or chirped mirrors High average power 70 Ytterbium : bulk oscilllator

 High average power  Low cost per watt  Compact  Pulse duration 300fs

71 Fiber-based oscillators

Gain media : fiber doped with Rare Earth ions (Large gain bandwidth)

72 Fiber-based oscillators

Large surface area Guided mode Low thermal effects Heat resistance of silica

73 Simple cavity of fiber-based oscillators

Bragg mirrors in the High gain efficiency of active fibers core of the fiber Low thermal effect Doped fiber Dichroic coupler Coupler Chirped fiber Passive modelocking Bragg mirror SESAM

Pump laser diode Output High beam quality Diode pumping Fiber couplers 74 Fiber-based oscillators

Long propagation distance : High gain, low thermal effects Spatial quality Stability Compactness Cost effective 500 mW, 90fs, 1560nm, 100MHz

Large variety of designs and specifications  LCF

1 W , 200fs , 1045 nm , 50 MHz fs pulses delivered by optical cable

75 Summary

Ultrashort pulses = broad spectra -> Large dispersion effects

Description in both time and frequency domain

Generation via modelocking thanks to nonlinear effects

Wide variety of femtosecond lasers