Femosecon laser pulses Inroucion on femosecon lasers Numerical analysis Compuer conrolle experimens Lab wor
Pulse shaping Femosecon laser pulses : lab wor Time omain eraher specroscopy Specral inerferomery Average e Curren na 4-1 3 4 Time ps Wavelengh
Femosecon laser pulses Sessions 1 an 3 : Inroucion o basic noions - Femosecon laser pulses - Use of Mlbf Malab for aa processing Sessions 4-9 : experimenal wor a Laboraoire Opique e Biosciences hp://www.enseignemen.polyechnique.fr/profs/physique/manuel.joffre/ea/ manuel.joffre@polyechnique.fr
Orers of magniue Perio Frequency Wavelengh λ λ ct 3 as 3 PH X rays 1 nm ν 33 as 3 PH 1 nm Ulra-viole -15 333 as 3 PH 1 nm 3 fs 33 fs 333 fs Visible 3 TH 1 µm 3 TH 3TH Infrare 1 µm 1 µm 1fs 1 1 as 1 c -18 s s.3µm/fs c 3 ps 33 ps 3 GH Micro waves 1 mm 3 GH 1 mm Raio waves
Inroucion o femosecon lasers 1. Represenaion of a femosecon pulse. Linear propagaion 3. Nonlinear propagaion 4. Femosecon laser sources
Represenaion of a femosecon pulse fs E Fourier ransform Joseph Fourier 1768-183 E E exp iϕ E Frequency Ampliue Phase
Properies of Fourier ransforms - 1 Parseval Plancherel heorem Complex conjugaion TF Derivaion TF TF
Properies of Fourier ransforms - Proucs an convoluion proucs TF TF avec Transforms of usual funcions δ f f
Represenaion of a femosecon pulse E E * + E E exp i Elecric fiel π E E exp iϕ E Specral ampliue ϕ Specral phase I E Specral linensiy i or specrum E real E E * E + *
φ E From real fiel o analyic represenaion E * Θ E + * E Θ exp iφ Complex fiel or analyic represenaion Θ [ [E]] cf Hilber ransform * + E Re φ Temporal phase I Temporal inensiy
Average values in ime an frequency We wrie A so ha is normalie : 1 π Δ Δ ² ² Pulse cener Cenral frequency carrier frequency π Δ Pulse uraion RMS Δ Specral wih RMS Δ Δ 1 Δ Δ
Group elay i i * π * i exp ϕ i exp ϕ ϕ i i + π ϕ π i + ϕ ϕ τ g Group elay ime of arrival of frequency componen τ g Group elay ime of arrival of frequency componen τ Pulse ime of arrival τ g Pulse ime of arrival
RMS pulse uraion i π exp ϕ i exp ϕ ϕ i i + π ϕ π + π π τ g + ϕ g τ g τ τ ϕ g g + Δ ϕ g g g τ ϕ Δ + Δ Δ
Pulse uraion an specral phase iϕ exp ϕ : specral phase τ g ϕ : group elay Δ Δ ϕ + Δτ g For a given he shores possible pulse is achieve when τ g is frequency inepenen Δτ g. This is a so-calle Fourier ransform limie pulse. Conversely when τ g varies wih frequency here is a frequency chirp.
1 ϕ ϕ Quaraic specral phase : Pulse lenghening an chirp ϕ τ ϕ g Δ Δϕ + ϕ Various frequency componens arrive one a a ime : frequency chirp. Δ ϕ τ g g E
Ranom specral phase : incoheren fiel Ch hamp élec crique SPECTRE 1 3 1 8 6 4 5 15 1 5 3 35 4 Fréquence [TH] Δ Δϕ + Δτ ϕ g 5 Phase [r] Champ élecrique Inensié 15 1 5-5 -1 PROFIL TEMPOREL -15-6 -4-4 6 Temps [fs] 16 14 1 1 8 6 4-6 -4-4 6 Temps [fs]
Specral wih an emporal phase iφ exp φ : emporal phase π φ φ Ω : insananeous frequency φ Δ Δ φ + ΔΩ Δ φ Ω E ² Δ
Linear propagaion of a femosecon pulse where : Propagaion equaion : n. c + Soluion : exp i Thus : ϕ ϕ + Group elay: ϕ ϕ τ g + τ g + V g Group velociy V g 1 V g
Linear ispersion in a ransparen meium n α Specre e l'impulsion L IR Zone e ransparence UV à 8 nm L 1cm Quaniy Definiion Uni SiO SF1 Phase inex n c / - 1.453 1.711 Group inex n g c - 1.467 1.751 Group velociy V 1/ c / µm/fs.4.171 g n g GVD Group Velociy Dispersion i f²/ fs²/cm 361 159 Group elay τ ϕ L fs 49E3 58E3 g GDD Group Delay Dispersion τ ϕ LL fs² 361 159 g TOD Thir Orer Dispersion τ ϕ L fs 3 74 111 g
Linear ispersion in a ransparen meium n α Specre e l'impulsion L IR Zone e ransparence UV 1 + + +... 1 ϕ ϕ + + + ϕ τ + + g τ g +... + The pulse acquires a quaraic specral phase resuling from group velociy ispersion GVD hus a frequency chirp....
Pulse lenghening 1 1 + + + ϕ ϕ + + τ ϕ τ g g + + τ τ Δ + Δ Δ Δ Δ Relaion hols for any pulse shape
Pulse envelope u is by efiniion he pulse envelope. u exp i u exp i + u is always cenere a. u is always cenere a. 1 exp i + + 1 u exp i u
From he soluion o he equaion i u u 1 exp p u i u u u u i NB : Slowly varying envelope approximaion i.e. conra-propagaing wave no aen ino accoun aen ino accoun.
Analogy wih he propagaion of a wavepace in quanum mechanics in quanum mechanics x ψ u x x m x i ψ ψ h h u u i x m i ψ ψ h h u u i m i ψ h u i exp i ϕ ψ ψ exp ϕ i u u m h ϕ 1 ϕ
Linear propagaion of a femosecon pulse Meium : fuse silica. n 1.4533 n g 1.4671 375 fs²/cm. Gaussian pulse. λ 8 nm.
Linear propagaion of a femosecon pulse Meium : fuse silica. n 1.4533 n g 1.4671 375 fs²/cm. Hypergaussian pulse. λ 8 nm.
3. Nonlinear propagaion
Nonlinear opics Linear regime Non-linear regime
Opical Kerr effec Thir-orer polariaion n I n + n I
Auofocusing nr n I n + n I ϕ x y π n + n I x y L λ
Generaion of specral coninuum n n + ni φ φ + n + n I v c c φ φ Φ Ω
Generaion of specral coninuum Ecole Polyechnique phoo G. Labroille P. Lavialle M. Joffre NB : Opical Kerr effec is only one of several nonlinear effecs conribuing o coninuum generaion.
4. Femosecon laser sources
Superposiion of longiuinal moes Frequency omain δ δ Time omain π/δ
General scheme for a femosecon laser Broaban amplifying meium L cav Energy gy source
A evice wih negaive ϕ" : he prism pair Dispersive Milieu ispersif meium GVD GVD compensaion
Anoher evice wih negaive ϕ" : he chirpe mirror
General scheme for a femosecon laser Group Velociy Dispersion Compensaion To achieve moe locing i is sufficien o mae sure ha losses are greaer when he specral phase is no fla i.e. when he pulse is longer. Moe-locing mechanism L cav Broaban amplifying meium Energy gy source
Dye laser Moe-locing mechanism : saurable absorban Mécanisme e blocage es moes : absorban saurable 6 nm.1 nj 3 fs 1 MH R6G AS Laser Argon
Tianium:Sapphire P.F. Moulon JOSAB 3 15 1986
Tianium:Sapphire laser Ti:S 8 nm nj 1 fs 1 MH Pump laser Moe-locing mechanism : Opical Kerr effe nr Ti:S
Tianium:Sapphire laser elivering ulrashor pulses 5.4 fs U. Morgner F. X. Kärner S. H. Cho Y. Chen H. A. Haus J. G. Fujimoo E. P. Ippen V. Scheurer G. Angelow T. Tschui Sub-wo-cycle pulses from a Kerr-lens moe-loce Ti:sapphire laser Op. Le. 4 411 1999.
Commercially available femosecon oscillaors 1 fs.7 1µm 1. 14 fs.7 -.93 µm hp://www.cohereninc.com/ 1 fs 8 nm hp://www.specraphysics.com/ 5 fs 1.55 µm hp://www.femolasers.com/ hp://www.menlosysems.com/
LOB Examples of femosecon amplifiers A. Bonvale e al. 1 mj / 1 fs 1 GW @ 1 H
Examples of femosecon amplifiers Laboraoire Opique Appliquée ENSTA Ecole Polyechnique 1J / 3 fs 3 TW @ 1 H
Examples of femosecon amplifiers Laboraoire Livermore Eas-Unis 1J/1ps 1 1PW