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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(it) TFE() 2 E() E(t) exp(it)dt TF 1E(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 Temporal field Temporal envelope wave FT-1 Spectral field Spectral field Spectral Gaussian envelope centered on the carrier frequency 15 Gaussian pulse Temporal intensity RMS width Spectral intensity 16 Gaussian pulse Temporal intensity RMS width i 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 Spectral amplitude Spectral ( ) ( ) exp( i ( )) Temporal amplitude Temporal Temporal amplitude Temporal 20 Temporal profile and spectral phase Spectral amplitude Spectral Spectral amplitude Spectral FT-1 FT-1 Temporal amplitude Temporal Temporal amplitude Temporal 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 i 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? z 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 z t 31 Duration after propagation in a dispersive material Materials transparent in the visible : k’’>0 of Fused silica Duration after(fs) propagation 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 L 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 GaAs Substrate 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? t 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
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