Femtosecond pulse generation

Transcription

1 Femtosecond pulse generation Marc Hanna Laboratoire Charles Fabry Institut d Optique, CNRS, Université Paris-Saclay

2 Outline Introduction 1 Fundamentals of modelocking 2 Femtosecond oscillator technology 3 The carrier-envelope phase Conclusion

3 Why ultrafast pulses? Shortest manmade events Laser matter interaction - Ultrafast dynamics - Frequency metrology - Attophysics - Multiphoton microscopy - Micromachining - XUV HHG sources P peak E t Lasik MPQ Garching MPQ

4 Ultrashort pulses I(t) I(ω) Δt Fourier Transform Δω t ω Time Bandwidth Product t K Short pulses imply broad spectra

5 Ultrashort pulses Spectral Bandwidth (nm) fs 20 fs 50 fs 100 fs 1 ps Center wavelength µm wavelength 34 nm µm wavelength 12 nm

6 Ultrafast sources are complex Apollon project diagram Oscillator Stretchers Amplifiers Nonlinear stages Postcompression Contrast OPA Pulse shaping Beam shaping Compressor

7 Outline Introduction 1 Fundamentals of modelocking 2 Femtosecond oscillator technology 3 The carrier-envelope phase Conclusion

8 Longitudinal modes in a laser Gain k k c L cav L cav

9 Longitudinal modes in a laser Consider N modes that oscillate simultaneously If the φ n are all equal Gain L cav /c 0 L opt

10 Longitudinal modes in a laser 50 modes oscillating Random phase modes In-phase modes For a 100 fs pulse, spectrum should be broader than 1500 GHz, typical free spectral range is 100 MHz thousands of modes!

11 Modelocked laser To operate in modelocked regime, we must favour pulsed mode vs CW mode i.e. favor large intensities: saturable absorption Gain Sat. Abs.

12 Propagation effects: GVD Propagating broadband pulses experience dispersion Group velocity Group-velocity dispersion (GVD) Propagation Material n(λ)

13 Propagation in a dispersive medium Field at the input of the medium : sum of monochromatic waves Propagation over z Dispersion: Phase accumulates over distance z according to a different propagation constant for each frequency component 13

14 For a Gaussian pulse The field at z is given by Phase velocity CEP Group velocity Pulse broadening Frequency chirp with Linear evolution of instantaneous frequency inst p t t

15 Spectrogram : similar to music sheet The spectrogram

16 Fréquency (THz) Fréquency (THz) Propagation effects: GVD Effect of GVD on the spectrogram Fourier-transform limited pulse 2 nd order dispersion Spectrum Time (fs) Temporal profile Time (fs)

17 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

18 Propagation effects: SPM Propagating intense pulses experience self-phase modulation n(t) n n I(t) 0 2 k0n(t)lc inst t I t

19 Fréquency (THz) Fréquence (THz) Propagation effects: SPM Effect of SPM on the spectrogram Fourier-transform limited pulse Self-phase modulation Spectrum Time (fs) Temporal profile Temps (fs)

20 Optical power Propagation effects: filtering Even if no filter are inserted in the cavity, the gain medium has a finite bandwidth that limits spectral extension Spectrum Increasing gain Gain narrowing λ 20

21 Modelocked laser ingredients Gain Sat. Abs. β 2 SPM Filter output Predicting output pulse involves finding the stationary solution Analytically Master Equation of Mode Locking Numerically Solving propagation equation over large # roundtrips

22 Fréquency (THz) Soliton modelocking Small changes per roundtrip (low loss low gain) Balance between anomalous GVD and SPM Often used in bulk oscillators Sat. Abs. β 2 <0 SPM Time (fs)

23 Soliton modelocking Intensity profile P( t) Soliton area theorem E P 2 2 sech ( t / 2 0 ) Intensity profile (a. u.) t/ t with γ given by 0 n 2 c A eff Determines the achievable pulse energy

24 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, (2008)

25 Pulse shaping mechanisms Gain Sat. Abs. β 2 SPM Filter output

26 Example: ANDi lasers All-normal dispersion lasers Output allow larger nonlinear phase shifts per roundtrip and energy scaling Andy Chong, William H. Renninger, and Frank W. Wise, "Properties of normal-dispersion femtosecond fiber lasers," J. Opt. Soc. Am. B 25, (2008)

27 Outline Introduction 1 Fundamentals of modelocking 2 Femtosecond oscillator technology 3 The carrier-envelope phase Conclusion

28 Gain media 1 Ti:Sapphire oscillators 2 Yb:bulk oscillators 3 RE:fiber oscillators

29 Ti:Sa is the best absorption Intensité (u.a.) émission Longueur d onde (nm) Extremely broad gain bandwidth (5 800 nm) Large emission cross section ( m 780 nm) Fluorescence lifetime 3 µs Thermal conductivity 35 W K -1 m -1

30 A standard Ti:Sa cavity HR mirror Prisms for GVD control Tuning slit KLM slit Green pump laser Output coupler Ti:Sa crystal Typical performances: nj pulse energy at 80 MHz (1-2 W) tunable from 700 to 1000 nm sub-100 fs pulses (down to 6 fs!)

31 Kerr lens saturable absorber n(x) n n I(x) 0 2 Usually requires additional perturbance to start modelocking vibrating mirror

32 Commercial Ti:Sa oscillators

33 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 extraordinary properties (extreme tunability and short pulsewidth)

34 Gain media 1 Ti:Sapphire oscillators 2 Yb:bulk oscillators 3 RE:fiber oscillators

35 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 980 nm!

36 Yb-doped materials Properties are very host-dependent σ λ m 2 nm τ fluo ms κ W/m/K Yb:YAG Yb:glass Yb:KYW Yb:CALGO Yb:CaF Most used material Yb:YAG But limited gain bandwidth: work on CaF 2, CALGO, KYW

37 Saturable absorption is usually implemented using a SESAM (SEmiconductor Saturable Absorber Mirror) A standard Yb:bulk cavity Laser diode Dichroic mirror Crystal Prism SESAM Prism Typical performances: nj pulse energy at 50 MHz (1-2 W) at 1030 nm 300 fs pulses

38 SESAM Design parameters: modulation depth saturation fluence recovery time nonsaturable losses Often self-starting

39 Commercial Yb:bulk oscillators Smaller footprint, less expensive than Ti:Sa but longer pulses

40 Gain media 1 Ti:Sapphire oscillators 2 Yb:bulk oscillators 3 RE:fiber oscillators

41 RE:fiber oscillators Yb Er Th Large and broad gain bandwdith (~ 100 fs pulsewidth) Monolithic integration, robutness, no spatial stability considerations Large design freedom (nonlinearity dispersion etc)

42 Example of a modelocked oscillator Erbium Ytterbium Thulium 50 pj 50 MHz (2.5 mw) 1550 nm 150 fs 100 pj 50 MHz (5 mw) 1030 nm 150 fs 100 pj 10 MHz (1 mw) 2000 nm 500 fs

43 Nonlinear Amplifier Loop Mirror Unbalanced Sagnac interferometer Relative phase depends on pulse intensity

44 Commercial RE:fiber oscillators Even smaller footprint, even less expensive than bulk but lower energies

45 Current research 1 Ti:Sapphire oscillators 2 Yb:bulk oscillators 3 RE:fiber oscillators

46 Selected current research Ti:Sa

47 Selected current research Ti:Sa 500 mw MHz Both SESAM and KLM «Low cost» Ti:Sa

48 Selected current research Yb:bulk 48

49 Selected current research Yb:bulk 242 W 1 ps 80 µj 3 MHz soliton modelocking HHG demonstrated with additional nonlinear compression

50 Selected current research Yb:fiber

51 Selected current research Yb:fiber Step like saturable absorber, must be injected to start

52 Outline Introduction 1 Fundamentals of modelocking 2 Femtosecond oscillator technology 3 The carrier-envelope phase Conclusion

53 The carrier-envelope phase Influence of a constant phase term φ CEP for a very short pulse E ( ) ( t) E 0 exp 2 t 2t 2 0 e i ( p t CEP ) CEP 0 Electric field (a.u.) Time (fs)

54 The carrier-envelope phase Influence of a constant phase term φ CEP for a very short pulse E ( ) ( t) E 0 exp 2 t 2t 2 0 e i ( p t CEP ) / CEP 2 Electric field (a.u.) Time (fs)

55 The carrier-envelope phase Influence of a constant phase term φ CEP for a very short pulse E ( ) ( t) E 0 exp 2 t 2t 2 0 e i ( p t CEP ) CEP Electric field (a.u.) Time (fs)

56 The carrier-envelope phase Influence of a constant phase term φ CEP for a very short pulse E ( ) ( t) E 0 exp 2 t 2t 2 0 e i ( p t CEP ) / 3 CEP 2 Electric field (a.u.) Time (fs)

57 The carrier-envelope phase Influence of a constant phase term φ CEP for a very short pulse E ( ) ( t) E 0 exp 2 t 2t 2 0 e i ( p t CEP ) CEP 0 Electric field (a.u.) Time (fs)

58 CEP vs propagation Field after propagation in a dispersive material 0 2 After propagation over z, maximum of the envelope for t max =z/v g At this point the phase is equal to pz z CEP( z) k pz 2 v L g CEP L CEP n g n

59 CEP vs propagation CEP phase is accumulated upon propagation due to difference between phase and group velocity pz z CEP( z) k pz 2 v L g CEP L CEP n g n Fused silica Air

60 Consequence of CEP evolution in a cavity? Gain Sat. Abs. β 2 SPM Filter output

61 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 frequency comb spacing

62 CEP phase slip The angular frequency ω CEO represents the rate at which the CEP phase drifts at the output of a mode-locked laser Fourier Transform

63 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

64 Outline Introduction 1 Fundamentals of modelocking 2 Femtosecond oscillator technology 3 The carrier-envelope phase Conclusion

65 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 any more

66 Bonus: Non modelocked fs sources 66

67 Bonus: Non modelocked fs sources 140 fs 2.4 µj 1030 nm without modelocking! 67

68 Thank you

69 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 70