IMPRS: Ultrafast Source Technologies

Transcription

1 IMPRS: Ultrafast Source Technologies Lecture III: Feb. 21, 2017: Ultrafast Optical Sources Franz X. Kärtner ms µs Is there a time during galloping, when all feet are off the ground? (1872) Leland Stanford Eadweard Muybridge, * 9. April 1830 in Kingston upon Thames; 8. Mai 1904, Britisch pioneer of photography What happens when a bullet rips through an apple? Harold Edgerton, * 6. April 1903 in Fremont, Nebraska, USA; 4. Januar 1990 in Cambridge, MA, american electrical engineer, inventor strobe photography

2 Physics on femto- attosecond time scales? X-ray EUV * ) Light travels: Time [attoseconds] A second: from the moon to the earth A picosecond: a fraction of a millimeter, through a blade of a knife A femtosecond: the period of an optical wave, a wavelength An attosecond: the period of X-rays, a unit cell in a solid *F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009) 2

3 How short is a Femtosecond Strobe photography 10-6 s = 1µs 1 s 250 Million years dinosaurs 60 Million years dinosaures extinct s = 1 fs 10 s 3

4 Pump - Probe Measurements 4

5 Todays Frontiers in Space and Time Structure, Dynamics and Function of Atoms and Molecules Struture of Photosystem I Chapman, et al. Nature 470, 73,

6 X-ray Imaging (Time Resolved) Optical Pump X-ray Probe Imaging before destruction: Femtosecond Serial X-ray crystalography Chapman, et al. Nature 470, 73,

7 Attosecond Soft X-ray Pulses Three-Step Model Corkum, 1993 Trajectories Ionization Electric Field, Position Time First Isolated Attosecond Pulses: M. Hentschel, et al., Nature 414, 509 (2001) Hollow-Fiber Compressor: M. Nisoli, et al., Appl. Phys. Lett. 68, 2793 (1996) High - energy single-cycle laser pulses! How do we generate them? 7

8 Short Pulse Laser Systems Laser Oscillators (nj), cw, q-switched, modelocked: Semiconductor, Fiber, Solid-State Lasers Laser Amplifiers: Solid-State or Fiber Lasers Regenerative Amplifiers Multipass Amplifiers Chirped Pulse Amplification Parametric Amplification and Nonlinear Frequency Conversion 8

9 Content 1. Basics of Optical Pulses 1.1 Dispersive Pulse Propagation 1.2 Nonlinear Pulse Propagation 1.3 Pulse Compression 2. Continuous Wave Lasers 3. Q-switched Lasers 4. Modelocked Lasers 5. Laser Amplifiers 6. Parametric Amplifiers 9

10 1. Basics of Optical Pulses T R : pulse repetition rate W : pulse energy P ave = W/T R : average power τ FWHM : Full Width Half Maximum pulse width Peak Electric Field: P p : peak power A eff : effective beam cross section Z Fo : field impedance, Z Fo = 377 Ω 10

11 Typical Lab Pulse: 11

12 Time Harmonic Electromagnetic Waves Transverse electromagnetic wave (TEM) (Teich, 1991) See previous class: Plane-Wave Solutions (TEM-Waves) 12

13 Optical Pulses ( propagating along z-axis) : Wave amplitude and phase c( Ω ) = c 0 n( Ω ) : Wave number : Phase velocity of wave 13

14 Absolute and Relative Frequency At z=0 Carrier Frequency For Example: Optical Communication; 10Gb/s Pulse length: 20 ps Center wavelength : λ=1550 nm. Spectral width: ~ 50 GHz, Center frequency: 200 THz, Spectrum of an optical pulse described in absolute and relative frequencies 14

15 Electric field and envelope of an optical pulse Pulse width: Full Width at Half Maximum of A(t) 2 ~ Spectral width : Full Width at Half Maximum of A(ω) _ 2 15

16 Often Used Pulses Pulse width and spectral width: FWHM 16

17 Fourier transforms to pulse shapes listed in table 2.2 [16] 17

18 Electric field and pulse envelope in time domain 18

19 Taylor expansion of dispersion relation at pulse center frequency 19

20 In the frequency domain: 1.1 Dispersion Taylor expansion of dispersion relation: i) Keep only linear term: Time domain: Group velocity: 20

21 Compare with phase velocity: Retarded time: ii) Keep up to second order term: 21

22 Gaussian Pulse: Pulse width z-dependent phase shift FWHM Pulse width: determines pulse width z = L chirp Initial pulse width: 22

23 Magnitude Gaussian pulse envelope, A(z, t ), in a dispersive medium 23

24 (a) Phase and (b) instantaneous frequency of a Gaussian pulse during propagation through a medium with positive or negative dispersion Phase: Instantaneous Frequency: k >0: Postive Group Velocity Dispersion (GVD), low frequencies travel faster and are in front of the pulse 24

25 Sellmeier Equations χ ( Ω) Example: Sellmeier Coefficients for Fused Quartz and Sapphire r 25

26 Typical distribution of absorption lines in medium transparent in the visible. 26

27 Transparency range of some materials, Saleh and Teich, Photonics p

28 Group Velocity and Group Delay Dispersion Group Delay: 28

29 1.2 Nonlinear Pulse Propagation The Optical Kerr Effect Without derivation, there is a nonlinear contribution to the refractive index: Polarization dependent Table 3.1: Nonlinear refractive index of some materials 29

30 Self-Phase Modulation (SPM) Spectrum of a Gaussian pulse subject to self-phase modulation 30

31 (a) Intensity, (b) phase and c) instantaneous frequency of a Gaussian pulse during propagation (a) Intensity Front Back Time t (b) Phase Time t (c) Instantaneous Frequency Time t. 31

32 Dispersion negligible, only SPM 1.3 Pulse Compression Optimium Dispersion and nonlinearity 32

33 Spectral Broadening with Guided Modes and Compression Fiber-grating pulse compressor to generate femtosecond pulses Pulse Compression: 33

34 Grating Pair Phase difference between scattered beam and reference beam Disadvantage of grating pair: Losses ~ 25% 34

35 Prism Pair 35

36 3.7.4 Dispersion Compensating Mirrors High reflecitvity bandwidth of Bragg mirror: 36

37 3.7.5 Hollow Fiber Compression Technique Hollow fiber compression technique 37

38 2 2 Continuous Wave Lasers 2.1 Laser Rate Equations How is inversion achieved? What is T 1, T 2 and σ of the laser transition? What does this mean for the laser dyanmics, i.e.for the light that can be generated with these media? a) b) N 2 2 N 2 R p γ 21 R p γ 21 1 N 1 1 N 1 0 γ 10 N 0 0 γ 10 N 0 γ 10 w = N 2 Figure 4.5: Three-level laser medium R p N 0 =0 w = N 1 38

39 Four-level laser 3 2 N 3 γ 32 N2 γ 10 γ 32 w = N R p γ 21 γ10 N1 N0 39

40 Rate Equations and Cross Section Rate equations for a laser with two-level atoms and a resonator. V:= A eff L Mode volume f L : laser frequency I: Intensity V g : group velocity at laser frequency N L : number of photons in mode w: inversion σ: interaction cross section 40

41 Laser Rate Equations: Intracavity power: P Round trip amplitude gain: g Output power: P out small signal gain ~ στ L - product 41

42 2.2 Continuous Wave Operation P vac = 0 Case 1: Case 2: Steady State: d/dt = 0 g s = g 0 P s = 0 Output power versus small signal gain or pump power 42

43 Lasers and Its Spectroscopic Parameters Spectroscopic parameters of selected laser materials 43

44 3 Q-Switched Lasers Here active Q-switching 44

45 4. Modelocked Lasers f 4 = f 0 +2 f f 2 = f 0 + f f 0 f 1 = f 0 - f f 3 = f 0-2 f Spectrum f 0, f 1, f 2 f 0, f 1, f 2, f 3, f 4 Pulse width time 45

46 4.1 Active Mode Locking Actively modelocked laser Master Equation: loss modulation Parabolic approximation at position where pulse will form; 46

47 Compare with Schroedinger Equation for harmonic oscillator with Eigen value determines roundtrip gain of n=th pulse shape Pulse shape with n=0, lowest order mode, has highest gain. This pulse shape will saturate the gain and keep all other pulse shapes below threshold. Pulse width: 47

48 Pulse shaping in time and frequency domain. Pulse width depends only weak on gain bandwidth ps pulses typical for active mode locking! 48

49 Active mode locking can be understood as injection seeding of neighboring modes by those already present. 1-M M M f n0-1 f n0 f n0+1 f 49

50 4.2 Passive Mode Locking Saturation characteristic of an ideal saturable absorber and linear approximation. 50

51 Fast Saturable Absorber Modelocking There is a stationary solution: Saturable absorber provides gain for the pulse Easy to check with: Shortest pulse: For Ti:sapphire 51

52 Kerr Lens Modelocking Das Bild kann zurzeit nicht angezeigt werden. Lens Refractive index n >1 Intensity dependent refractive index: "Kerr-Lens" Self-Focusing Aperture Laser beam Intensity Intensity Intensity Time Time Time 52

53 Semiconductor Saturable Absorbers Semiconductor saturable absorber mirror (SESAM) or Semiconductor Bragg mirror (SBR) 53

54 Modelocking: Historical Development Pulse width of different laser systems by year. 54

55 5. Laser Amplifiers 5.1 Cavity Dumping 5.2 Laser Amplifiers Frantz-Nodvick Equation Regenerative and Multipass Amplifiers 5.3 Chirped Pulse Amplification 5.4 Stretchers and Compressors 5.5 Gain Narrowing 55

56 Pulse energies from different laser systems 10 3 Regen + multipass amplifiers Pulseenergy (J) Regenerative amplifiers Cavity-dumped oscillators W average power 10-9 Oscillators Repetition Rate, Pulses per Second 56

57 5.1 Cavity Dumping With Bragg cell With Pockels cell 57

58 5.2 Laser Amplifiers Pump pulse Amplified pulse Energy levels of amplifier medium Laser oscillator Seed pulse Amplifier medium Laser amplifier: Pump pulse should be shorter than upper state lifetime. Signal pulse arrives at medium after pumping and well within the upper state lifetime to extract the energy stored in the medium, before it is lost due to energy relaxation. 58

59 5.2.1 Franz-Nodvik Equations Multi-pass gain and extraction F: Fluence = F ext F in Amplifier medium Energy Area F out G = F out / F in G 0 = F = F in / F sat η = F out / F ext 59

60 5.2.2 Basic Amplifier Schemes a) Multi-pass amplifier b) Regenerative amplifier input pump output pump gain input/output gain polarizer Pockels cell 60

61 Multipass amplifier pulse-growth/gain-extraction Pulse growth dynamics dictated by the system s GAIN and LOSS ratio ( F i /F sat ) J' 0, n Fluence DIODE PUMP n Initial gain Go ( G i ) g' 0, n g' o 0.2 Gain 0.1 Round-trip transmission T PASS NUMBER n Multipass amplifier: Theory and numerical analysis Lowdermilk and Murray, JAP 51, No. 5 (1980) 61

62 5.3 Chirped-Pulse Amplification Short pulse oscillator G. Mourou and coworkers 1985 Dispersive delay line t Chirped-pulse amplification involves stretching the pulse before amplifying it, and then compressing it later. Solid state amplifier(s) Pulse compressor t Stretching factors of up to 10,000 and recompression for 30fs pulses can be implemented. 62

63 Chirped Pulse Amplifier System Oscillator Stretcher Multiple Amplifiers - Compressor Chain Oscillator Stretcher Amplifier 1 Amplifier 2 Amplifier 3 Compressor 63

64 5.4 Stretchers and Compressors positive dispersion grating grating negative dispersion f 2f f-d Phase Mask grating grating f 2f f+d 64

65 5.5 Gain Narrowing 10-fs sech 2 pulse in 1 Ti:sapphire gain cross section 3 In general when applying gain G with bandwidth Normalized spectral intensity nm FWHM 32-nm FWHM longer pulse out Normalized Gain) to a pulse with input bandwidth the output bandwidth is Wavelength (nm) Influence of gain narrowing in a Ti:sapphire amplifier on a 10 fs seed pulse Rouyer et al., Opt. Lett. 18, 214 (1993). 65

66 6. Optical Parametric Amplifiers Non-linear polarization effects (1) (2) 2 (3) P = ε 0χ E + ε 0χ E + ε 0χ E 3 + ω 1 ω 2 χ (2) ω 1 ω 1 ω 2 2ω 1 2ω 2 Optical Parametric Amplification (OPA) ω signal ω signal ω 2 ω 1 + ω 2 ω pump ω idler = ω p - ω s Energy conservation: ω s + ω = Momentum conservation (vectorial): (also known as phase matching) i ωp k s Broadband gain medium! + k = i k i k p k s α k p Courtesy of Giulio Cerullo 66

67 Ultrabroadband Optical Parametric Amplifier Broadband seed pulses can be obtained by white light generation Broadband amplification requires phase matching over a wide range of signal wavelengths G. Cerullo and S. De Silvestri, Rev. Sci. Instrum. 74, 1 (2003). 67

68 Phase matching bandwidth in an OPA If the signal frequency ω s increases to ω s + ω, by energy conservation the idler frequency decreases to ω i - ω. The wave vector mismatch is k = ks ω + ω ki ω = ω 1 v gs 1 v gi ω The phase matching bandwidth, corresponding to a 50% gain reduction, is ν 2 ( ln 2) π 1/ 2 1/ 2 γ 1 L 1 1 v gs v gi the achievement of broad gain bandwidths requires group velocity matching between signal and idler beams 68

69 Broadband OPA configurations v gi = v gs : Operation around degeneracy ω i = ω s = ω p /2 Type I, collinear configuration Signal and idler have same refractive index v gi v gs : Non-collinear parametric amplifier (NOPA): Pump and Signal at angle α Pump k s α k p Signal k i 69

70 Noncollinear phase matching: geometrical interpretation In a collinear geometry, signal and idler move with different velocities and get quickly separated v gi v gs In the non-collinear case, the two pulses stay temporally overlapped k p α k i Ω k s v gi Ω v gs v gs =v gi cosω Note: this requires v gi >v gs (not always true!) 70

71 Broadband OPA configurations Pump wavelength NOPA Degenerate OPA 400 nm (SH nm nm Ti:sapphire) 800 nm (Ti:sapphire) µm µm OPAs should allow to cover nearly continuously the wavelength range from 500 to 2000 nm (two octaves!) with few-optical-cycle pulses 71

72 Tunable few-optical-cycle pulse generation D Brida et al., J. Opt. 12, (2010). Can we tune our pulses even more to the mid-ir? Yes, using the idler! 72

73 Broadband pulses in the mid-ir Gain [ 10 4 ] Intensity (arb. un.) 1,0 0,5 0,0 1,0 0,5 0,0 0,9 1 1,1 1,2 1,3 (a) (c) TL duration: 19 fs 0,9 1 1,1 1,2 1,3 Signal Wavelength (µm) LiIO3 KNbO3 PPSLT Simulations confirm the generation of broadband idler pulses, with 20-fs duration ( 2 optical cycles) at 3 µm (b) (d) TL duration: 22.3 fs Idler Wavelength (µm) 73

74 References B.E.A. Saleh and M.C. Teich, "Fundamentals of Photonics," John Wiley and Sons, Inc., P. G. Drazin, and R. S. Johnson, Solitons: An Introduction, Cambridge University Press, New York (1990). R.L. Fork, O.E. Martinez, J.P. Gordon: Negative dispersion using pairs of prisms, Opt. Lett (1984). M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, F. Krausz: A novel high energy pulse compression system: generation of multigigawatt sub-5-fs pulses, Appl. Phys. B (1997). J. Kuizenga, A. E. Siegman: "FM und AM mode locking of the homoge- neous laser - Part II: Experimental results, IEEE J. Quantum Electron. 6, (1970). H.A. Haus: Theory of mode locking with a slow saturable absorber, IEEE J. Quantum Electron. QE 11, (1975). K. J. Blow and D. Wood: "Modelocked Lasers with nonlinear external cavity," J. Opt. Soc. Am. B 5, (1988). J. Mark, L.Y. Liu, K.L. Hall, H.A. Haus, E.P. Ippen: Femtosecond pulse generation in a laser with a nonlinear external resonator, Opt. Lett. 14, (1989) E.P. Ippen, H.A. Haus, L.Y. Liu: Additive pulse modelocking, J. Opt. Soc. Am. B 6, (1989). D.E. Spence, P.N. Kean, W. Sibbett: 60-fsec pulse generation from a self-mode-locked Ti:Sapphire laser, Opt. Lett. 16, (1991). H. A. Haus, J. G. Fujimoto and E. P. Ippen, Structures of Additive Pulse Mode Locking, J. Opt. Soc. Am. 8, pp (1991). U. Keller, Semiconductor nonlinearities for solid-state laser modelock- ing and Q-switching, in Semiconductors and Semimetals, Vol. 59A, edited by A. Kost and E. Garmire, Academic Press, Boston Lecture on Ultrafast Amplifiers by Francois Salin, D. Strickland and G. Morou: "Compression of amplified chirped optical pulses," Opt. Comm. 56, ,(1985). G. Cerullo and S. De Silvestri, "Ultrafast Optical Parametric Amplifiers," Review of Scientific Instr. 74, pp (2003). 74