DESY Summer School Lasers and Optics

Transcription

1 DESY Summer School 2015 Lasers and Optics Franz X. Kärtner: Bldg. 99, O & phone: Assistant: Christine Berber O3.095, phone x-6351, 1

2 General Information Prerequisites: Basic course in electrodynamics Further Reading: Fundamentals of Photonics, B.E.A. Saleh and M.C. Teich, Wiley, Lasers, A. Siegman, 1986 Ultrafast Optics, A. M. Weiner, Hoboken, NJ, Wiley Ultrashort Laser Pulse Phenomena, Diels and Rudolph, Elsevier/Academic Press, 2006 Optics, Hecht and Zajac, Addison and Wesley Publishing Co., Principles of Lasers, O. Svelto, Plenum Press, NY, Waves and Fields in Optoelectronics, H. A. Haus, Prentice Hall, NJ,

3 Lasers Today: Ultrashort Pulse Lasers 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

4 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) 4

5 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 5

6 Pump - Probe Measurements! 6

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

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

9 Attosecond Soft X-ray Pulses Three-Step Model Corkum, 1993 Electric Field, Position Trajectories Ionization 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?! 9

10 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! 10

11 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! 11

12 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 12

13 Typical Lab Pulse: 13

14 Time Harmonic Electromagnetic Waves Transverse electromagnetic wave (TEM) (Teich, 1991) See previous class: Plane-Wave Solutions (TEM-Waves) 14

15 Optical Pulses ( propagating along z-axis) : Wave amplitude and phase c( Ω ) = c 0 n( Ω ) : Wave number : Phase velocity of wave 15

16 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 16

17 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 17

18 Often Used Pulses Pulse width and spectral width: FWHM 18

19 Fourier transforms to pulse shapes listed in table

20 Electric field and pulse envelope in time domain 20

21 Taylor expansion of dispersion relation at pulse center frequency 21

22 1.1 Dispersive Pulse Propagation In the frequency domain: Taylor expansion of dispersion relation: i) Keep only linear term: Time domain: Group velocity: 22

23 Compare with phase velocity: Retarded time: ii) Keep up to second order term: 23

24 Gaussian Pulse: Pulse width z-dependent phase shift FWHM Pulse width: determines pulse width z = L chirp Initial pulse width: 24

25 Magnitude Gaussian pulse envelope, A(z, t ), in a dispersive medium 25

26 (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 26

27 Sellmeier Equations χ ( Ω) Example: Sellmeier Coefficients for Fused Quartz and Sapphire r 27

28 Typical distribution of absorption lines in medium transparent in the visible. 28

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

30 Group Velocity and Group Delay Dispersion Group Delay: 30

31 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 31

32 Self-Phase Modulation (SPM) Spectrum of a Gaussian pulse subject to self-phase modulation 32

33 (a) Intensity, (b) phase and c) instantaneous frequency for Gaussian pulse propagation (a) Intensity Front Back Time t (b) Phase Time t (c) Instantaneous Frequ ency Time t. 33

34 1.3 Pulse Compression Dispersion negligible, only SPM Optimium Dispersion and nonlinearity 34

35 Spectral Broadening with Guided Modes and Compression Fiber-grating pulse compressor to generate femtosecond pulses Pulse Compression: 35

36 Grating Pair Phase difference between scattered beam and reference beam γ α k out γ l k in D Disadvantage of grating pair: Losses ~ 25% 36

37 Prism Pair 37

38 3.7.4 Dispersion Compensating Mirrors High reflecitvity bandwidth of Bragg mirror: 38

39 Hollow Fiber Compression Technique Hollow fiber compression technique 39

40 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 à w = N 2 Figure 4.5: Three-level laser medium R p à N 0 =0 w = N 1 40

41 Four-level laser 3 2 N 3 γ 32 N 2 γ 10 à γ 32 à w = N R p γ 21 γ10 N1 N0 41

42 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 into one direction v g : group velocity at laser frequency N L : number of photons in mode W = N 2 : inversion σ: interaction cross section T 1 = τ L = upper state lifetime T = output coupler transmission 1 for ring cavity 2* = 2 for linear cavity 42

43 Laser Rate Equations: Intracavity power: P Round trip amplitude gain: g T R = v g /2L = round-trip time Output power: P out small signal gain ~ στ L - product 43

44 Continuous Wave Operation P vac = 0 Case 1: Case 2: Steady State: d/dt = 0 g s = g 0 P s = 0 Output Power, Gain g= g th =l P=0 g= =l 0 g th Small signal gain g 0 Output power versus small signal gain or pump power e 4.9: Output power and gain of a laser as a function of pump power. 44

45 Lasers and Its Spectroscopic Parameters 45

46 3 Q-Switched Lasers Here active Q-switching (a) Losses High losses, laser is below threshold t (b) Losses Gain t Build-up of inversion by pumping (c) Losses Gain t In active Q-switching, the losses are reduced, after the laser medium is pumped for as long as the upper state lifetime. Then the loss is reduced rapidly and laser oscillation starts. (d) Losses "Q-switched" Laserpuls Gain t Laser emission stops after the energy stored in the gain medium is extracted. Length of pump pulse 46

47 4. Modelocked Lasers f 4 = f 0 +2 Δ f f 2 = f 0 + Δ f f 0 f 1 = f 0 - Δ f f 3 = f 0-2 Δ f Spectrum f 0, f 1, f 2 f 0, f 1, f 2, f 3, f 4 Pulse width time 47

48 4.1 Active Mode Locking Actively modelocked laser Master Equation: loss modulation Parabolic approximation at position where pulse will form; 48

49 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: 49

50 Pulse shaping in time and frequency domain. Pulse width depends only weak on gain bandwidth ps pulses typical for active mode locking! 50

51 Active mode locking: Injection seeding of neighboring modes 1- M M M f n0-1 f n0 f n0 +1 f 51

52 4.2 Passive Mode Locking Saturation characteristic of an ideal saturable absorber and linear approximation. 52

53 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 53

54 Kerr Lens Modelocking Lens Refractive index n >1 Intensity dependent refractive index: "Kerr-Lens" Self-Focusing Aperture Laser beam Das Bild kann nicht angezeigt werden. Dieser Computer verfügt möglicherw eise über zu wenig Arbeitsspei cher, um das Bild zu öffnen, oder das Bild ist beschädigt. Starten Sie Intensity Intensity Intensity Time Time Time Response time of electronic Kerr effect in glass < 3 fs! 54

55 Semiconductor Saturable Absorbers Semiconductor saturable absorber mirror (SESAM) or Semiconductor Bragg mirror (SBR) Response time of semi. saturable absorbers typ. > 50 fs! 55

56 Broadband, Prismless Ti:sapphire Laser 1mm BaF2 OC PUMP Laser crystal: 2mm Ti:Al 2 O 3 φ = 10 ο L = 10 cm BaF2 - wedges Silver mirror Base Length = 15cm for 200 MHz Laser 56

57 Experimental results! IAC TIME DELAY, FS SPECTRAL DENSITY, a.u FWHM (FTL) = 4.3 fs WAVELENGTH, NM POWER [arb.] 5.0 fs PHASE [RAD.] TIME [fs] WAVELENGTH [NM]

58 Modelocking: Historical Development Pulse width of different laser systems by year. 58

59 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 59

60 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 60

61 5.1 Cavity Dumping With Bragg cell With Pockels cell 61

62 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. 62

63 Fluence : F(z) = Multi-pass gain and extraction I(z,t)dt " L % Small signal gain : G o = exp$ g 0 (z,t)dz' # 0 & Fluence after roundtrip i : F i = F sat ln! " 1+G o Gain after roundtrip i : G i =! 1 e F i 1 " /Fsat F: Fluence = F ext F in Franz-Nodvik Equations Amplifier medium Energy Area F out ( e F i 1 /Fsat 1) # $ 1 1/ G # ( i 1 ) $ G = F out / F in G 0 = F = F in / F sat extractable energy : F ext = F pump f L f p pump efficiency η = F out / F ext 63

64 5.2.2 Basic Amplifier Schemes a) Multi-pass amplifier b) Regenerative amplifier input pump output pump gain input/output gain polarizer Pockels cell 64

65 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 n PASS NUMBER Multipass amplifier: Theory and numerical analysis Lowdermilk and Murray, JAP 51, No. 5 (1980) 65

66 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. 66

67 Chirped Pulse Amplifier System Oscillator Stretcher Multiple Amplifiers - Compressor Chain Oscillator Stretcher Amplifier 1 Amplifier 2 Amplifier 3 Compressor 67

68 5.4 Stretchers and Compressors positive dispersion grating grating negative dispersion f 2f f-d Phase Mask grating grating f 2f f+d 68

69 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 Δλ Fluo Normalized spectral intensity nm FWHM 32-nm FWHM longer pulse out Normalized Gain) to a pulse with input bandwidth Δλ = Δλ 0 the output bandwidth is Δλ 0 " 1+ ln(g) $ # Δλ 0 Δλ Fluo % ' & 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). 69

70 6. Parametric oscillators and amplifiers Favorite parametric oscillator? Optical parametric process Swing NLO (1) (2) 2 (3) P = ε 0χ E + ε 0χ E + ε 0χ E Optical Parametric Oscillator Amplifier (OPO)! (OPA)! 3 + ω signal ω signal ω pump ω idler = ω p - ω s Lift center of gravity = change length of pendulum; twice per period: DMPO k P = k s + k i 70

71 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 = Momentum conservation (vectorial):" (also known as phase matching)" "!ω! ω s! i p Broadband gain medium! " k! + s k! = i "k! " p k i k s α k p Courtesy of Giulio Cerullo 71

72 Ultrabroadband Optical Parametric Amplifier n Broadband seed pulses can be obtained by white light generation n Broadband amplification requires phase matching over a wide range of signal wavelengths G. Cerullo and S. De Silvestri, Rev. Sci. Instrum. 74, 1 (2003). " 72

73 Phase matching bandwidth in an OPA If the signal frequency ω s increases to ω s +Δω, by energy conservation the idler frequency decreases to ω i -Δω. The wave vector mismatch is Δk = ks Δω + ω ki Δω = ω 1 v gs 1 v gi Δω The phase matching bandwidth, corresponding to a 50% gain reduction, is Δν 2 ( ln2) 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 73

74 Broadband OPA configurations v gi = v gs : Operation around degeneracy ω i = ω s = ω p /2 ü Type I, collinear configuration ü Signal and idler have same refractive index v gi v gs : Non-collinear parametric amplifier (NOPA): ü Pump and Signal at angle α Pump k s α k p Signal k i 74

75 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!) 75

76 Broadband OPA configurations Pump wavelength 400 nm (SH! Ti:sapphire)! 800 nm! (Ti:sapphire)! NOPA! Degenerate OPA! nm! nm! µm! µm! OPAs should allow to cover nearly continuously the wavelength range from 500 to 2000 nm (two octaves!) with few-optical-cycle pulses 76

77 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! 77

78 Broadband pulses in the mid-ir 0,9 1 1,1 1,2 1, ,0 (a) (b) Gain [ 10 4 ] 0,5 0,0 LiIO3 KNbO3 PPSLT Intensity (arb. un.) 1,0 0,5 0,0 (c) TL duration: 19 fs 0,9 1 1,1 1,2 1,3 Signal Wavelength (µm) Idler Wavelength (µm) l Simulations confirm the generation of broadband idler pulses, with 20-fs duration ( 2 optical cycles) at 3 µm (d) TL duration: 22.3 fs 78

79 Further Reading and 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). 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). 79