Content. Laser structure. Laser principle. Lecture 1. Introduction. a.laser b.light matter interaction c.laser driven nuclear fusion

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1 13 Content Lecture 1 Introduction a.laser b.light matter interaction c.laser driven nuclear fusion 1 Laser principle Laser structure 1. gain medium. pumping source 3. high reflector 4. output coupler 5. laser beam Stimulated emission of radiation 3 Laser: light amplification by stimulated emission of radiation 4 1

2 13 Invention history Influence of laser 1917 Einstein stimulated emission of radiation 1953 Townes, Basov, Prokhorov microwave amplifier (maser) 1957 Gould optical resonator 1959 Gould coined laser 196 Maiman the first laser (ruby, red light) 1964 Townes, Basov, Prokhorov Nobel Prize Science: Nobel Prize on physics (8), chemistry (1) Medicine: surgery (eye, dental etc.) Industry: micro machining Military: weapon, guiding, targeting Energy: laser driven nuclear fusion Laser: one of the greatest inventions 5 6 Trend of laser Maximizing power & energy 1PW, 1MJ Minimizing pulse duration few fs or even as Extending to new waveband THz, XUV, x ray, γ ray etc. 7 Terminology Symbol Name Value GW gigawatt 1e9 W TW terawatt 1e1 W PW petawatt 1e15 W EW exawatt 1e18 W kj kilojoule 1e3 J MJ megajoule 1e6 J ns nanosecond 1e 9 s ps picosecond 1e 1 s fs femotosecond 1e 15 s as attosecond 1e 18 s THz terahertz 1e1 Hz 8

3 13 History of laser intensity High power laser Ti: Sapphire, 8nm,.1 1Hz, >1PW(1), ~3fs 9 1 High power laser Nd: glass, 1.5μm, >times/hour, >1PW(1999), ~5fs High energy laser Nd: glass, 1.5μm (351nm), >1MJ, >times/day, ns Trident@LANL Trident@LANL 11 NIF@LLNL 1 3

4 13 Laser waveband Waveband Waveband EM Wave Wavelength Energy Frequency gamma ray <.1nm > 1keV x ray (.1 1) nm (.1 1) kev extreme ultraviolet (1 14) nm (1 14) ev (XUV/EUV) ultraviolet (UV) (1 38) nm (3 14) ev visible (38 7) nm infrared (IR) 7nm 1mm terahertz (THz) (.1 1) mm (.3 3) THz microwave 1mm 1m.3GHz.3THz radio 1mm 1km 3kHz.3THz 15 Tough waveband THz: gap between optical and microwave XUV, x ray, γ ray: no proper gain medium and reflective mirror 16 4

5 13 Solutions to tough waveband Case I: Free electron laser (FEL) THz Quantum cascade laser, free electron laser, laser plasma interaction. XUV, x ray, γ ray Free electron laser, high harmonics from ionized atoms, lasing from highly excited ions in plasmas, laser plasma interaction, positronium annihilation. e source 1971 Madey FEL principle undulator EM wave 17 Microwave hard x ray (1keV,1) 18 Case II: X ray laser Case III: laser atom interaction 3 Ge + 1 Ne like, 6 Sm Ni like LOA LaserStars XUV and soft x ray (5 ev) 19 High harmonic generation: XUV, x ray 5

6 13 Case III: laser plasma interaction Generalized definition Laser: all kinds of coherent light sources, no matter what radiation mechanisms. THz Wu x ray, γ ray MPQ 1 Content Reflection &refraction a.laser b.light matter interaction c.laser driven nuclear fusion 3 APPhys. Fresnel equations 4 6

7 13 Refraction index Refraction index Re(n) 1 n( ω) = 1 C ω ω + iγω r r ( r ) Material EM Wave n vacuum all =1 dielectric IR, Visible > 1 dielectric UV, x ray < 1 plasma all < 1 metamaterial structure determined < ω IR ω UV ω X Refraction index is a valid concept in the whole EM waveband and depends on light frequency. Sudden change of n is around atom resonant frequencies. 5 n= c/ v, v is phase velocity p p n> 1, v < c; n< 1, v > c p p 6 Microscopic picture Dispersion n( ω) = 1 C ω ω + iγω r r ( r ) 7 ω r all resonant frequencies of atoms. 8 7

8 13 Total reflection Group velocity dispersion θ < θ c n < 1 cosθc = n n 1, θ (1 n) = δ c Wave number in dispersive media k 1 ( ) n ω ω = ( ω) = k + k 1( ω ω) + ( )... c k ω ω + ω k = n c dk 1 1 dn k1 = = = ( n+ ω ) dω v c dω g Carbon: 3keV x ray, δ=5e 5, θ c =.6 o k dk dn dn = = + ω 1 ( ) dω c dω dω 9 3 Pulse stretching Chirped pulse k > : normal dispersion k > : normal dispersion: up /positively chirped pulses front tail front tail δω k < : anomalous dispersion k < : anomalous dispersion: down/negatively chirped

9 13 Math of GVD A i z k A t = Ezt (, ) = Azt (, )exp( ikz iω t) t t Azt (, ) exp( ic ) T T 1 1 t A(, t) exp( ), T1 = T 1 + ( z/ LD ),sgn( C) = sgn( k) T L = T / k : dispersion length D 33 1 GVD effect t t Ezt (, ) exp( ic iω t) T T1 T = T 1 + ( z/ L ),sgn( C) = sgn( k ) L<< L D : L L D : 1 D δω = Ct / T 1 GVD is negligible >> stretch factor 1/ T T z 34 Chirped pulse compression Nonlinear optics Dispersion compensation: up (down) chirped pulses can be compressed by anomalously (normally) dispersive medium. P = ε E + χ EE + χ EEE + (1) () ( 3) ( χ : M...) T 1 z min t t A(, t) = A exp( ic ) z T T z T C = 1 + C min min 1 = T L 1+ C D χ (1) : χ () : refraction index, dispersion nd harmonic, sum frequency etc. (absent for uniform isotropic media) χ (3) : 3rd harmonic, four wave mixing, and nonlinear refraction index etc

10 13 Kerr effect Self phase modulation (SPM) Nonlinear refraction index 3 (3) n( ω, E ) = n( ω) + n E, n = Re( χ ) 8n A + γ A A =, γ i z (, ) (, )exp[ ] Azt = A t i n A(, t) z A L NL n( ω) front Δn tail 37 z A(, t) δω = L t A NL LNL t A(, t) = A exp( ) 1 = ( γ P) : nonlinear length P laser power T 38 Frequency broadening GVD vs. SPM z A(, t) δω = L t A NL L >> L> L : only GVD (weak short pulse) NL D front red shift Δn() t tail δω blue shift tail L >> L> L : only SPM (high power pulse) D NL L> L, L : GVD + SPM (high power short pulse) NL D A z k A t i + γ A A=,

11 13 Temporal soliton A z k A t i + γ A A=, k <, LNL = LD A sec h( t/ T ) Self focusing effect n( ω, E ) = n( ω) + n E E exp[ ( x + y ) / w ] Pcr =.15 λ /( n n ) Air: P =.4GW Δn( xy, ) cr 41 4 Spatial soliton Breakdown A + α + γ =, z i A A A PRL P> P cr Science Filament

12 13 Turbulent filamentation Beyond nonlinear optics Extreme nonlinear optics (violent) I= W/cm Ionization, high harmonics... PRL Relativistic optics (extremely violent) I= W/cm Energetic particles & photons P = P 35 cr Content Crisis a.laser b.light matter interaction c.laser driven nuclear fusion Energy crisis: fossil fuels (coal, oil, gas etc.) are going to be depleted completely in this century. How about the next century or even next millennium 3XXX? Greenhouse effect: CO (fuel burning) leads to global warming, extreme weather events, sea level rise etc. Clean energy: wind, solar, hydropower and fusion

13 13 Fusion energy Nuclear fusion ITER D + T 4 He (3.5 MeV) + n (14.1 MeV) 49 5 Fusion medium Controlled nuclear fusion Lawson criterion: N e T 1 s/m 3 Plasma ITER Magnetic confinement Inertial confinement LANL

14 13 Tokamak IC fusion LLE Leipzig N e 1e14cm 3, T=sec-minute 53 N e 1 solid density, T.1ns 54 Indirect IC fusion NIF ignition Indirect drive is supposed to decrease the rigorous demanding of focusing symmetry compared with direct drive. LLNL LLNL LLNL However, laser backscattering in the underdense plasmas within hohlraum and hydro instability (RT) complicate ICF physics. Intensive theory works are needed

15 13 Fast ignition Fast ignition Osaka PPCF York Cone attached capsule target Laser fusion projects Suggested reading Indirect drive NIF (LLNL, USA), 19 beams, 1.8MJ LMJ (France), 4 beams, 1.8MJ ShenGuang III (CAEP, China), 4 beams,.15mj Fast ignition OMEGA EP (LLE, University of Rochester, USA) GEKKO XII (ILE, Osaka University, Japan) HiPPER (European Union), kj driver, 7kJ heater Refraction index: Attwood, Soft X rays and Extreme Ultraviolet Radiation: Principles and Applications, Cambridge University (1999). GVD, SPM and soliton: Agrawal, Nonlinear Fiber Optics & Applications of Nonlinear Fiber Optics, Elsevier Science (1). Self focusing: Shen, The Principles of Nonlinear Optics, Wiley Interscience (). Spatial soliton: Segev & Stegeman, Physics Today, 51 (iss8), 4 (1998). Laser filament: Berge et al., Rep. Prog. Phys., 7, 1633 (7). Laser fusion: Atzeni & Meyer ter Vehn, The Physics of Inertial Fusion, Oxford University (4)

16 13 Problems 1 Why can t THz, XUV and x ray be efficiently produced by conventional laser technique? Plot a chirped Gaussian laser pulse with C= 8 and T =5λ /c. What dispersive medium is able to compress it? What is the minimum duration after the compression? 3 Describe the role of Kerr effect in both temporal and spatial solitons? 4 Given the DT plasma density of 1e19cm 3, how long should this plasma sustain for fusion occurrence? 5 Describe different ignition schemes for laser fusion