iCONTENTS11.4 Four-Wave Mixing:38012PulseAmplification385
CONTENTS i 11.4 Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . 380 12 Pulse Amplification 385
Chapter 1Introduction1.1 Course Mission·Generation of ultrashort pulses:Nano-,Pico-,Femto-,AttosecondPulses. Propagation of ultrashort pulses●Linearandnonlineareffects. Applications in high precision measurements, nonlinear optics, opticalsignal processing, optical communications, x-ray generation,....1.2Pulse CharacteristicsMost often, there is not an isolated pulse, but rather a pulse train.nT.(n-1)Ta(n+1)T,Figure 1.l: Periodic pulse train1
Chapter 1 Introduction 1.1 Course Mission • Generation of ultrashort pulses: Nano-, Pico-, Femto-, Attosecond Pulses • Propagation of ultrashort pulses • Linear and nonlinear effects. • Applications in high precision measurements, nonlinear optics, optical signal processing, optical communications, x-ray generation,. 1.2 Pulse Characteristics Most often, there is not an isolated pulse, but rather a pulse train. Figure 1.1: Periodic pulse train 1
2CHAPTER1.INTRODUCTIONTr: pulse repetition timeW : pulse energyPave = W/Tr : average powerTrwHM is the Full Width at Half Maximum of the intensity envelope of thepulse in the time domain.ThepeakpowerisgivenbyWTRPp =(1.1)PaveTFWHMTFWHMand the peak electric field is given byPp2ZF0(1.2)Ep =oAeffAef is the beam cross-section and Zro= 3772 is the free space impedance.Time scales:1ns~30cm(high-speed electronics,GHz)1 ps~300μm1 fs~300nm1as = 10-18s ~ 0.3nm = 3A (typ-lattice constant in metal)The shortest pulses generated to date are about 4 - 5fs at 800nm (/c =2.7fs),less than two optical cycles and 250 as at 25 nm.For few-cycle pulsesthe electric field becomes important, not only the intensity!5fsFigure 1.2: Electric field waveform of a 5 fs pulse at a center wavelength of800 nm. The electric field depends on the carrier-envelope phase
2 CHAPTER 1. INTRODUCTION TR: pulse repetition time W : pulse energy Pave = W/TR : average power τFWHM is the Full Width at Half Maximum of the intensity envelope of the pulse in the time domain. The peak power is given by Pp = W τFWHM = Pave TR τFWHM , (1.1) and the peak electric field is given by Ep = r 2ZF0 Pp Aeff . (1.2) Aeff is the beam cross-section and ZF0 = 377 Ω is the free space impedance. Time scales: 1 ns ∼ 30 cm (high-speed electronics, GHz) 1 ps ∼ 300 µm 1 fs ∼ 300 nm 1 as = 10−18 s ∼ 0.3 nm = 3 ˚A (typ-lattice constant in metal) The shortest pulses generated to date are about 4 − 5 fs at 800 nm (λ/c = 2.7 fs), less than two optical cycles and 250 as at 25 nm. For few-cycle pulses, the electric field becomes important, not only the intensity! Figure 1.2: Electric field waveform of a 5 fs pulse at a center wavelength of 800 nm. The electric field depends on the carrier-envelope phase
31.3.APPLICATIONSaverage power:Pave ~1W, up to 100 W in progress.kW possible, not yet pulsedrepetition rates:Trl = fr= mHz - 100 GHzpulse energy:W = lpJ- 1kJpulse width:5 fs - 50 ps,modelockedTFWHM=30 ps -100 ns,Q- switchedpeak power:1kJ~1PW,Pp1psobtained with Nd:glass (LLNL - USA, [1][2][3])For a typical lab pulse, the peak power is10nJPp~1MW10 fspeak field of typical lab pulse:V106 × 1012 V10V~10101/2×377Ep=元× (1.5)mmnm1.3Applications High time resolution: Ultrafast Spectroscopy, tracing of ultrafast phys-ical processes in condensed matter (see Fig. 1.3), chemical reactions,physical and biological processes, influence chemical reactions with fem-tosecond pulses: Femto-Chemistry (Noble Prize, 2000 to A. Zewail),high speed electric circuit testing and sampling of electrical signals, seeFig. 1.4
1.3. APPLICATIONS 3 average power: Pave ∼ 1W, up to 100 W in progress. kW possible, not yet pulsed repetition rates: T −1 R = fR = mHz − 100 GHz pulse energy: W = 1pJ − 1kJ pulse width: τFWHM = 5 fs − 50 ps, modelocked 30 ps − 100 ns, Q − switched peak power: Pp = 1 kJ 1 ps ∼ 1 PW, obtained with Nd:glass (LLNL - USA, [1][2][3]). For a typical lab pulse, the peak power is Pp = 10 nJ 10 fs ∼ 1 MW peak field of typical lab pulse: Ep = s 2 × 377 × 106 × 1012 π × (1.5)2 V m ≈ 1010 V m = 10 V nm 1.3 Applications • High time resolution: Ultrafast Spectroscopy, tracing of ultrafast physical processes in condensed matter (see Fig. 1.3), chemical reactions, physical and biological processes, influence chemical reactions with femtosecond pulses: Femto-Chemistry (Noble Prize, 2000 to A. Zewail), high speed electric circuit testing and sampling of electrical signals, see Fig. 1.4