Nonlinear Optics (WiSe 2015/16)

Transcription

1 Nonlinear Optics (WiSe 2015/16) Franz X. Kärtner & Oliver Mücke, Bldg. 99, Room O3.097 & O & phone: Office hour: Tuesday, 9-10 am Lectures: Fr SemRm 4 Recitations: Fr SemRm 4 Start: Teaching Assistant: Frederike Ahr, Office O3.089, phone , frederike.ahr@cfel.de Hisang-Yu Chung, Office O3.107, phone , hisang-yu.chung@cfel.de Yizhou Liu, Office O3.107, phone , yizhou.liu@cfel.de Office hour: Thursday 9:30-11am Course Secretary: Christine Berber O3.095, phone x-6351, christine.berber@cfel.de. Class website: x_rays_division/teaching 1

2 Prerequisites: A basic course in Electrodynamics Required Text: Class notes will be distributed in class. Requirements: 10 Problem Sets, Term Paper, and Term paper presentation Collaboration on problem sets is encouraged. Grade breakdown: Problem set (30%), Participation (30%), Term paper (40%) Recommended Text: R. W. Boyd, Nonlinear Optics, Academic Press. Additional References: The Principles of Nonlinear Optics, Y. R. Chen, J. Wiley & Sons NY (1984). The Elements of Nonlinear Optics, P. N. Butcher & D. Cotter, Cambridge Studies in Modern Optics 9, (1990). Nonlinear Fiber Optics, G. P. Agrawal, Academic Press (1998). Solitons: an introduction, P. G. Drazin & R. S. Johnson, Cambridge Texts In Applied Mathematics, NY, (1989). 2

3 Syllabus 3

4 Syllabus 4

5 Syllabus 5

6 C. Manzoni et al. LPR 9, 129 (2015) O. D. Mücke et al., IEEE J. Sel. Top. Quantum Electron. 21, (2015)

7 Syllabus

8 High Order Harmonic Generation (HHG) High Energy Pulse Tunnel Ionization + Propagation + Recombination E(t) Electron Position Most energetic trajectory Gas nozzle Time ω = I U cutoff p p P. Corkum, Phys. Rev. Lett. 71, 1994 (1993) K. C. Kulander, SILAP Conference (1992) 8

9 Maximizing the recollision energy within a period 800nm + 400nm + 267nm + 200nm nm ω + 2ω + 3ω + 4ω ω perfect waveform for HHG maximize sinusoidal synthesized cut-off energy ~ 3.17U P ~ 9U P L. E. Chipperfield et al., Phys. Rev. Lett. 102, (2009) C. Jin et al., Nature Commun. 5:4003 (2014) S. Haessler et al., Phys. Rev. X 4, (2014) 9

10 1.1 Why Nonlinear Optics 10

11 Typical optical nonlinearities are weak 2 11

12 1.2 How does Nonlinear Optics work? P: Polarization (Dipole moment / unit volume) p: dipole moment per atom or molecule N: Number density q: charge that is displaced l: displacement Figure 1.1: A simple atom model explaining the effect of in optical electric field on the induced polarization in an atom: (a) without field, (b) with field. 12

13 Perturbation Expansion p: nonlinear dipole moment of atom or molecule α (ι) : typical excursion of electron cloud at the critical field is on the order of the Bohr radius Ε a : critical field where perturbation theory breaks down: Ionization field strength 13

14 Estimate for nonlinear susceptibilities Nonlinear susceptibilities 14

15 Estimate for (nonlinear) susceptibilities Refractive index: About right! 15

16 1.3 Important nonlinear optical processes Let s assume: 16

17 Important nonlinear processes 17

18 1.3.1 Linear electro-optical or Pockels Effect KDP: Potassium dihydrogen phosphat: KH 2 PO 4 E z Induced birefringence when electric field is applied in z- direction 18

19 Electro-optic modulator KDP: Potassium dihydrogen phosphat: Induzed birefringence when electric field is applied in z- direction 19

20 Electro-optic modulator 20

21 Modulator transmission 21

22 Estimate for nonlinear susceptibilities Nonlinear susceptibilities 22

23 1.3.2 Self-phase modulation 23

24 Das Bild kann zurzeit nicht angezeigt werden Self-focussing Lens Refractive index n >1 Intensity dependent refractive index: "Kerr-Lens" Catastrophic self-focusing Kerr Lens Modelocking Self-Focusing Aperture Laser beam Intensity Intensity Intensity Time Time Time 24

25 1.3.4 Optical Solitons Nonlinear Schrödinger Equation (NLSE) β2 D2 = β2 2 is GVD. 25

26 2 Nonlinear optical susceptibilities 26

27 Nonlinear optical susceptibilities 27

28 Nonlinear optical susceptibilities 28

29 2.2 Classical model for nonlinear optical suszeptibility Perturbation Solution: 29

30 Zero order solution 30

31 2.2.1 Linear Susceptibility 31

32 Real and Imaginary Part of the Susceptibility 32 32

33 Real and Imaginary Part of the Susceptibility 33

34 Real and Imaginary Part of the Susceptibility 34

35 Nonlinear susceptibility 35

36 Susceptibilities 36

37 2.3 Miller s δ-coefficient 37