Zheng-Ming Sheng Institute of Physics, CAS, China

1. Sino-Germany Symposium on Quantum Engineering Celebrating the Einstein Year of Physics, Nov. 23-27, 2005, Beijing, China a) Manipulation of high power laser pulses by plasma gratingsb) Powerful terahertz emssion from laser wakefield in plasma Zheng-Ming Sheng Institute of Physics, CAS, China H. C. Wu: Institute of Physics, CAS, China J. Zhang: Institute of Physics, CAS, China K. Mima: Institute of Laser Engineering, Osaka University, Japan

2. Outline • Motivations • Formation of plasma grating by intersecting laser pulses • Dispersion of the plasma Bragg grating • Manipulation of intense laser pulses by plasma Bragg grating • THz emission from laser wakefields • Summary

3. G. Mourouet al., Physics Today 1998 Relativistic Laser-Plasma Interaction GeV protons GeV electrons hn

4. J. Meyer-ter-Vehn, MPQ Garching Few-cycle laser pulses produce 100 MeV – 1 GeV electron pulses comparable to conventional accelerators, but on mm rather than km distances 100 years after Einstein´s papers on special relativity, they create macroscopic relativistic plasma on the table top with exciting applications.. He would have liked it !

5. Motivation Current high power lasers are produced by the CPA technology. The maximum power is limited significantly by the damage threshold of gratings, which is usually less than 1J/cm2. Plasma doesn’t have such limit. Does such a grating exist that can serve for pulse stretching and compressing? All optical elements for ultra-high intensity laser will be made by plasma -----J. Meyer-ter-Vehn

6. Pump Light I Pump Light II Formation of Plasma Bragg Grating Uniform Plasma The ponderomotive force of the interference fields of the two pump pulses pushes the electrons, which further drag the heavy ions through Coulomb force. Finally, an electrically neutral PBG forms, which can last as long as a few picoseconds. Z.-M. Sheng et al., Appl. Phys. B 77, 673 (2003).

7. Interaction of intersecting laser beams in plasma I ky kx x-y

8. Strong ponderomotive force

9. Formulations of the problem

10. Approximate stationary solution Assuming that quasi-charge-neutrality is fulfilled at long time, ni ≈ne, ∂pe,x/∂t=0, ∂pi,x/∂t=0, one obtains If a1=a2=0.1, Te=10eV, Ti=1eV, one obtains nmax=38.2n0. This proves to be overestimated as compared to the numerical results.

11. 1D PIC simulation parameters Two identical pulses: a=a0sin2(pt/t), 0≤t≤t a0~ 0.1, t ~60t0, Te=10eV, Ti=1eV, n0/nc=0.3

12. Initial Conditions in 1D-PIC Simulation: n0=0.3nc, L=100 λ0; a=0.03, T＝200τ0. The PBG begins to build up at t=300 τ0 and stays at the deepest modulation almost unchanged during 700-1300 τ0. The PBG begins to attenuate after t=1600 τ0, and completely disappears at t=2000 τ0.

13. Λ Theory of Light Propagation in an Uniform PBG Bragg principle: The light with λ=2Λ is fully reflected by PBG. Frequency of this light is named as Bragg frequencyωB. Key property of a grating: Bragg reflection occurs over a range of frequencies centered about ωB. This frequency range is photonic bandgap (i.e. forbidden gap).

14. Transmission Spectrum of UPBG Bandgap width: 0.12 ωB, i.e. 96nm for λ0=800nm.

15. 1D wave equation in underdense plasma: where: Bragg wave number Electron density of PBG: where:

16. Nonlinear coupled-mode equations (NLCME) : where:

17. Linearized coupled-mode equations (LCME): Dispersion relation: where: In homogeneous plasma: In homogeneous plasma gratings:

18. Group-velocity dispersion (GVD) The grating dispersion is normalon the lower branch of the bandgap; the dispersion is abnormal on the upper branch. Moreover, the grating dispersion approaches infinite at the bandgap edges.

19. Light Speed Reduction Signal light of ω=0.93ωBpropagates in the PBG at a group velocity of 0.34c only, which corresponds to 40% of the light speed in the uniform plasma (n0=0.3nc).

20. Pulse Stretching Signal light: a0=0.04, T0＝10τ0,a0exp(-t2/T02). The pulse is stretched faster when the light frequency is closer to the bandgap edge (0.935ωB). This is due to the increasing dispersion at the bandgap edge.

21. Chirped Pulse Compression (CPC) Signal light: a0=0.01, T0=50τ0, C=-4,a0exp[-(1+iC)t2/T02)]. The pulse is compressed faster when the light frequency is closer to the bandgap edge (0.935ωB).

22. Fast Compression of Bragg Grating Soliton (BGS) Mechanism of soliton formation in abnormal medium: Compensation between the abnormal GVD and SPM leads to the formation of optical soliton. Making the pulse negative chirped. Abnormal GVD: Self-phase modulation (SPM): Stretching the pulse spectrum, and making its center positive chirped.

23. Large grating dispersion on the upper branch of bandgap can reduce the length of soliton evolution. So one can compress the intense pulse in PBG faster than in uniform plasma. Signal light: a0=0.15, T0＝20τ0,a0exp(-t2/T02). In PBG, the pulse can be effiently compressed in the distance less than 100λ0. However, in the uniform plasma, the pulse have a maximum compression at z=500λ0.

24. Pump Light I Pump Light II Pump lights meet together Nonuniform ponderomotive force leads to NUPBG Formation of NUPBG Uniform Plasma

25. Perfect chirped-pulse compression in NUPBG dn small dn large Compressing positive chirped pulses Compressing negative chirped pulses Bandgap width: Δω/ωB=δn1(x)/nc

26. Reflection for high frequency components Reflection for low frequency components Compression of positive chirped pulses

27. Signal light: a0=0.01, T0=60τ0, C=4,ω0 = 0.975ωB Compression efficiency: ≥90% Energy loss: ≈0%.

28. PBG can be a novel tool for light control, and fast compression in the high intensity regime, because of their ultrahigh damage threshold >1000J/cm2. Shaper Filter Strecher Compressor PBG PBG can be a novel tool for ultra-intense light control H.C. Wu et al., Phys. Plasmas 12, 113103 (2005); Appl. Phys. Lett.87, 201502 (2005).

29. Terahertz wave Applications: Material characterization by THz spectroscopy; Tomographic imaging; Biomaterial applications. B. Ferguson and X.-C. Zhang, Nature Materials 1, 26 (2002)

30. THz Wave Emitters • Photoconductive dipole antenna • Optical rectification in Electro-optic crystals with femtosecond laser • Upconversion of radio frequency sources or downconversion of optical (Gunn, Bloch oscillator, gas lasers, optical parametric generators and oscillators) • Semiconductor THz laser “The lack of a high-power, low-cost, portable room-temperature THz source is the most significant limitation of modern THz system.” --- B. Ferguson and X.-C. Zhang, Nature Materials 1, 26 (2002).

31. An electron plasma wave is potentially a high-power THz source • Plasma waves that can be driven by ultrashort laser pulses oscillate typically at the THz range (e.g., ne=1018cm-3, wp/2p=9THz). • The field strength before wave-breaking is as high as 100 GV/m for ne=1018cm-3. • How can an electrostatic wave be converted • to an electromagnetic wave?

32. THz radiations from a vacuum-plasma interface by introducing an inhomogeneous plasma region w ~2p/tL tL ZM Sheng, HC WU, K Li, J Zhang, Phys. Rev. E 69, 025401(R) (2004). ZM Sheng, K Mima, J Zhang, H Sanuki, PRL 94, 095003 (2005). ZM Sheng, K. Mima, and J. Zhang, to appear in Phys. Plasmas.

33. Model calculation: schematic view

34. Plasma oscillations in inhomogeneous plasmas

35. Wave vector of a plasma wave in inhomogeneous plasmas

36. Dispersion of electromagnetic waves and electron plasma waves w EM wave Slope c wpe Langmuir waves Slope 31/2vte ES wave klDe 1 They meet each other only at k=0

37. Evolution of plasma waves in inhomogeneous plasmas from simulations x=ct/3

38. Mode conversion theory ES Conversion efficiency from electromagnetic waves into electrostatic wavesh is the same as its inverse problem q EM nccos2q nc Emission spectrum from wakefield is calculated by EM q ES nccos2q nc

39. 1D simulation at oblique incidence q=15, L=60l, dL=10, a0=0.5

40. Comparison with model

41. Energy conversion efficiency scaling C mainly depends upon the incident angle and the pulse profile. n0 dL L

42. Controlling of the bandwidth n2 n1

43. Effect of laser beam diameters Laser Beam Fourier transform of beam profile

44. Wakefield of an ultrashort laser pulse: the longitudinal electric field Laser n The local phase velocity is changing with time! (a=0.5, T=20t, n/L=0.01nc/60l)

45. Transverse magnetic field ZM Sheng, HC WU, K Li, J Zhang, Phys. Rev. E 69, 025401(R) (2004). (a=0.5, T=20t, n/L=0.01nc/60l)

46. Radiation pulse and spectra a0=0.5, L=60l0, T=20t0, w0=20l0

47. Two-dimensional simulation of oblique incidence W=10l, q=15o, t=160 W=20l, q=15o, t=160

48. Experimental observation of quasi-monoenergetic electron beams from laser wakefield acceleration C. G. R. Geddes et al., Nature 431, 538 (2004). E. Miura, K. Koyama et al., APL 86, 251501 (2005). @2TW, 50fs, 5mm, 1020cm-3 J. Faure et al., Nature 431, 541 (2004). S. P. D. Mangles et al., Nature 431, 535 (2004).

49. Laser 200 l 0.005 0.045 50 l 100 l 50 l Emission from a plasma channel (produced for GeV energy gain) J. Zheng 2005

50. Summary • Plasma Bragg gratings can be a novel tool for light control and fast compression in the high intensity regime, because of their ultrahigh damage threshold >1000J/cm2. • The radiations result from the excited large-amplitude plasma waves at the plasma boundary and through mode conversion from electrostatic to electromagnetic waves, where the plasma inhomogeneity plays a crucial role. The emission can both serve as a high intensity THz source and an easy diagnostic tool for the wakefield amplitude.