1. 2004 CLEO/IQEC, San Francisco, May 15-21 Optical properties of the output of a high-gain, self-amplified free- electron laser Yuelin Li Advanced Photon Source, Argonne National Laboratory

2. 2004 CLEO/IQEC, San Francisco, May 15-21 Self Amplified free electron laser Continuously tunable Produce reliable coherent X-ray radiation

3. 2004 CLEO/IQEC, San Francisco, May 15-21 The low-energy undulator test line FEL: future ALFF 6 Hz, 0.5 ps, 50  J @ 120-530 nm Milton et al., Science 292, 2037 (2001)

4. 2004 CLEO/IQEC, San Francisco, May 15-21 The facility and application experiment Single Photon Ionization or Resonant Ionization at Threshold FEL undulator hall Li et al., PRL 89 234801 (2002).

5. 2004 CLEO/IQEC, San Francisco, May 15-21 The FROG experiment at 530 nm

6. 2004 CLEO/IQEC, San Francisco, May 15-21 The field of a SASE FEL (by solving Green’s function) is [S. Krinsky and Z. Huang, Phys. Rev. ST Accel. Beams 6, 050702 (2003).] Temporal structure: Analysis   resonant frequency  t coherence length   /  z electron beam energy chirp Goodman, Statistical Optics, (John Wiley & Sons, New York, 1985), p. 35. S. Krinsky, PRSTAB 6, 050701 (2003). Summing of random phasors: Chaotic light

7. 2004 CLEO/IQEC, San Francisco, May 15-21 Interest in temporal structure Experimental data Simulation Analytical theory

8. 2004 CLEO/IQEC, San Francisco, May 15-21 Li et al., PRL 91 243602 (2003). Temporal structure: spike width and spacing  = 52 fs Follow statistics for chaotic light exactly.

9. 2004 CLEO/IQEC, San Francisco, May 15-21 Li et al., PRL 91 243602 (2003). Derivative of phase (frequency)   =0.0094 rad/fs Each intensity spike is a coherence mode.

10. 2004 CLEO/IQEC, San Francisco, May 15-21 Frequency domain statistics correlation with time domain Phase derivative Spike number correlation between time and frequency domain Each spike in freq domain is a coherence mode The number of spikes in the two domains are statistically one to one.

11. 2004 CLEO/IQEC, San Francisco, May 15-21 Frequency domain statistics correlation with time domain Envelope   2.42    2/T  m freq       (1/2  t )/(2/T)  T/4  t  m time Number of spikes in time and frequency domain T=4m  t T=2m/  

12. 2004 CLEO/IQEC, San Francisco, May 15-21 SASE FEL output is chaotic: fully coherent transversely, but only partially coherent longitudinally Through measurement of the spectra, one can statisticall determine the temporal domain property, the most important one is the pulse duration for the future X-ray sources. Also the first time a chaotic light source is fully characterized. Conclusion

13. 2004 CLEO/IQEC, San Francisco, May 15-21 Chaotic light Candles + incandescent lights but with longer coherence length and a single spatial mode. Each time spike represents a coherence region. The sun Stars SASE FELs are chaotic light sources……

14. 2004 CLEO/IQEC, San Francisco, May 15-21 Seeding a SASE for better ……. Better longitudinal coherence/coherence control Shorter pulse duration/Pulse shaping Partly losing tunability…… FERMI@ELETTRA, scheme demonstrated at Brookhaven National Lab

15. 2004 CLEO/IQEC, San Francisco, May 15-21 J. Lewellen, V. Sajaev, K.-J. Kim, S. V. Milton, O. Makarov, R. Dejus (ANL) S. Krinsky (BNL) Z. Huang (SLAC) Work supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Contract No. W-31- 109-ENG-38. Acknowledgements