Characterization of a Chaotic Optical Field Using a High-Gain, Self-Amplified Free-Electron Laser

We report on a characterization of the chaotic optical field from a high-gain, self-amplified spontaneous-emission (SASE) free-electron laser. The temporal structure of the amplitude and phase are measured in a single-shot mode, with a resolution well below the coherence length, and the statistics over multiple pulses is determined. The measurement is in excellent quantitative agreement with the prediction based on analysis of random noise, and further verifies the chaotic nature of the SASE optical field.

Figure 1

(a)–(c) Examples of the raw and the reconstructed FROG traces, along with the field intensity and phase as a function of time and wavelength. Red: intensity; Blue: phase.

Figure 2

Field intensity (solid line) and phase (dashed line) as a function of time from a simulation with an electron bunch that is long compared to the coherence length using Eq. (1).

Figure 3

Distribution of (a) the spike width $\Delta \tau$ and (b) the peak-to-peak spacing $\Delta t$ between the intensity spikes normalized to the average spike width $⟨\Delta \tau ⟩$. Experimental data (symbols), theoretical calculation (solid line), and simulation results (dashed lines) are all presented when possible.

Figure 4

Distribution of phase derivative at the intensity maxima (a) and minima (b) normalized to the rms SASE FEL bandwidth. Experimental data (symbols), theoretical calculations (solid lines), and simulation results (dashed lines) are all presented. Note the different horizontal scales for (a) and for (b).