Pulse duration of a partially coherent soft X-ray laser estimated from far-field speckle statistics

A novel method for estimating the pulse duration of partially coherent soft X-ray pulses from a far-field intensity pattern is presented. The method is based on intensity statistics at a single point in space and time, which allows the number of coherent longitudinal modes to be measured. Utilizing the knowledge of the coherence time of the radiation, either from the measurement of the spectral bandwidth or from numerical simulations, the duration of each individual pulse can be evaluated. This method was used to estimate the pulse duration of the laser-driven nickel-like molybdenum soft X-ray laser that is based on amplified spontaneous emission from a narrow plasma column and emits at a wavelength of 18.9 nm. By varying the length of the gain medium, a clear dependence of the number of modes caused mainly by the spectral line narrowing was observed. Supported by simulations of radiative transfer and pulse propagation, the pulse duration at the end of a 3 mm long gain medium was estimated to be 3.5 ps. The experimental data from far-field intensity patterns were also analyzed by applying the generalized van Cittert-Zernike theorem, providing a lower bound of effective source size.