An Investigation of Possible Non-Standard Photon Statistics in a Free-Electron Laser

Abstract

In an experiment performed some time ago, it was reported that the photon statistics of the 7th harmonic radiation of MARK III free-electron laser (FEL) was sub-Poissonian-neither Poissonian as expected from a coherent FEL output nor chaotic as expected from an incoherent radiation source. Whether FEL light exhibits such non-standard behavior is an important issue; if it does, our understanding of the FEL needs to be radically modified. This dissertation is an attempt to perform a comprehensive investigation of the conclusions of the above experiment. The investigation is performed from several perspectives-theoretical basis for the non-standard photon statistics as well as a re-examination of the data analysis of that experiment. The observed behavior may arise from the quantum nature of the FEL dynamics. Therefore, first, we take a critical look at the experiment; we revisit the semiclassical radiation theory and the standard theory of FEL photon statistics of the fundamental mode starting from the noise, and then develop the simplest quantum extension of the classical theory of harmonic radiation production as driven by the fundamental mode. We include the cavity loss with a beam splitter model, and compute the photon statistics of the harmonic modes. We show that the statistics cannot be sub-Poissonian for any initial state of the electrons. The main argument made from the experiment was that the Fano factor F (the ratio of photon number variance to the average photon number) was lower than the value expected from a Poissonian source and also exhibits a significantly different behavior from a chaotic source. If non-standard FEL dynamics are ruled out, the effect must be due to some features of photon detecting schemes which are difficult to study analytically. We have therefore performed a comprehensive simulation of the Fano factor measurement set-up, starting from the FEL simulation using the GINGER code, and photon-detection simulation incorporating photon clustering and the photon counter’s dead time effect. According to the re-examination, we find that the observed value of F could be explained within the standard FEL theory if one combines the detector dead time effect with photon clustering arising from the FEL gain. Therefore, we propose an improved experiment for a more definitive measurement of the FEL photon statistics.