In this work, we investigate the stability of the nitrogen fluorescence signal emitted by a femtosecond laser filament as
an example of a high order nonlinear optical process. It is found that the root-mean-square fluctuation of the fluorescence
signal emitted from the filament is less than 1 %. The corresponding estimated laser intensity fluctuation is as low as
0.14%, which is at least one order of magnitude lower than the input laser pulse power fluctuation. Further numerical
simulation has confirmed that the intensity clamping phenomenon is responsible for this observation. Since the intensity
clamping is an intrinsic property of filamentation phenomenon, it is expected that any intensity sensitive optical
interaction taking place inside filament could lead to highly stabilized outcome. This conclusion potentially affects
various applications of ultra-short laser filamentation.
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