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Abstract
Filamentation with the amplitude modulation of Mathieu beam in air is investigated numerically. Non-diffracting characteristic of Mathieu beam is partly maintained in the intense femtosecond laser area even though it is only an amplitude modulation. The amplitude modulation of Mathieu beam delays filament onset and the high intensity will be regenerated in the on-axis area when intensity clamping disappears. During the evolution process, the bunch of filaments merges into a single filament eventually only by the property of non-diffraction. Using an amplitude modulation of an invariable beam as an initial condition of intense femtosecond laser pulse offers a new way to control filaments’ onset, distribution and prolongation, which would be useful in their potential applications.