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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. [ABSTRACT FROM AUTHOR]

A unique splitter is proposed and demonstrated to realize the generation and separation of autofocusing and autodefocusing circular Airy beams (CABs). The design of the splitter is derived from the Fourier transform of a CAB associated with the Pancharatnam-Berry phase, and the fabrication is carried out via a liquid-crystal photo-patterning technique. Autofocusing and autodefocusing CABs of orthogonal circular polarization states are spatially diffracted under the modulation of the splitter, and the energy distribution between these two CABs can be controlled by the incident polarization. A focal length of 40 cm is obtained, which can be customized as required. The propagation dynamics of the generated autofocusing and autodefocusing CABs are investigated, and the experimental results are in good accordance with the corresponding simulations. The additional merits of the splitter, such as reconfigurability, tunability, high efficiency, and wide operating wavelength range, may motivate novel applications of CABs in the areas of laser optics, biomedicine, and modern displays.