Fourier-space modification of a circular Airy beam and the creation of an optical needle

The propagation characteristics of a circular Airy beam (CAB) with Fourier spectrum modified by high-pass, low-pass and band-pass filters (HCAB, LCAB and BCAB for short) are investigated in detail in this paper. Compared with a common CAB, the abruptly autofocusing property of the HCAB is greatly enhanced, while the focal position, focal trajectory and the size of the focal spot do not change. Similar to a CAB with a low-pass filter, a BCAB can form an optical needle but with a much stronger maximum intensity. Not only does the width of this optical needle decrease by half, but also the intensity gradient increases by eight times.