Generation of ultra-long optical needles with dual-ring cosine filter

Combining the advantages of phase and amplitude modulation, we designed a dual-ring cosine filter which was consisted by an inner and outer ring, and the two rings have different number of paired cosine phase. Using the dual-ring cosine filter, ultra-long longitudinally polarized optical needles were obtained by tight focusing radially polarized Bessel-Gaussian beams with a single lens system. The obtained optical needles have a depth of focus of 268 lambda, lateral full width of 0.37 lambda at half height, the beam quality of 94%, and axial uniformity of 95%. In addition, we found that the depth of focus of obtained optical needles can be further stretched and the lateral dimension can be further compressed by increasing the number of paired cosine phase. The ultra-long optical needles were appropriately applied in the fields of optical beam lithography, laser direct writing, particle acceleration, and optical trapping.