Martínez Herrero, María RosarioMaluenda, DavidJuvells, IgnasiCarnicer, Artur2023-06-172023-06-172019-02-18978-1-5386-6013-310.1109/WIO.2018.8643545https://hdl.handle.net/20.500.14352/13995©2018 IEEE Computer Society Workshop on Information Optics (17. 2018. Quebec, Canadá) ISSN: 2472-159X R.M.H. and A.C. acknowledges support from Ministerio de Economia y Competitividad (MINECO) grant number FIS2016-75147-C3-1-P.According to intensity consideration along the propagation axis, we derived mathematical conditions for a family of modulating functions able to produce needles of arbitrary length, sub-wavelength width and almost constant irradiance. These functions are derived by introducing mathematical constrains on the on-axis power content. As a result, the modulating distribution is continuous with no jumps within or at the edge of the pupil. Numerical results suggests that the proposed approach is suitable for producing high quality needles.engbook parthttp://dx.doi.org/10.1109/WIO.2018.8643545https://ieeexplore.ieee.orgopen access535Longitudinally polarized-lightDepthFilterFocusLensSpotLight needlesHigh numerical aperture optical systemsPolarizationÓptica (Física)2209.19 Óptica Física