Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation

We report a new method to create high purity longitudinally polarized field with extremely long depth of focus in the focal volume of a high numerical aperture (NA) objective lens. Through reversing the radiated field from an electric dipole array situated near the focus of the high-NA lens, the required incident field distribution in the pupil plane for the creation of an ultra-long optical needle field can be found. Numerical examples demonstrate that an optical needle field with a depth of focus up to 8λ is obtainable. Throughout the depth of focus, this engineered focal field maintains a diffraction limited transverse spot size (<0.43λ) with high longitudinal polarization purity. From the calculated pupil plane distribution, a simplified discrete complex pupil filter can be designed and significant improvements over the previously reported complex filters are clearly demonstrated.