Discrete complex amplitude filter for ultra long optical tube

Abstract

We proposed a discrete complex amplitude filter to create a focused hollow field with ultra long depth of focus. As for a high numerical aperture lens (NA=0.95), the focused field in the focal region can be engineered into a field like a long "tube" with flat wall through manipulating the distribution of the transmitted amplitude and phase at the pupil plane. This complex amplitude filter at the pupil plane can be discretized into multiple annular zones with different radius, transmittances and phase delays. A focused tube field with long depth of focus(~9λ) has been created as an example through separating and averaging of the projected pupil radiation pattern of magnetic dipole array in the focal region. Imperfections of the designed filter will influence the quality of the generated optical tube field and tolerance deviation of the radius, transmittance and phase delay in each zone is discussed. For the optical trapping, this created tube field can expand the manipulated distance and increase the trapped particles' numbers.