Engineering arrays of diffraction-limited hollow tubes and doughnut spots with prescribed distributions

Based on the principle of antenna pattern multiplication as the product of the element pattern and the array factor, a simple and flexible method to generate diffraction-limited optical hollow-tube and doughnut-spot arrays with predetermined properties is proposed. This approach can be realized in a 4Pi focusing system by reversing the field radiated from the collinear antenna array whose elements are isotropic magnetic current sources. Both hollow tubes and doughnut spots produced by this method are pure azimuthally polarized fields whose intensity distribution is nearly unchanged along the entire depth of focus. Numerical results show that the appearance and position of the focal field is determined by the element pattern and the array factor, respectively. These peculiar optical focal fields may find applications in multi-particle trapping and manipulation, materials processing, data storage, super-resolution optical microscopy and optical lithography.