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Analytical inversion of the focusing of high-numerical-aperture aplanatic systems

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Abstract

We propose a method for an analytical inversion of the electric and magnetic fields at the focus of a high-NA aplanatic system to obtain incident light beam distribution. Our approach is based on an inverse Fourier transform of the Richards–Wolf formalism for targeted longitudinal fields along the radial or axial directions at the non-paraxial focus. Analytical solutions are discussed for both axial and radial focal fields for a radially polarized incident light beam, and a criterion is defined to access a physically valid solution. We also validate the method according to results found in the literature. Finally, we show how the method can be generalized to other incident field distributions.

© 2019 Optical Society of America

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