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A technique using vector Slepian harmonics and multipole fields is presentedfor a general treatment of the inverse problem of high numerical aperturefocusing. A prescribed intensity distribution or electric field distribution inthe focal volume is approximated using numerical optimization and thecorresponding illuminating field at the entrance pupil is constructed. Threeexamples from the recent literature have been chosen to illustrate the method.

Solving the inverse problem of high numerical aperture focusing using vector Slepian harmonics and vector Slepian multipole fields