The introduction of the concept of gradient force and scattering and absorption force is an important milestone in optical trapping. However the profiles of these forces are usually unknown, even for standard setups. Here, we successfully calculated them analytically via multipole expansion and numerically via Mie theory and fast Fourier transform. The former provides physical insight, while the latter is highly accurate and efficient. A recipe to create truly conservative energy landscapes is presented. These may open up qualitatively new features in optical manipulation.
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