formalism to minimize the focal spot size and discuss the appearance of superoscillating fields. For these applications, we describe, respectively, the electromagnetic field as a superposition of scalar Laguerre-Gaussian beams, vectorial Bessel beams or more general plane waves within the angular spectral decomposition representation of light. In the third part of the paper, we report a particular experimental implementation of the OEi method using computer controlled spatial light modulators to squeeze the spot size of a superposition of Bessel beams. In the last part of the paper, the method is applied in numerical 3D modelling to determine the OEi yielding the largest transmission through a sub-wavelength aperture and the largest optical force on a micrometer sized particle. The paper concludes with a discussion of the particular results obtained and with general comments on the versatility of the OEi method to a wide range of problems. A short annex compares the convergence properties of the OEi approach with standard phase front correction methods.

Method {#s:fundcon}
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The OEi method exploits both the linearity of Maxwell’s equations and the quadratic dependence of light-matter interactions on the electromagnetic field $\{\mathbf{E},\mathbf{H}\}$ where $\mathbf{E}$ and $\mathbf{H}$ denote the electric and magnetic field vectors, respectively. Table 