Imaging with singular electromagnetic beam

Laguerre-Gaussian beams are considered as basis functions for inverse scattering applications. First order perturbation theory is applied to paraxial higher order Gaussian beams. Information about the scattering potential is deduced from the coupling coefficients between otherwise orthogonal modes. This leads to a theoretical description analogous to plane wave diffraction tomography. Differences between the plane wave model and the Laguerre-Gauss formalism highlight both limitations as well as opportunities for applying singular Gaussian beams to the inverse scattering problems. The perturbation analysis is applied to a number of examples illustrating how information about the scattering object can be deduced from measurements of the scattered paraxial field.

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