Decomposition of a field with smooth wavefront into a set of Gaussian beams with non-zero curvatures.

Decomposition of a general arbitrary field into a set of Gaussian beams has been one of the challenges in the Gaussian beam decomposition method for field propagation through optical systems. The most commonly used method in this regard is the Gabor expansion, which decomposes initial fields into shifted and rotated Gaussian beams in a plane. Since the Gaussian beams used have zero initial curvatures, the Gabor expansion method does not utilize the ability of the Gaussian beams to represent the quadratic behavior of the local wavefront.

Decomposition of the total wave aberration in generalized optical systems.

The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process, surface-by-surface aberration contributions are of special interest. The expansion of the wave aberration function into field- and pupil-dependent coefficients is an analytical method used for that purpose.

Mapping Atomic Orbitals with the Transmission Electron Microscope: Images of Defective Graphene Predicted from First-Principles Theory.

Transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time. Here, we explore its capabilities by a first-principles approach. For the example of defected graphene, exhibiting either an isolated vacancy or a substitutional nitrogen atom, we show that three different kinds of images are to be expected, depending on the orbital character.