Trajectory displacement in a multi beam scanning electron microscope.

The analytical theory of statistical Coulomb interactions allows to determine the trajectory displacement in a single rotationally symmetrical beam with well-behaved spatial and angular particle distributions. This can be used to estimate the trajectory displacement in a multi-beam system using the so called fully-filled segment approximation. This approach predicts full compensation of trajectory displacement for a specific setup of the system. We show that this prediction is not consistent with Monte Carlo simulations and we develop a new approach to the calculation, showing that two independent trajectory displacement contributions are present in a multi-beam system. We support this calculation with Monte Carlo simulations as well as with experimental data from a multi-beam system.

Analytical formulae for trajectory displacement in electron beam and generalized slice method.

Trajectory displacement due to statistical Coulomb interactions can play a major role in determining the performance of a charged particle beam system. Accurate estimation of the trajectory displacement is thus an important part of the design procedure of such an optical system. Traditionally, there are three approaches to determine the trajectory displacement: Monte Carlo simulation, the slice method, where trajectory displacement is integrated along the beam length and finally a full analytical formula describing transparently the dependence of the trajectory displacement on the parameters of the system. The latter two were developed thoroughly by Jansen and Jiang. We revise Jansen's slice method and the derivation of the integral formulae in Holtzmark and pencil-beam regimes. We show the integral formula fails to give accurate results in case a transition between the regimes occurs and we derive a new analytical expression unifying the Holtzmark and pencil-beam regime into a single formula. Furthermore, we generalize the slice method for arbitrary beam trajectory, hugely increasing its accuracy for non-ideal systems.

Robustness of Light-Transport Processes to Bending Deformations in Graded-Index Multimode Waveguides.

Light transport through a multimode optical waveguide undergoes changes when subjected to bending deformations. We show that optical waveguides with a perfectly parabolic refractive index profile are almost immune to bending, conserving the structure of propagation-invariant modes. Moreover, we show that changes to the transmission matrix of parabolic-index fibers due to bending can be expressed with only two free parameters, regardless of how complex a particular deformation is. We provide detailed analysis of experimentally measured transmission matrices of a commercially available graded-index fiber as well as a gradient-index rod lens featuring a very faithful parabolic refractive index profile. Although parabolic-index fibers with a sufficiently precise refractive index profile are not within our reach, we show that imaging performance with standard commercially available graded-index fibers is significantly less influenced by bending deformations than step-index types under the same conditions. Our work thus predicts that the availability of ultraprecise parabolic-index fibers will make endoscopic applications with flexible probes feasible and free from extremely elaborate computational challenges.