| Abstrakt: |
State-of-the-art computational methods combined with common idealized structural models provide an incomplete understanding of experimental observations on real nanostructures, since manufacturing introduces unavoidable deviations from the design. We propose to close this knowledge gap by using the real structure of a manufactured nanostructure as input in computations to obtain a realistic comparison with measurements on the same nanostructure. We demonstrate this approach on the structure of a real inverse woodpile photonic bandgap crystal made from silicon, as previously obtained by synchrotron X-ray imaging. A 2D part of the dataset is selected and processed into a computational mesh suitable for a Discontinuous Galerkin Finite Element Method (DGFEM) to compute broadband optical transmission. We compare this to the transmission of a utopian crystal: a hypothetical model crystal with the same filling fraction where all pores are taken to be identical and circular. The shapes of the nanopores in the real crystal differ in a complex way from utopian pores due to scallops, tapering, or roughness. Hence, the transmission spectrum is complex with significant frequency speckle both outside and inside the main gap. The utopian model provides only limited understanding of the spectrum: while it accurately predicts low frequency finite-size fringes and the lower band edge, the upper band edge is off, it completely misses the presence of speckle, the domination of speckle above the gap, and possible Anderson localized states in the gap. Moreover, unlike experiments where one can only probe from the outside of a real crystal, the use of a numerical method allows us to study all fields everywhere. While at low frequencies the effect of the pore shapes is minimal on the fields, major differences occur at higher frequencies including the gap such as high-field states localized deep inside the real crystal. We conclude that using only external measurements and utopian models may give an erroneous picture of the fields and the local density of states (LDOS) inside a real crystal, while this is remedied by our new approach. |
