B-spline modal method: a polynomial approach compared to the Fourier modal method.

A detailed analysis of the B-spline Modal Method (BMM) for one- and two-dimensional diffraction gratings and a comparison to the Fourier Modal Method (FMM) is presented. Owing to its intrinsic capability to accurately resolve discontinuities, BMM avoids the notorious problems of FMM that are associated with the Gibbs phenomenon. As a result, BMM facilitates significantly more efficient eigenmode computations. With regard to BMM-based transmission and reflection computations, it is demonstrated that a novel Galerkin approach (in conjunction with a scattering-matrix algorithm) allows for an improved field matching between different layers. This approach is superior relative to the traditional point-wise field matching. Moreover, only this novel Galerkin approach allows for an competitive extension of BMM to the case of two-dimensional diffraction gratings. These improvements will be very useful for high-accuracy grating computations in general and for the analysis of associated electromagnetic field profiles in particular.

A construction guide to analytically generated meshes for the Fourier Modal Method.

The concepts of adaptive coordinates and adaptive spatial resolution significantly enhance the performance of Fourier Modal Method for the simulation of periodic photonic structures, especially metallo-dielectric systems. We present several approaches for constructing different types of analytical coordinate transformations that are applicable to a great variety of structures. In addition, we analyze these meshes with an emphasis on the resulting convergence characteristics. This allows us to formulate general guidelines for the choice of mesh type and mesh parameters.

Titania woodpiles with complete three-dimensional photonic bandgaps in the visible.

Titania woodpile photonic crystals are fabricated by a combination of stimulated-emission depletion direct laser writing and a novel titania double-inversion procedure. The procedure relies on atomic-layer deposition, which is also used to fine-tune the template geometry to maximize the gapsize. Angle- and polarization-resolved transmittance spectroscopy and a comparison with theory provide evidence for the first complete photonic bandgap in the visible.