Information on propagating and evanescent Bloch modes as well as on remaining disorder is provided by experiments on titania woodpile photonic crystals with a complete three-dimensional photo­nic bandgap at visible wavelengths. Such frequency-resolved reciprocal-space mapping of visible spontaneous emission from 3D photonic crystals is analogous to angle-resolved photoemission spectroscopy (ARPES) on ordinary crystals.

We present a cluster coherent potential approach for disordered photonic crystals (PhCs) that is based on maximally localized Wannier functions. In particular, the Wannier basis facilitates an efficient representation of the photonic band structure of a defect-free PhC and the Green’s function thereof, which we discuss first. Moreover, the Wannier basis allows for adapting elaborate approaches developed for the analysis of disorder in electronic and phononic systems to PhCs.

Angle-resolved polarized transmission spectra of thin-film opals are studied experimentally and theoretically as a function of the azimuthal rotation of the plane of incidence at different angles of light incidence. In such 3-dimensional lattices, the refraction acquires the form of diffraction orders, each with a distinct spectrum, that propagate simultaneously along different directions. The corresponding continuous and patchy stop-bands in the photonic energy band structure of the opal photonic crystal are determined numerically.

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.

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.

The radiation dynamics of a magnetic dipole located inside a photonic crystal has been considered as an analogue for optical emission of a point-like emitter in such a crystal. We have experimentally realized this situation by fixing a single crystal yttrium iron garnet (YIG) sphere of 1.7 mm diameter inside a photonic crystal consisting of dielectric alumina rods. These rods form a woodpile structure of size 16 × 6 × 6 cm3 . The photonic crystal shows a band gap at microwave frequencies between 12.9 and 14.3 GHz as calculated and verified from the transmission characteristics of the crystal.

A simple protocol for the fabrication of three-dimensional (3D) photonic crystals in silicon is presented. Surface structuring by nanosphere lithography is merged with a novel silicon etching method to fabricate ordered 3D architectures. The SPRIE method, sequential passivation reactive ion etching, is a one-step processing protocol relying on sequential passivation and reactive ion etching reactions using C4F8 and SF6 plasma chemistries.

We report on the generation of maximally localized photonic Wannier functions under constraints. This allows us to impress certain symmetry properties of the underlying Photonic Crystal onto the Wannier functions. This added flexibility enhances the utility of the Wannier function approach to Photonic Crystal circuits by providing deeper physical insight and making computations more efficient.

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.