Since the very first proposition of photonic crystals, their influence on the dynamics of spontaneous emission has been of great interest. The radiation dynamics is described by an integration kernel which--in a spectral representation--comprises two equally important contributions: the Lamb shift and the radiative contribution to the linewidth. The latter is connected to the density of states via Fermi's golden rule. To our knowledge, we present the first spatially resolved measurement of the complete radiation dynamics in a photonic crystal and of its local density of states over a wide spectral range. To this end we study a single magnetic dipole situated in a photonic crystal with a band gap at microwave frequencies and find non-Markovian behavior in excellent agreement with ab initio calculations.

Abstract: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 metallodielectric 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.

Abstract: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.

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. For diffraction at high Miller index planes, the diffraction pattern is often distorted due to multiple‐wave diffraction. The finite stacking of hexagonally close‐packed layers leads to an intrinsic 3‐fold rotation symmetry of these spectra, which is particularly pronounced in transmission for frequencies that correspond to wave vectors within the 1st Brillouin zone. Despite the cubic symmetry of the opal lattice, cross‐polarization coupling effects occur in the volume of the opal crystal. These effects are associated with the fact that, the opal eigenmodes are Bloch waves whose electromagnetic field distributions and dispersion relations are markedly different from plane waves.

Abstract:The concepts of adaptive coordinates and adaptive spatial resolution have proved to be a valuable tool to improve the convergence characteristics of the Fourier Modal Method (FMM), especially for metallo-dielectric systems. Yet, only two-dimensional adaptive coordinates were used so far. This paper presents the first systematic construction of three-dimensional adaptive coordinate and adaptive spatial resolution transformations in the context of the FMM. For that, the construction of a three-dimensional mesh for a periodic system consisting of two layers of mutually rotated, metallic crosses is discussed. The main impact of this method is that it can be used with any classic FMM code that is able to solve the large FMM eigenproblem. Since the transformation starts and ends in a Cartesian mesh, only the transformed material tensors need to be computed and entered into an existing FMM code.