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Optical coherence tomography, or in short OCT, is a measurement technique established in the early 1990s for the non-invasive imaging of interfaces in the bulk of biological tissues or other samples. A full-field OCT setup is built from a microscope combined with a Michelson interferometer, where the mirror in one arm is replaced by the sample. Using white light, which is temporally partially coherent, interference fringes disclose the presence of an interface whenever the lengths of both interferometer arms are nearly equal. Scanning one arm allows for a volumetric reconstruction of all interfaces inside the sample. While the importance of OCT in medicine is indisputable, it is hard to teach students the basic aspects of such technology as most available setups tend to be rather complex. It is our purpose to present a fully functional full-field OCT setup that is stripped-down to its essential components and to promote its use in an undergraduate lab course. The contribution is complemented by a description of the basic theory necessary to understand the working principle of OCT.

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.

The Fourier modal method (FMM) has advanced greatly by using adaptive coordinates and adaptive spatial resolution. The convergence characteristics were shown to be improved significantly, a construction principle for suitable meshes was demonstrated and a guideline for the optimal choice of the coordinate transformation parameters was found. However, the construction guidelines published so far rely on a certain restriction that is overcome with the formulation presented in this paper. Moreover, a modularization principle is formulated that significantly eases the construction of coordinate transformations in unit cells with reappearing shapes and complex sub-structures.

We prepared thin film opal crystals and studied their angle-resolved transmission spectra in linear and circular polarized light as a function of the incidence angle and the azimuth rotation angle. We also explored the polarization conversion in linear and circular polarized light. Based on the spectra analysis we ascribed the polarization conversion in opal photonic crystal to properties of the Bloch modes of 3-dimensional photonic crystal.

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.

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.

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. © 2012 American Physical Society.

Studies of polarized light propagation in 3-dimensional photonic crystals (PhCs) allow the assessment of fundamental aspects of light-to-structure interaction. Among many works addressing polarization anisotropy of the PhC optical response, the investigations of cross-polarized coupling are surprisingly rare and incomplete in spite of their immense importance for designing functional optical materials.

Artificial opals are a popular platform for investigating fundamental properties of Photonic Crystals (PhC). In this work, we provide a theoretical analysis of polarization‐resolved transmission experiments through thin opal films. Despite the full cubic symmetry of the PhC, this system provides a very efficient mechanism for manipulating the polarization state of light. Based on band structure calculations and Bloch mode analysis, we find that this effect closely resembles classical birefringence. Due to the cubic symmetry, however, a description using tensorial quantities is not possible. This indicates fundamental limitations of effective material models for Photonic Crystals and demonstrates the importance of accurately modelling the microscopic geometry of such systems.

The Fourier modal method (FMM) is a common tool when transmittance or reflectance spectra of periodic structures are needed. In this work, we investigate an approach one could call the B‐spline modal method (BMM). We use an S‐matrix algorithm for connecting different layers but instead of a Fourier basis we use B‐splines to solve Maxwell’s equations in each layer. The advantage of B‐splines compared to plane waves is that they can represent discontinuities accurately. These discontinuities (naturally arising at interfaces between different materials) are problematic for the FMM since a finite Fourier series will always be smooth and one has to deal with Gibbs’ phenomenon. In this work, we present a comparison of the convergence behavior between FMM and BMM.