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As the index contrast between the alternating layers is increased, the selectivity of the transmitted and reflected wavelengths is also increased. When generalized to two- and three-dimensions, this selectivity gives rise to high mode confinement. While 1D thin-film stacks have been known for over a century, their generalization to higher dimensions was not proposed until the 1970s by Bykov [5-8] as a potential means of inhibiting spontaneous emission. Bykov proposed the use of a periodic structure that served to inhibit certain electromagnetic frequencies, thereby disallowing spontaneous emission.
The slab structures discussed above have both rectangular and triangular hole grids. The triangular hole grids are not simply modeled in the Cartesian coordinate FDTD codes and use non-orthogonal FDTD formulation as discussed by Kuang, Kim and O'Brien [20]. An example of this calculation is shown in Fig. 4. Propagation Calculations The FDTD approach also allows the calculation of propagation in photonic crystals of finite size, for example the structure shown in Fig. 18. The plane wave technique is not able to do this as it only deals with infinite structures.
Along these lines, optical properties such as transmission, reflection, diffraction, and dispersion were measured in artificial opal structures made from monodisperse polystyrene colloids [27-36]. Transmission data showed dips corresponding to directional stop bands on a wavelength scale comparable to the spacing of the spheres.