Mr. Andreas Rung Profile

Andreas Rung

at Uppsala Univ

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Proceedings Article | 29 December 2003 Paper

Interaction between photonic and polaritonic gaps studied with photonic band structure calculations

Andreas Rung, Herman Hogstrom, Carl Ribbing

Proceedings Volume 5184, (2003) https://doi.org/10.1117/12.504717

KEYWORDS: Polaritons, Photonic crystals, Dielectrics, Photon polarization, Sodium, Infrared radiation, Dispersion, Transmittance, Beryllium, Oxides

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The interaction between the two kinds of gaps that appear in the band structure of a photonic crystal has been studied. The structure gap appears as a consequence of diffraction in the periodic structure, if the optical contrast between the the two matrials is sufficiently strong. The width of such gaps increases with the optical contrast and the position, for a given structure, scales with the lattice constant. Secondly, the dielectric function of one of the materials may be such that the photonic crystal exhibits an effective stop band. Metals have a dielectric function with a large negative real part in the visible and infrared wavelength regions. Metallo-dielectric photonic crystals have been intensively studied recently, and interesting results have been obtained. Alternatively, a Reststrahlen band can be used, within which the dielectric function is metal-like. The physical mechanism behind such a band is the excitation of polaritons, i.e. lattice oscillations. Only compounds have Reststrahlen bands, and they appear in the infrared. We refer to the corresponding stopband as a polaritonic gap. Transfer matrix calculations have been used to obtain the photonic bandstructure in the infrared for a 2-D square structure consisting of beryllium oxide cylinders in air. Photonic band structure calculations across a reststrahlen band region are numerically demanding because of the strong dispersion. Calculations were made with different lattice constants and fill factors. We have compared a situation when the two gaps are widely separated, with one where the gaps are close or even on top of each other. We report two kinds of forbidden gap states as a function of the imaginary wave-vector. We use normal incidence transmittance spectra to define phonomenological gaps, and report their variation with linear density and lattice constant.

Proceedings Article | 29 December 2003 Paper

Si/SiO2 multilayer: a one-dimensional photonic crystal with a polaritonic gap

Herman Hogstrom, Andreas Rung, Carl Ribbing

Proceedings Volume 5184, (2003) https://doi.org/10.1117/12.504710

KEYWORDS: Silicon, Reflectivity, Dielectrics, Photonic crystals, Semiconducting wafers, Multilayers, Metals, Infrared radiation, Refractive index, Oxidation

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The silicon-silicondioxide system is used to illustrate the effect of interaction between a photonic gap in a periodic structure and a polaritonic gap originating from one of the constituent materials. Si is a near ideal dielectric material in the infrared region with a high refractive index and modest dispersion for λ>4 μm. Amorphous SiO₂ has lattice absorption in the infrared, with a strong Reststrahlen band covering the wavelengths 8-9.3 μm. Optical multilayer calculations of reflectance spectra for Si/SiO₂ double- and multilayers have been made. The results illustrate the effect of the metal-like optical properties of SiO₂ in the Reststrahlen region. The high reflectance band persists in thin double layers and combines with conventional interference in the dielectric Si-film. From conventional optical coating technology it is known since long that a dielectric coating can be used to broaden and strengthen a Reststrahlen band, but this has not previously been applied to photonic crystals. For the experimental part, the Si/SiO₂-system was prepared using standard microelectronic fabrication technology. Polycrystalline Si (poly-Si) and amorphous SiO₂ (a-SiO₂) were both deposited by CVD processes. Si from silane, and SiO₂ from decomposition of tetra-ethoxy-silane (TEOS). a-SiO₂ is also grown by wet- and dry oxidation of a Si wafer. The calculated and the measured reflectance spectra for Si/SiO₂ double-layers are compared, and the overall agreement is very satisfactory. In particular, we can observe the Reststrahlen band of high reflectance and the interaction between this material stop band and the designed stop band, defined by the layer thicknesses.

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