By Massaro, A.; Akowuah, E.K.; Gorman, T.; Ademgil, H.; Haxha, S.; Robinson, G.K.; Oliver, J.V
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Extra resources for A Novel Compact Photomic Crystal Fibre Surface Plasmon Resonance Biosensor for an Aqueous Environment
Introduction A crystal is a periodic arrangement of atoms or molecules. The pattern with which the atoms or molecules are repeated in space is the crystal lattice. The crystal presents a periodic potential to an electron propagating through it, and both the constituents of the crystal and the geometry of the lattice dictate the conduction properties of the crystal. Importantly, however, the lattice can also prohibit the propagation of certain waves. There may be gaps in the energy band structure of the crystal, meaning that electrons are forbidden to propagate with certain energies in certain directions.
J, µj and dj are v the electric permittivity, the magnetic permeability, respective the thickness of the layer. v is the phase speed and ω is the angular frequency. The relationship between the wavelength λ and the angular frequency ω is v f 2 v . Be multiplying the M1 , M 2 , , Mm matrices we obtain a final matrix of the following shape: M M 11 M 21 M12 M 22 (3) 44 Photonic Crystals – Innovative Systems, Lasers and Waveguides Using the matrix obtained above we calculate the optical transmission with the following relationship: 2 T M11 M 22 i M12 M 21 2 (4) The MATLAB code is based on these equations for optical transmission calculus.
Importantly, however, the lattice can also prohibit the propagation of certain waves. There may be gaps in the energy band structure of the crystal, meaning that electrons are forbidden to propagate with certain energies in certain directions. If the lattice potential is strong enough, the gap can extend to cover all possible propagation directions, resulting in a complete band gap. For example, a semiconductor has a complete band gap between the valence and conduction energy bands. The optical analogue is the photonic crystal, in which the atoms or molecules are replaced by macroscopic media with differing dielectric constants, and the periodic potential is replaced by a periodic dielectric function (or, equivalently, a periodic index of refraction).
A Novel Compact Photomic Crystal Fibre Surface Plasmon Resonance Biosensor for an Aqueous Environment by Massaro, A.; Akowuah, E.K.; Gorman, T.; Ademgil, H.; Haxha, S.; Robinson, G.K.; Oliver, J.V