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<<Simulation and Investigation of Finite Photonic Crystals Made of Biisotropic or Chiral Material
D.D.Karkashadze1, F.G.Bogdanov1, R.S.Zaridze1, Ch. Hafner2
1Tbilisi State University,
Chavchavadze Ave., 380028 Tbilisi, Georgia Fax: +995 32 290845; email: HYPERLINK "mailto:lae@access.sanet.ge" lae@access.sanet.ge
2Swiss Federal Institute of Technology,
CH-8092 Zurich, Switzerland
Fax: +41 1 632 1198; email: HYPERLINK "mailto:Hafner@ifh.ee.ethz.ch" Hafner@ifh.ee.ethz.ch
Abstract
Recently, the Band-Gap phenomenon in doped photonic crystals has been widely used to design various components of Integrated Optics. Various shapes and material fillings of primitive cells of photonic crystals have been investigated and applied to efficiently create bandgap structures with desired properties. In the design of large-scale Photonic Integrated Circuits (PIC), there is a strong trend towards much smaller components, such as Finite Photonic Band-Gap (PBG) structures, which cannot be efficiently simulated by traditional methods. Furthermore, a need arises to more neatly consider realistic material properties of these crystals.
A goal of the present work is to develop an efficient technique to simulate electromagnetic scattering and propagation processes in finite photonic crystals, taking into account the magnetic activity of such crystals, i.e. their sensitivity with regard to the rotation direction of the primary field polarization plane. To model such effects, the anisotropic as well as the chiral nature of majority of crystals was taken into account.
The simulation process is subdivided into the following two steps.
First, an interaction model of a primary field with a single primitive cell of the given crystal is being developed. As such a primitive cell, a domain Do, confined by some surface S and filled with a homogeneous medium is considered. In this work, a general type, four-parameter biisotropic (including chiral) medium with complex material parameters EMBED Equation.3 is investigated. In order to obtain the desired interaction model, the surface S, as well as the parameters EMBED Equation.3 should be chosen in such a way that the absorption spectrum, the spectral line intensity, and the spectral line width of a given primitive cell are simulated as accurately as possible. Since the complex materials are always sensitive to the rotation direction of polarization plane, the biisotropic medium with 8 degrees of freedom allows one to adequately simulate the given absorption and scattering processes.
In the second step, the scattering process in finite photonic crystals, representing spatial gratings of primitive cells is investigated. The shape and material properties of the grating cells are taken from the first step of the problem solution. This allows one to simulate scattering and propagation processes in photonic crystals with given crystallographic structure in the presence of certain defects, such as extrinsic cells, vacancies, dislocations and so on. Moreover, the influence of inter-cell interaction on the dispersion properties of a single cell - such as the shift of resonance frequencies, spectral line spreading, changes in the sensitivity to the rotation direction of the primary field polarization plane, etc. may be studied.
The technique described above has been applied to simulate scattering and propagation processes in concrete photonic crystals. The obtained detailed results will be presented and discussed.
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