OPTICAL MODES OF A DISPERSIVE PERIODIC NANOSTRUCTURE
| Autor: | Alexei Deinega, G. Alagappan |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Nanostructure
Mathematical analysis Physics::Optics Perturbation (astronomy) Basis function Rational function Dielectric Cubic crystal system Condensed Matter Physics Electronic Optical and Magnetic Materials Condensed Matter::Materials Science Electrical and Electronic Engineering Eigenvalues and eigenvectors Photonic crystal Mathematics |
| Zdroj: | Progress In Electromagnetics Research B. 52:1-18 |
| ISSN: | 1937-6472 |
| Popis: | We show that the optical modes of a periodic nanostruc- ture with frequency dependent dielectric constant (i.e., a dispersive optical nanostructure), in general can be written as an ordinary eigen- value problem of a \dielectric function operator", for each distinct sym- metry representation of the periodic nanostructure. For a frequency dependence in the form of polynomial rational function, the problem translates to a polynomial eigenvalue equation in the frequency of the mode. The resulting problem can be solved using the basis functions of a dielectric backbone structure, which has a frequency independent dielectric constant. Rapid convergence is achieved when the basis func- tions are selected to be the modes of a dielectric backbone structure that minimizes the frequency perturbation of the dielectric function of the optical nanostructure. In particular, using a two dimensional photonic crystal constructed with a polar crystal as an example, we demonstrate that, remarkable simple cubic equations are su-cient to obtain accurate descriptions of eigenfrequencies. |
| Databáze: | OpenAIRE |
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