A novel 3D pseudo-spectral analysis of photonic crystal slabs

Baghai - Wadji, A and Varis, K 2004, 'A novel 3D pseudo-spectral analysis of photonic crystal slabs', Applied Computational Electromagnetics Society Journal, vol. 19, no. 1b, pp. 101-111.

Document type: Journal Article
Collection: Journal Articles

Title A novel 3D pseudo-spectral analysis of photonic crystal slabs
Author(s) Baghai - Wadji, A
Varis, K
Year 2004
Journal name Applied Computational Electromagnetics Society Journal
Volume number 19
Issue number 1b
Start page 101
End page 111
Total pages 11
Publisher Applied Computational Electromagnetics Society
Abstract We consider a double-periodic slab which is characterized by two lattice vectors a1 and a2 on the (x,y)-plane, the thickness hz and a three-dimensional scalar function epsilon(x,y,z) specifying the dielectric constitution of the slab. Above and below the slab is free space. These assumptions imply that the z-direction is special in this problem. Therefore, following a general scheme we diagonalize the Maxwell's equations with respect to this direction. The periodicity in two directions suggests the use of spatially harmonic functions as a basis. We exploit this property; however, contrary to the traditional schemes, we propose an expansion of the fields in the form Psi(r,z) = Sigma nfn(z)exp(jKn·r) allowing fn(z) to be a fairly general function of the z-coordinate, rather than an exponential function. In this expression r is the position vector in the (x,y-) transversal plane. To guarantee maximum flexibility we discretize f in terms of finite differences. We demonstrate the superiority of our method by discussing the following properties: i) Diagonalization only involves the transversal field components, ii) Diagonalization allows us easily to construct and implement various boundary conditions at the bounding surfaces z = 0 and z = hz, iii) The resulting discretized system is extraordinarily stable and robust, and facilitates fast computations; from the computational performance point of view it compares well with existing methods, while it by far applies to larger class of problems, iv) It allows to use both the radian frequency omega and the wavevector K as input parameters. Therefore, the resulting discrete system can be solved at individual omega, K)-points of interest, v) Finally, the method is applicable to both the eigenstate end the excitation problems.
Subject Numerical Solution of Differential and Integral Equations
ISSN 1054-4887
Version Filter Type
Citation counts: Scopus Citation Count Cited 3 times in Scopus Article | Citations
Access Statistics: 206 Abstract Views  -  Detailed Statistics
Created: Wed, 22 Dec 2010, 10:15:00 EST by Catalyst Administrator
© 2014 RMIT Research Repository • Powered by Fez SoftwareContact us