Math @ Duke

Publications [#244158] of Stephanos Venakides
Papers Published
 Haider, MA; Shipman, SP; Venakides, S, Boundaryintegral calculations of twodimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances,
Siam Journal on Applied Mathematics, vol. 62 no. 6
(July, 2002),
pp. 21292148, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/02/23)
Abstract: We compute the transmission of twodimensional (2D) electromagnetic waves through a square lattice of lossless dielectric rods with a channel defect. The lattice is finite in the direction of propagation of the incident wave and periodic in a transverse direction. We revisit a boundaryintegral formulation of 2D electromagnetic scattering [Venakides, Haider, and Papanicolaou, SIAM J. Appl. Math., 60 (2000), pp. 16861706] that is Fredholm of the first kind and develop a secondkind formulation. We refine the numerical implementation in the above paper by exploiting separability in the Green's function to evaluate the farfield influence more efficiently. The resulting cost savings in computing and solving the discretized linear system leads to an accelerated method. We use it to analyze Epolarized electromagnetic scattering of normally incident waves on a structure with a periodic channel defect. We find three categories of resonances: waveguide modes in the channel, highamplitude fields in the crystal at frequencies near the edge of the frequency bandgap, and very highamplitude standing fields at frequencies in a transmission band that are normal to the direction of the incident wave. These features are captured essentially identically with the firstkind as with the secondkind formulation.


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