Modeling the optical response of 3D disordered structures using the Korringa–Kohn–Rostoker method

GABRIEL LOZANO, LUIS A. DORADO, HERNÁN MÍGUEZ AND RICARDO DEPINE

Optical Properties of Photonic Structures: Interplay of Order and Disorder (Series in Optics and Optoelectronics)

Taylor & Francis Group

Lugar: LONDRES; Año: 2012; p. 39 - 54

In this chapter we use the Korringa–Kohn–Rostoker (KKR) method, a rigorous method valid for perfectly periodic structures, to simulate disorder effects in 3D PCs. Two approaches are considered: extinction methods and statistical methods. In extinction methods, energy losses are artificially added to perfectly periodic crystals made of transparent materials. These artificial losses take into account the light scattered by imperfections in the crystalline structure. In statistical  methods, however, deviations from perfect periodicity are modeled by statistical distributions of sizes, shapes, and vacancies of the PC building blocks. Examples will be given for the case ofsynthetic opals made of dielectric spheres, a case for which several measured optical spectra are available. Thus, the chapter is organized as follows. In Section 2.3.2, we review the framework of the KKR multiple scattering approach for spherical particles. In Section 2.3.3, we present a description of the optical properties of defect-free artificial opals. We start by describing the band structure and predicting the optical response of a lattice with no losses. In Section 2.3.4, we gradually introduce defects in the model by an extinction approach and another one based on a statistical distribution of imperfections.  In particular, the focus of the formulation is placed on disorder effects related to polydispersity or variations in the size of particles as well as sphere vacancies. At those energies for which very low-dispersion propagation modes are attained, we predict that perfect lattices should present a strongly fluctuating optical response that rapidlysmoothes out as the amount of imperfections gradually increases. The comparison between the results obtained using the two different approaches is addressed in Section 2.3.5. Finally, in Section 2.3.6, the more outstanding results are summarized and discussed.