Method for retrieving the refractive index of ordered particles from data on the photonic band gap
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Method for Retrieving the Refractive Index of Ordered Particles from Data on the Photonic Band Gap A. A. Miskevich* and V. A. Loiko** Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, 220072 Belarus *email: [email protected]net.by **email: [email protected]net.by Received November 15, 2013
Abstract—A method for retrieving the refractive index of spherical particles arranged into ordered structures is proposed. It is based on the solution of the inverse problem using data on the photonic band gap. The solu tion has been obtained within the quasicrystalline approximation of the multiple wave scattering theory and the transfermatrix method. Quantitative results are presented for systems of silicon oxide particles. The effective refractive indices of synthetic opal particles have been found from the available experimental data on the spectral position of the photonic band gap. The described technique is applicable for retrieving not only the refractive index of particles but also other characteristics of ordered particulate structures from the coher ent transmittance spectra. DOI: 10.1134/S106377611408010X
1. INTRODUCTION Among the great variety of natural and artificial particulate media, the systems with an ordered struc ture occupy a special place. In particular, these include photonic crystals (PCs) [1–4]. Interest in their inves tigation stems from the fact that their spectra exhibit a photonic band gap (PBG) [5], the wavelength range in which a sharp decrease in transmittance and an increase in reflectance take place [2]. The PBG effect is attributable to the interference of waves during the interaction of radiation with an ordered structure. Photonic crystals are used to create bandpass filters, selective reflectors, and waveguides, when making lin ear and nonlinear optical and electrooptical devices: lightemitting diodes, solar cells, displays, lasers, etc. [6–13]. It becomes possible to create increasingly per fect PCs in connection with the development of engi neering and technology [14]. The PBG depth, width, and spectral position depend on the PC structure and the refractive index of its constituent particles. Therefore, it is important to study the relationship between the PBG and structure characteristics. In [15, 16], the Bragg diffraction and the second order reflection in PCs were investigated by the cou pledmode method, and an analytical expression was derived for the diffraction efficiency. In [17], when describing the interaction of radiation with the three dimensional structure of a PC based on a synthetic opal, the latter was considered as a multilayer consist ing of monolayers of independent particles. In this case, first, the transmittance and reflectance of indi vidual monolayers were calculated in the singlescat
tering approximation, and then they were used to cal culate the multilayer transmittance and reflectance by the transfermatrix method [18]. The correlation between particles and the multiple scattering effects i
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