Fano Resonance between Mie and Bragg Scattering in Photonic Crystals

Abstract

We report the observation of a Fano resonance between continuum Mie scattering and a narrow Bragg band in synthetic opal photonic crystals. The resonance leads to a transmission spectrum exhibiting a Bragg dip with an asymmetric profile, which can be tunably reversed to a Bragg rise. The Fano asymmetry parameter is linked with the dielectric contrast between the permittivity of the filler and the specific value determined by the opal matrix. The existence of the Fano resonance is directly related to disorder due to non-uniformity of a-SiO2 opal spheres. Proposed theoretical "quasi-3D" model produces results in excellent agreement with the experimental data. PACS numbers: 42.70Qs, 42.25.Fx, 42.79.Fm Mie and Bragg scattering are key optical phenomena in photonic crystals (PhC) composed of spherical or nearly spherical particles. Light scattering by an isolated spherical particle can be described by Mie theory [1]. Considering PhC composed of a periodic array of such spheres, interference of scattered waves results in the transformation of Mie scattering into Bragg scattering and gives rise to formation of the photonic band structure [2]. The underlying Mie scattering is therefore hidden in perfectly ordered PhC and as a result, it has been insufficiently studied so that its role is clear only for the case of perfect structures. The resulting Bragg scattering, on the other hand, has been intensively examined, both experimentally and theoretically in great detail [2,3,4,5,6,7]. In particular, the multiple Bragg diffraction phenomenon in PhC, which occurs when two narrow Bragg bands demonstrate the avoided crossing effect [7,8,9, 10] has been thoroughly studied. Departing from this phenomenon and with intention to further deepen our understanding of light scattering in PhC, a number of challenging problems can be formulated: What can we expect if a spectrally narrow Bragg band interacts with a broad spectrum originating from certain scattering mechanisms such as Mie or Fabry-Perot scattering? Is it possible to observe the consequences of this interaction or simply Mie scattering experimentally? What are the effects of inherent disorder in the structural components of opal-based PhC, beyond the well-known broadening and degradation of stop bands [6,11,12,13,14,15]?If a narrow Bragg band interacts with the continuum spectrum through an interference effect constructively or destructively, we can expect an interaction of Fano-type [16], a phenomenon well-known across many different branches of physics. The Fano resonance between continuum and discrete states manifests as an asymmetric profile of narrow band in the transmission spectrum, which in general has the form:where Ω = (ω − ω B )/(γ B /2), ω B is the frequency, γ B is the width of the narrow band, and q is the Fano asymmetry parameter. It was shown theoretically that Fano-type asymmetric line shapes can be created in the response function of certain PhC. In general these systems consist of a waveguide with forward and backward propagating waves being indirectly...

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