Abstract
This article describes a new two–dimensional physical topology–merged lattice, that allows dense number of wave localization states. Merged lattices are obtained as a result of merging two lattices of scatters of the same space group, but with slightly different spatial resonances. Such merging creates two–dimensional scattering “beats” which are perfectly periodic on the longer spatial scale. On the shorter spatial scale, the systematic breakage of the translational symmetry leads to strong wave scattering, and this causes the occurrences of wave localization states. Merged Lattices promises variety of localization states including tightly confined, and ring type annular modes. The longer scale perfect periodicity of the merged lattice, enables complete prediction and full control over the density of the localization states and its’ quality factors. In addition, the longer scale periodicity, also allows design of integrated slow wave components. Merged lattices, thus, can be engineered easily to create technologically beneficial applications.
Highlights
The single 2D dielectric beat [i.e., the primitive unit cell of the Merged lattices (MLs)] itself has no translational symmetries within, and it enables creation of large number of scattering loop that facilitates polychromatic, light localization
Before we discuss the optical properties of the 2D structures created from MLs, let us briefly review the band structure of the conventional 2D square lattice photonic crystal (PC) with the period a
Rod PC with a square lattice is favorable for the transverse magnetic (TM) polarization [electric field along the axis of the rod]5
Summary
The single 2D dielectric beat [i.e., the primitive unit cell of the ML] itself has no translational symmetries within, and it enables creation of large number of scattering loop that facilitates polychromatic, light localization. Unlike quasi–periodic dielectric structures[18,19], or random dielectric structures[25,26,27,28], such light localizations in dielectric MLs are completely predictable (and controllable) using photonic band structures. Merged lattices (MLs) lie in between the two extremes of completely random system (where Anderson localization[23,24,25,26,27,28] prevails), and the conventional periodic system of photonic crystals[4,5]. In the MLs, the periodicity prevails on the longer spatial scale (spatial distance >Ra). The translational symmetry is completely broken on the spatial scale
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