We introduce a concept of phase transitions between photonic crystals and all-dielectric metamaterials suggesting a phase diagram that places two classes of such artificial structures on a common parameter plane.1 We consider photonic crystals and all-dielectric metamaterials composed of the similar structural elements and arranged in the similar geometry of a two-dimensional (2D) square lattice of dielectric cylinders of large dielectric permittivity. Such structures can display negative magnetic permeability in the TE-polarization due to the Mie resonance that occurs below the lowest Bragg resonance.2 We define a point of transition from photonic crystals to all-dielectric metamaterials as a point when the lowest Mie resonance splits from the lowest Bragg resonance creating the lowest photonic gap. Based on the numerical results, we construct the phase diagram photonic crystals - all- dielectric metamaterials for the 2D square lattice of circular rods for the TE polarization. We have verified our theoretical concept experimentally by engineering a “metacrystal” composed of glass tubes filled with water forming a 2D square lattice with a variable lattice constant.
Mikhail V. Rybin, Dmitry S. Filonov, Kirill B. Samusev, Pavel A. Belov, Yuri S. Kivshar, and Mikhail F. Limonov, "Transition from photonic crystals to dielectric metamaterials: A phase diagram and the order parameter," Proc. SPIE 9885, Photonic Crystal Materials and Devices XII, 98850R (Presented at SPIE Photonics Europe: April 07, 2016; Published: 18 April 2016); https://doi.org/10.1117/12.2223721.
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