Complete photonic bandgaps in self-assembled square bilayer structures

The photonic bandgap properties of colloidal photonic crystals assembled under confinement are simulated. Confinement self-assembly provides a rich diversity of phases for anisotropic particles as a function of confinement height due to incommensurate gap height and layer number. In particular, we investigate the square bilayer phase of cut spheres, which displays high Brillouin zone isotropy and a complex basis. These features are known to open complete photonic bandgaps. Here, a wide range of structures with complete bandgaps is obtained as a function of the dielectric contrast, dielectric filling fraction, and slab height. A large, complete bandgap (gap-to-midgap ratio, 10.2%) is found between the tenth and eleventh bands in the direct structure at a dielectric contrast of 12. In the inverted structure, two smaller bandgaps between the fourth and fifth and the eighth and ninth bands are found. The electric displacement field density shows that the bandgaps arise due to shifts in the mode field concentration to complementary high dielectric regions. Such bandgaps are often associated with Mie scattering; however, the particle basis is tangent, promoting a strong Bragg scattering component. An equifrequency contour analysis is also performed to demonstrate the potential of the square bilayer slab for negative refraction. Right-handed negative refraction is predicted in the second band for the direct structure.