Fabrication of 3D Photonic Crystals of Ellipsoids: Convective Self‐Assembly in Magnetic Field

Abstract

In photonic crystals, two materials with different refractive indexes alternate with a specific periodicity on the opticalwavelength scale. Analogous to the band-gap for electrons in semiconductors, the spatially periodic structure in photonic crystals results in a forbidden stop-band for a particular spectral range of photons, the so-called photonic band-gap. Since being first proposed by Yablonovich and John, [1,2] photonic crystals have been desired to give complete photonic band-gap in the optical regime. In other words, within a specific range of frequencies photons should not be allowed to propagate in all three dimensions inside photonic crystals. Because of the optical scale of the periodicity in refractive index, the fabrication of photonic crystals with complete photonic band-gaps in the optical regime remains a challenge. Physical top-down approaches, including lithographic techniques starting from bulk materials, have proven their efficacy in the long-wavelength radar range, but are difficult to extend to the optical spectrum. Chemical bottom-up techniques, for example self-assembly of highly monodisperse and spherical colloidal particles, offer a viable alternative based on the combined ease of fabrication and low cost. Such photonic crystals from highly ordered colloidal particles are also known as artificial opals. However, in the crystallization of spherical colloids, only two most-stable crystal structures with high filling fraction have been obtained (for face-centered cubic, FCC, and for random hexagonal closed packing, RHCP).It has been suggested by previous studies that for an FCC lattice consisting of colloidal spheres there only exists a pseudo photonic band-gap in the photonic band structure, no matter how high the dielectric contrast, because of a symmetry-induced degeneracy at the W-or U-point of the band structure. [3,4] As suggested by computational studies, this degeneracy can be broken using shape-anisotropic [5] or dielectrically anisotropic [6] colloidal particles as building blocks.Early research in this direction mainly focused on the deformation of colloidal building blocks from spheres to ellipsoids after their being self-assembled into colloidal crystals. This ''post-crystallization treatment'' includes high-energy ion irradiation [7] and uniaxial mechanical stretching, [8,9] leading to colloidal crystals with ellipsoidal silica (SiO 2 ), zinc sulfide (ZnS), and polystyrene (PS) optical atoms. However, these deformation strategies applied on prefabricated colloidal crystals may cause the nonuniform deformation in different parts of the photoniccrystal film, or even to the destruction of the whole periodic superlattice. Direct self-assembly of nonspherical colloidal particles has been studied as an alternative strategy. Polystyrene ellipsoids were used as building blocks for direct self-assembly. The lack of long-range order indicated the difficulty of organizing nonspherical colloids into 3D crystalline lattices.[9] In recent years, Liddell et al. demonstrated the fabrication ...

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