Abstract
We study theoretically the band-gap structures of several types of three-dimensional photonic crystals with the fcc lattice symmetry: synthetic opals, inverted yablonovite and woodpile. The samples of inverted yablonovite, inverted yablonovite with a glassy superstructure and woodpile are fabricated by two-photon polymerization through a direct laser writing technique, which allows the creation of complex three-dimensional photonic crystals with a resolution better than 100 nm. A material is polymerized along the trace of a moving laser focus, thus enabling the fabrication of any desirable three-dimensional structure by direct “recording” into the volume of a photosensitive material. The correspondence of the structures of the fabricated samples to the expected fcc lattices is confirmed by scanning electron microscopy. We discuss theoretically how the complete photonic band-gap is modified by structural and dielectric parameters. We demonstrate that the photonic properties of opal and yablonovite are opposite: the complete photonic band gap appears in the inverted opal, and direct yablonovite is absent in direct opal and inverted yablonovite.
Highlights
Periodic order in a photonic crystal provides coherent scattering of light from a precise geometrical arrangement of identical scatterers that leads to the formation of band gaps, where destructive wave interference prevents light propagation in specific directions or the formation of the omnidirectional complete photonic band gap over a specific energy range
To realize the two-photon polymerization technique for the fabrication of the woodpile photonic crystals, we use a train of femtosecond pulses centered at around 780 nm wavelength and at a repetition frequency of 80 MHz (12.5 ns of time between adjacent pulses)
The structure is defined by the vectors of translations, and voxels are superimposed along the required lines. This approach is ideally suited for creating different photonic crystals, as demonstrated in Figure 1f by the example of the inverted yablonovite structure
Summary
Periodic order in a photonic crystal provides coherent scattering of light from a precise geometrical arrangement of identical scatterers that leads to the formation of band gaps, where destructive wave interference prevents light propagation in specific directions or the formation of the omnidirectional complete photonic band gap over a specific energy range. The high resolution of the method is due to the intensity-threshold character of the polymerization process, which occurs in a region with sizes significantly smaller than the size of the focused beam. This technique makes it possible to form a 3D photonic crystal with a transverse resolution below 100 nm [26,28,29,30]. Using direct laser writing technique, one can introduce defects into 3D photonic crystals or design a structure with a disordered glassy superstructure; something not possible using other methods [31,32]
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