Band structure calculations of 2D photonic pseudoquasicrystals obtainable by holographic lithography

Abstract

The most interesting phenomena in photonic crystals stipulate the presence of omnidirectional band gap, i.e. overlapping of stop bands in all directions. Higher rotational symmetry and isotropy of quasicrystals in comparison with ordinary crystal give a hope to achieve a gap opening at lower dielectric contrasts. But nonperiodic nature of quasicrystals makes the size of stop bands lower than in the case of ordinary periodic crystal. We study transition from periodic structure to nonperiodic one by considering pseudoquasicrystals -quasicrystal approximants with growing period to weigh advantages and disadvantages of quasicrystals. We consider the structures that can be obtained by multiple exposure holographic lithography for the case of 2, 3, 4, and 6-fold exposure by two wave interference pattern, corresponding square, hexagonal, 8-fold and 12-fold symmetry lattice.

Complete photonic band gap in icosahedral quasicrystals with a body-centered six-dimensional lattice

“…For higher-order approximants 1/1AS, 1/1DR, and 1/1FDR, the threshold values were found to be th ε =5.3, th ε =7.4, and th ε =5.8, respectively. For 1/0DR and 1/1FDR, the PBG threshold was found to be practically the same, which means that further increasing approximant order brings us to the same, or a bit less, threshold value [18]. Similar conclusions can be made with respect to the approximants 1/0AS and 1/1AS.…”

“…Consequently, with increasing approximant order, the complete PBG is retained and, hence, it will also be peculiar to the corresponding quasicrystal [17,18]. Figure 8 shows the band gap size as a function of permittivity.…”

“…The authors of Ref. [18] showed that higherorder quasicrystal approximants had the band gap threshold equal to that in quasicrystals.…”

Control over Light Emission in Low‐Refractive‐Index Artificial Materials Inspired by Reciprocal Design

“…In this publication, we define the RI contrast as the ratio of the refractive indices of two constituent media, n 1 / n 2 , where n 1 is larger than n 2 , so that the minimal contrast is 1. To increase the range of available materials for PBG applications, there have been considerable efforts to minimize the required RI contrast employing periodic [ 4,22–26 ] and aperiodic [ 21,27–35 ] structures. As aperiodic structures are not limited by the crystallographic theorem and thus are allowed for a more flexible positioning of Bragg peaks and smoother effective Brillouin zones, they are generally considered superior for low‐contrast CPBGs.…”

“…In real space, the leveled‐wave approach is used to obtain structures made of a single material. The approach is somewhat similar to the holographic dual‐beam exposure technique [ 33–37 ] but with random phase shifts between the individual lattices in our case. [ 38,39 ] This randomization leads to isotropic structures and allows us to draw important conclusions about the connection between the total RI contrast and the directional bandgaps.…”