Moiré photonic crystals PERSPECTIVES photonic crystals than between 2D materials, because photonic modes have a longer evanescent tail than electronic orbitals. This coupling can be tuned by adjusting the interlayer distance: the closer the two layers, the stronger the interlayer coupling. However, contrary to what one might think, the strongest interlayer coupling is not necessarily optimal as it must be balanced with the intralayer coupling.
Working with photonic crystals, completely different moiré geometries can also be explored. The lattices are not restricted to honeycomb structures, they can also be square, triangular, or even one-dimensional( 1D). The mismatch parameter that generates the moiré pattern can arise either from a rotation or from a slight difference in lattice parameters. Figure 5 presents different types of moiré patterns. In particular, the moiré pattern made of two 1D photonic crystals with slightly different periods has been studied as a simplified
Figure 4. Flat band formation within graphenelike geometry.
system to explore the mechanism of flat bands formation. It has been shown to exhibit flat bands as well as the graphene-like geometry for specific“ magic configurations” [ 4 ]. This 1D moiré pattern is strictly periodic with period Λ if the two periods a 1 and a 2 satisfy Λ =( N + p) a 1 = N a 2, where N and p are positive
integers. For simplicity, p is generally chosen to be equal to 1. The moiré number N is the mismatch parameter that plays a role analogous to that of the twist angle. With this geometry, the balance between intra and interlayer couplings can be easily tuned, by adjusting the relative width of the rods and grooves and the interlayer distance respectively. This flexibility makes it easier to reach a“ magic configuration”, regardless the value of the mismatch parameter N.
PART 3: PROPERTIES Initially, the main interest of photonic crystals was their capacity to control emission or absorption rates. An emitter emits photons at a rate proportional to the ability of the surrounding medium to support photonic modes, i. e. proportional to the photonic density of states. In free space, a photon with frequency 0 must have a wavevector with k = ω 0
—, which limits c the number of available states. In a moiré photonic crystal with a
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