Analytical treatment of long range magneto-dipole interactions is a bottle-neck of magnonics and more generally of the theory of spin waves in non-uniform media.
There has been much recent interest in the electromagnetic response of metamaterials, particularly those containing metals. Almost all the work thus far has explored regular periodic structures. In this project we wish to explore aperiodic or locally ordered structures which are well specified but not periodic (or random). One such example are quasicrystal structures where one has local 2D icosahedral, or dodecahedral symmetry elements (Penrose tilings is another example) which are then ‘patched’ together into a perfectly periodic superlattice or made to fill space with no overall translational symmetry at all. Because of the strong interaction of electromagnetic radiation with matter the 5-fold or 10 fold symmetry does not have to extend very far in space (for example with plasmonic metals a propagation length of microns is common, so with a building block of 100s of nm less than 10 building block units are required to give very strong effects) and it leads to new optical stop bands and band gaps which are not possible with lower symmetries. Another, less local example is that of square Fibonacci tiling or Archimedean tiling. The simplest Fibonnacci structure is obtained using the Fibonnacci line spacings of 1 and t (where t = (root(5) + 1)/2 = 1.618033) in a 2D lattice. Remembering that the Fibonnacci sequence is obtained from the simple rule A-->AB and B-->A, beginning at A,B the series develops as: AB,A; AB,A,AB; AB,A,AB,AB,A; AB,A,AB,AB,A,AB,A,AB; AB,A,AB,AB,A,AB,A,AB,AB,A,AB,AB,A etc, never repeating itself. Then replacing every A by 1 and B by t and forming a rectangular array this may be reduced to two sizes of square patches of sizes 1x1 and t x t only but in an aperiodic array. This project will be to build and to characterize such metamaterial structures.