; A honeycomb lattice of dielectric rods in air. (This structure has ; a complete (overlapping TE/TM) band gap.) A honeycomb lattice is really ; just a triangular lattice with two rods per unit cell, so we just ; take the lattice, k-points, etcetera from tri-rods.ctl. (define-param r 0.14) ; the rod radius (define-param eps 12) ; the rod dielectric constant ; triangular lattice: (set! geometry-lattice (make lattice (size 1 1 no-size) (basis1 (/ (sqrt 3) 2) 0.5) (basis2 (/ (sqrt 3) 2) -0.5))) ; Two rods per unit cell, at the correct positions to form a honeycomb ; lattice, and arranged to have inversion symmetry: (set! geometry (list (make cylinder (center (/ 6) (/ 6) 0) (radius r) (height infinity) (material (make dielectric (epsilon eps)))) (make cylinder (center (/ -6) (/ -6) 0) (radius r) (height infinity) (material (make dielectric (epsilon eps)))))) ; The k-points list, for the Brillouin zone of a triangular lattice: (set! k-points (list (vector3 0 0 0) ; Gamma (vector3 0 0.5 0) ; M (vector3 (/ -3) (/ 3) 0) ; K (vector3 0 0 0))) ; Gamma (define-param k-interp 4) ; number of k-points to interpolate (set! k-points (interpolate k-interp k-points)) (set-param! resolution 32) (set-param! num-bands 8) (run-tm) (run-te) ; Since there is a complete gap, we could instead see it just by using: ; (run) ; The gap is between bands 12 and 13 in this case. (Note that there is ; a false gap between bands 2 and 3, which disappears as you increase the ; k-point resolution.)
