; A line-defect waveguide in a 2d triangular lattice of dielectric ; rods (c.f. tri-rods.ctl), formed by a row of missing rods along the ; "x" direction. (Here, "x" and "y" refer to the first and second ; basis directions.) This structure supports a single guided band ; within the band gap, much like the analogous waveguide in a square ; lattice of rods (see "Photonic Crystals" by Joannopoulos et al.). (define-param supercell-y 7) ; the (odd) number of lateral supercell periods (set! geometry-lattice (make lattice (basis1 (/ (sqrt 3) 2) 0.5) (basis2 (/ (sqrt 3) 2) -0.5) (size 1 supercell-y no-size))) (define-param eps 12) ; the dielectric constant of the rods (define-param r 0.2) ; the rod radius in the bulk crystal (set! geometry (list (make cylinder (center 0 0 0) (radius r) (height infinity) (material (make dielectric (epsilon eps)))))) (set! geometry (append ; duplicate the bulk crystal rods over the supercell: (geometric-objects-lattice-duplicates geometry) ; add a rod of air, to erase a row of rods and form a waveguide: (list (make cylinder (center 0) (radius r) (height infinity) (material air))))) (define Gamma (vector3 0 0 0)) (define K' (lattice->reciprocal (vector3 0.5 0 0))) ; edge of Brillouin zone. (set! k-points (interpolate 4 (list Gamma K'))) ; the bigger the supercell, the more bands you need to compute to get ; to the defect modes (the lowest band is "folded" supercell-y times): (define-param extra-bands 5) ; number of extra bands to compute above the gap (set! num-bands (+ supercell-y extra-bands)) (set-param! resolution 32) ; Compute the TM modes, outputting the Ez field in the *middle* of the ; band. (In general, the guided mode in such an air defect may have ; exited the gap by the time it reaches the edge of the Brillouin ; zone at K'.) (run-tm (output-at-kpoint (list-ref k-points (quotient (length k-points) 2)) fix-efield-phase output-efield-z))
