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; This file contains the Scheme commands from the user tutorial section
; of the manual. It is meant to be run interactively by the user.
; *** Our First Band Structure ***
(print "********** Square lattice of rods in air **********\n")
(set! num-bands 8)
(set! k-points (list (vector3 0 0 0) ; Gamma
(vector3 0.5 0 0) ; X
(vector3 0.5 0.5 0) ; M
(vector3 0 0 0))) ; Gamma
(set! k-points (interpolate 4 k-points))
(set! geometry (list (make cylinder
(center 0 0 0) (radius 0.2) (height infinity)
(material (make dielectric (epsilon 12))))))
(set! geometry-lattice (make lattice (size 1 1 no-size)))
(set! resolution 32)
(print "********** Square lattice of rods: TE bands**********\n")
(run-te)
(print "********** Square lattice of rods: TM bands **********\n")
(run-tm)
(print "********** Square lattice of rods: TM, w/efield **********\n")
(run-tm output-efield-z)
(print "********** Square lattice of rods: TE, w/hfield & dpwr **********\n")
(run-te (output-at-kpoint (vector3 0.5 0 0) output-hfield-z output-dpwr))
; *** Bands of a Triangular Lattice ***
(print "********** Triangular lattice of rods in air **********\n")
(set! geometry-lattice (make lattice (size 1 1 no-size)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)))
(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
(set! k-points (interpolate 4 k-points))
(run-tm)
; *** Maximizing the First TM Gap ***
(print "********** Maximizing the first TM gap **********\n")
(define (first-tm-gap r)
(set! geometry (list (make cylinder
(center 0 0 0) (radius r) (height infinity)
(material (make dielectric (epsilon 12))))))
(run-tm)
(retrieve-gap 1)) ; return the gap from TM band 1 to TM band 2
(set! num-bands 2)
(set! mesh-size 7) ; increase from default value of 3
(define result (maximize first-tm-gap 0.1 0.1 0.5))
(print "radius at maximum: " (max-arg result) "\n")
(print "gap size at maximum: " (max-val result) "\n")
(set! mesh-size 3) ; reset to default value of 3
; *** A Complete 2D Gap with an Anisotropic Dielectric ***
(print "********** Anisotropic complete 2d gap **********\n")
(set! geometry (list (make cylinder
(center 0 0 0) (radius 0.3) (height infinity)
(material (make dielectric-anisotropic
(epsilon-diag 1 1 12))))))
(set! default-material (make dielectric-anisotropic (epsilon-diag 12 12 1)))
(set! num-bands 8)
(run) ; just use run, instead of run-te or run-tm, to find the complete gap
; *** Finding a Point-defect State ***
(print "********** 5x5 point defect **********\n")
(set! geometry-lattice (make lattice (size 5 5 no-size)))
(set! geometry (list (make cylinder
(center 0 0 0) (radius 0.2) (height infinity)
(material (make dielectric (epsilon 12))))))
(set! geometry (geometric-objects-lattice-duplicates geometry))
(set! geometry (append geometry
(list (make cylinder (center 0 0 0)
(radius 0.2) (height infinity)
(material air)))))
(set! resolution 16)
(set! k-points (list (vector3 0.5 0.5 0)))
(set! num-bands 50)
(run-tm)
(output-efield-z 25)
(get-dfield 25) ; compute the D field for band 25
(compute-field-energy) ; compute the energy density from D
(print
"energy in cylinder: "
(compute-energy-in-objects (make cylinder (center 0 0 0)
(radius 1.0) (height infinity)
(material air)))
"\n")
(print "********** 5x5 point defect, targeted solver **********\n")
(set! num-bands 1) ; only need to compute a single band, now!
(set! target-freq (/ (+ 0.2812 0.4174) 2))
(set! tolerance 1e-8)
(run-tm)
; *** Tuning the Point-defect Mode ***
(print "********** Tuning the 5x5 point defect **********\n")
(define old-geometry geometry) ; save the 5x5 grid with a missing rod
(define (rootfun eps)
; add the cylinder of epsilon = eps to the old geometry:
(set! geometry (append old-geometry
(list (make cylinder (center 0 0 0)
(radius 0.2) (height infinity)
(material (make dielectric
(epsilon eps)))))))
(run-tm) ; solve for the mode (using the targeted solver)
(print "epsilon = " eps " gives freq. = " (list-ref freqs 0) "\n")
(- (list-ref freqs 0) 0.314159)) ; return 1st band freq. - 0.314159
(define rooteps (find-root rootfun 0.01 1 12))
(print "root (value of epsilon) is at: " rooteps "\n")
(define rootval (rootfun rooteps))
(print "root function at " rooteps " = " rootval "\n")
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