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;; polarization grating from C. Oh and M.J. Escuti, Optics Letters, Vol. 33, No. 20, pp. 2287-9, 2008
;; note: reference uses z as the propagation direction and y as the out-of-plane direction; this script uses x and z, respectively
(set-param! resolution 50) ; pixels/μm
(define-param dpml 1.0) ; PML thickness
(define-param dsub 1.0) ; substrate thickness
(define-param dpad 1.0) ; padding thickness
(set! k-point (vector3 0 0 0))
(define boundary-layers (list (make pml (thickness dpml) (direction X))))
(set! pml-layers boundary-layers)
(define n0 1.55)
(define delta-n 0.159)
(define eps-diag (matrix3x3 (vector3 (sqr n0) 0 0)
(vector3 0 (sqr n0) 0)
(vector3 0 0 (sqr (+ n0 delta-n)))))
(define-param wvl 0.54) ; center wavelength
(define fcen (/ wvl)) ; center frequency
(define-param d 1.7) ; chiral layer thickness
(define-param ph 70) ; chiral layer twist angle
(define-param gp 6.5) ; grating period
(define-param nmode 5) ; number of mode coefficients to compute
(set! ph (deg->rad ph))
(define sx (+ dpml dsub d d dpad dpml))
(define sy gp)
(define cell (make lattice (size sx sy no-size)))
(set! geometry-lattice cell)
; linear-polarized planewave pulse source
(define src-pt (vector3 (+ (* -0.5 sx) dpml (* 0.3 dsub)) 0 0))
(define lp-src (list (make source
(src (make gaussian-src (frequency fcen) (fwidth (* 0.05 fcen))))
(component Ez)
(center src-pt)
(size 0 sy 0))
(make source
(src (make gaussian-src (frequency fcen) (fwidth (* 0.05 fcen))))
(component Ey)
(center src-pt)
(size 0 sy 0))))
(set! sources lp-src)
(set! default-material (make medium (index n0)))
(define tran-pt (vector3 (- (* 0.5 sx) dpml (* 0.5 dpad)) 0 0))
(define tran-flux1 (add-flux fcen 0 1 (make flux-region (center tran-pt) (size 0 sy 0))))
(run-sources+ 100)
(define input-flux (get-fluxes tran-flux1))
(reset-meep)
(set! geometry-lattice cell)
(set! pml-layers boundary-layers)
(set! sources lp-src)
(set! k-point (vector3 0 0 0))
(set! default-material air)
; twist angle of nematic director; from equation 1b
(define phi (lambda (p)
(let ((xx (- (vector3-x p) (+ (* -0.5 sx) dpml dsub))))
(if (and (>= xx 0) (<= xx d))
(+ (* pi (vector3-y p) (/ gp)) (* ph xx (/ d)))
(+ (* pi (vector3-y p) (/ gp)) (- (* ph xx (/ d))) (* 2 ph))))))
(define lc-epsilon-diag (vector3 0 0 0))
(define lc-epsilon-offdiag (vector3 0 0 0))
(define lc-epsilon (matrix3x3 (vector3 0 0 0) (vector3 0 0 0) (vector3 0 0 0)))
; return the anisotropic permittivity tensor for a uniaxial, twisted nematic liquid crystal
(define lc-mat (lambda (p)
(let
; rotation matrix for rotation around x axis
((Rx (matrix3x3 (vector3 1 0 0)
(vector3 0 (cos (phi p)) (sin (phi p)))
(vector3 0 (- (sin (phi p))) (cos (phi p))))))
(set! lc-epsilon (matrix3x3* Rx (matrix3x3* eps-diag (matrix3x3-transpose Rx))))
(set! lc-epsilon-diag (vector3 (vector3-x (vector3-x lc-epsilon))
(vector3-y (vector3-y lc-epsilon))
(vector3-z (vector3-z lc-epsilon))))
(set! lc-epsilon-offdiag (vector3 (vector3-x (vector3-y lc-epsilon))
(vector3-x (vector3-z lc-epsilon))
(vector3-y (vector3-z lc-epsilon))))
(make medium (epsilon-diag lc-epsilon-diag) (epsilon-offdiag lc-epsilon-offdiag)))))
(set! geometry (list
(make block
(center (+ (* -0.5 sx) (* 0.5 (+ dpml dsub))) 0 0)
(size (+ dpml dsub) infinity infinity)
(material (make medium (index n0))))
(make block
(center (+ (* -0.5 sx) dpml dsub d) 0 0)
(size (* 2 d) infinity infinity)
(material (make material-function (material-func lc-mat))))))
(define tran-flux2 (add-flux fcen 0 1 (make flux-region (center tran-pt) (size 0 sy 0))))
(run-sources+ 300)
(define res1 (get-eigenmode-coefficients tran-flux2 (arith-sequence 1 1 nmode) #:eig-parity (+ ODD-Z EVEN-Y)))
(define res2 (get-eigenmode-coefficients tran-flux2 (arith-sequence 1 1 nmode) #:eig-parity (+ EVEN-Z ODD-Y)))
(define t-coeffs1 (list-ref res1 0))
(define t-coeffs2 (list-ref res2 0))
(define kdom (list-ref res1 3))
(map (lambda (nm)
(let ((mode-angle (acos (/ (vector3-x (list-ref kdom nm)) fcen)))
(mode-tran (/ (+ (sqr (magnitude (array-ref t-coeffs1 nm 0 0))) (sqr (magnitude (array-ref t-coeffs2 nm 0 0)))) (list-ref input-flux 0))))
(print "tran:, " nm ", " (rad->deg mode-angle) ", " mode-tran "\n")))
(arith-sequence 0 1 nmode))
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