Finite-Difference Time-Domain Method (FDTD)
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1 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Computatioal Photoics Semiar 05, 0 Jue 04 Fiite-Differece Time-Domai Method (FDTD) Lear how to implemet a D versio of FDTD xted the code to 3D problems (volutar) lear how to save simulatio results i movie format
2 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch D FDTD: Yee Grid for & compoets chagig of idex otatio to iteger idices t().5 t() x(i) t t j i i i i i 0i x 0i t i i i i 0 x 3 x(i) t t j i i i i i 0i x 0i t i i i x 0 i
3 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch 3D FDTD: lectric field compoets chagig of idex otatio to iteger idices (k) x x x (j) x x(i),,,, t i j k i j k i, j, k i, j, k x i, j, k x j i, j, k x i, j, k 0 i, j, k j t x,, x,, i j k i j k i, j, k i, j, k i, j, k i, j, k i, j, k 0i, j, k x,,,, x t i j k i j k i, j, k x i, j, k i, j, k j i, j, k i, j, k 0 i, j, k x
4 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch 3D FDTD: Magetic field compoets chagig of idex otatio to iteger idices (k) x x x (j) x x(i) x t,,,, i j k i j k i, j, k i, j, k i, j, k x i, j, k 0 t,,,, x i j k i j k i, j, k x i, j, k i, j, k i, j, k 0 x,,,, t x i j k x i j k i, j, k i, j, k i, j, k i, j, k 0 x
5 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch 3D FDTD: Field discretiatio ad boudar coditios Number of grid poits i Yee grid:,,,,,,,,,,,, x x x x N N N N N N x x N N N N N N x x N N N N N N Boudar coditios for ud fields: x x x x x(i) (k) (j) x :,,: 0, :,:, 0 :, N,: 0, :,:, N 0 x x x,:,: 0, :,:, 0 N,:,: 0, :,:, N 0 x,:,: 0, :,,: 0 N,:,: 0, :, N,: 0 x
6 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Task I: Implemetatio of D FDTD method Phsical problem: Simulate propagatio of a ultrashort pulse i a dispersio-free dielectric medium (x) See what happes whe the pulse hits the iterface betwee two differet dielectric media xcitatio: curret source (A/m ) with frequec 5*0 5 (red light) with delta-shaped spatial profile ad Gauss-shaped temporal pulse profile of width w 0 = fs Simulatio grid: spatial sie of 8 µm with discretiatio x=30m ad metallic walls ( =0 at the boudaries) temporal sie of 60 fs with discretiatio t=x/(c) Result output: graphical presetatio ad for ever 5 th calculatio step Useful Matlab fuctios: roud, drawow, subplot c= *0 8, µ 0 =4p*0-7, 0 =/(c *µ 0 )
7 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Task I: Implemetatio of D FDTD method fuctio [,,X,T] = fdtd_d(eps_rel, grid_sie, time_spa,... source_freuqec, source_positio, source_pulse_legth) % FUNCTION CALL: % [,,X,T] = fdtd_d(eps_rel,grid_sie, time_spa,... source_freuqec, source_positio, source_pulse_legth) % VARIABLS: % eps_rel epsilo distributio i the simulatio area % grid_sie spatial sie of simulatio grid % time_spa time spa of simulatio % source_frequec frequec of curret source % source_positio spatial positio of curret source % source_pulse_legth temporal width of Gauss-shaped source(w0) %
8 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Task II: Implemetatio of 3D FDTD method Phsical problem: Watch radiatio characteristics of pulsed ertia dipole Simulatio grid: spatial sie of 0xx3 grid poits with discretiatio x===30m metallic wall boudar coditios temporal sie of 0 fs with discretiatio t=x/(c) xcitatio: curret source (A/m ) with frequec 5*0 5 (cw red light) delta-shaped spatial profile i ceter of computatio grid Result output: graphical represetatio of i the x- plae cetered i the middle alog the directio (plot ever 5 th calculatio step) Possibl useful Matlab fuctios: pcolor, mod
9 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Task II: Implemetatio of 3D FDTD method fuctio fdtd_3d(eps_rel,dr,time_spa,source_frequec,source_pulse_legth,jx,j,j,... plot_field_compoet, plotlaer) % FUNCTION CALL % fdtd_3d(eps_rel,dr,time_spa,source_frequec,source_pulse_legth,jx,j,j,... % plot_field_compoet, plotlaer) % VARIABLS: % eps_rel epsilo distributio i the simulatio area (3D arra) % dr spatial discretiatio of simulatio grid % time_spa time spa of simulatio % source_frequec frequec of curret source % source_pulse_legth temporal width of Gaussia pulse % jx,j,j compoets of source curret (3D arra) % plot_field_compoet field compoet to be plot % plotlaer idex of slice, i which result is plotted i D
10 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Task III*: FDTD movie volutar task Output the result of the FDTD as a plaable movie file! Remark: This fuctioalit will deped o the video codecs istalled o the specific sstem! Possibl useful MATLAB fuctios: switch, avifile, getframe, addframe, close
11 Computatioal Photoics, Summer Term 04, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch omework 4 ( Jue 04) Solve at least tasks I & II. Prepare a oe page report about our solutio with a figure of some calculated example. Submit our m-files of our program together with our oe page report electroicall to teachig-aooptics@ui-jea.de b 3 Jue 0. Please put everthig together i oe sigle which cotais our ame (FAMILY NAM, Give Name) ad matriculatio umber. Late submissios will ot be accepted! 4 Jue the solutios of the tasks will be available olie at the lectures homepage >>> Computatioal Photoics. You are expected to solve the task ourself ad a declaratio of idepedet work must be siged b ever studet at the ed of the semester.
Finite-Difference Time-Domain Method (FDTD)
Computatioal Photoics, Summer Term 0, Abbe School of Photoics, FSU Jea, Prof. Thomas Pertsch Computatioal Photoics Semiar 06, 8 Jue 0 Fiite-Differece Time-Domai Method (FDTD) Lear how to implemet a oe-dimesioal
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