Lecture 23. Multilayer Structures

Transcription

1 Lcu Mullay Sucus In hs lcu yu wll lan: Mullay sucus Dlcc an-flcn (AR) cangs Dlcc hgh-flcn (HR) cangs Phnc Band-Gap Sucus C Fall 5 Fahan Rana Cnll Unvsy Tansmssn Ln Juncns and Dscnnus - I Tansmssn ln dscnnus gna flcns ( ) ( ) < Bunday cndns: > ) Cnnuy f vlag a : ) Cnnuy f cun a : Γ T C Fall 5 Fahan Rana Cnll Unvsy

2 Tansmssn Ln Juncns and Dscnnus - II ( ) < ( ) > Can als plac h nfn ansmssn ln n h gh by a lumpd mpdanc Whch gvs: - Γ ( ) ( Γ) Γ T C Fall 5 Fahan Rana Cnll Unvsy Unmachd Tansmssn Lns - I Qusn: Hw ds n slv a pblm l hs? l ( ) ( l) ( l ) < l ( ) l< < ( ) > In ach sgmn (xcp h gh ms n), h wav s wn such ha h phas s a h gh nd f h sgmn In ach sgmn, h phas has h wavvc cspndng ha sgmn C Fall 5 Fahan Rana Cnll Unvsy

3 Unmachd Tansmssn Lns - II Qusn: Hw ds n slv a pblm l hs? l STP : Rplac h las ln wh a lumpd quvaln mpdanc (cspndng an nfn ln) l Γ Nw calcula h mpdanc (-l ): Γ STP : Rplac h mddl ln wh h mpdanc (-l ) ( l) l Γ l ( l) Γ ( l) ( l) C Fall 5 Fahan Rana Cnll Unvsy Machng Tansmssn Lns - I Qusn: Is pssbl us a ansmssn ln pfcly mach w dssmla ansmssn lns s ha h s n flcn? l Wha s h apppa mpdanc? Wha s h apppa lngh l? Us a Qua-Wav Tansfm: Supps h lngh l f h nmda ansmssn ln s qua-wavlngh l λ π l ( ) n( ) n( ) λ A qua-wavlngh lng ansmssn n n( ) ln nvs h nmald mpdanc C Fall 5 Fahan Rana Cnll Unvsy

4 C Fall 5 Fahan Rana Cnll Unvsy ( ) ( ) n n n λ Th acual mpdanc a -λ / s hn: n λ λ T hav n flcn w nd: λ Th mpdanc f h qua-wavlngh lng ansmssn ln mus b h gmc man f h mpdancs f h w ansmssn lns Machng Tansmssn Lns - II λ C Fall 5 Fahan Rana Cnll Unvsy ( ) < ( ) > Γ Wavs a Infacs and Tansmssn Lns ˆ H ˆ H ˆ H µ ε µ ε ( ) x x < ˆ ˆ Bunday cndns: () ( ) ( ) x > ˆ Bunday cndns: () ( ) Γ

5 T-lay Sucu - I - - l Qusn: Hw d w calcula h flcn cffcn f h abv sucu? Γ? Answ: Us h mhd mplyd al n h quvaln ansmssn ln pblm l C Fall 5 Fahan Rana Cnll Unvsy T-lay Sucu - II - - l ( ) ( l) ( l ) x <l ( ) x l< < ( ) x > In ach sgmn (xcp h gh ms n), h wav s wn such ha h phas s a h gh nd f h sgmn In ach sgmn, h phas has h wavvc cspndng ha sgmn C Fall 5 Fahan Rana Cnll Unvsy 5

6 T-lay Sucu - III - - l STP : Calcula h flcn a : Γ l Γ Γ And calcula h ffcv mpdanc a -l : ( l) l STP : Nw h pblm bcms: ( l) - l Calcula h flcn cffcn as: Γ ( l) ( h) C Fall 5 Fahan Rana Cnll Unvsy Dlcc An-Rflcn (AR) Cangs - I - Qusn: Is pssbl smhw ma h flcn cffcn? Answ: Us h qua-wav ansfm cncp: - l λ C Fall 5 Fahan Rana Cnll Unvsy 6

7 Dlcc An-Rflcn (AR) Cangs - II - l λ STP : Calcula h nmald mpdanc a and a -λ / ( ) n( ) n( ) λ n n( ) STP : Nw h pblm bcms: A qua-wavlngh lng sgmn nvs h nmald mpdanc ( l ) l T hav flcn Γ λ λ ( l) n C Fall 5 Fahan Rana Cnll Unvsy Dlcc An-Rflcn (AR) Cangs - III Qusn: Hw d qua-wavlngh lng machng lays w? Wav flcd a h nd nfac Wav flcd a h s nfac Wavs flcd a h w nfacs cancl ach h u n h bacwad dcn λ C Fall 5 Fahan Rana Cnll Unvsy 7

8 Fquncy Dpndnc f Dlcc AR Cangs: xampl - A.5 Slcn l Cnsd h AR cang n a Slcn phdc ha s dsgnd f dcng gn lgh whch has a fquncy ω f.65x 5 ad/sc and a wavlngh f.5 mc-m n f-spac λ 6 g.5.5 l m Qusn: Hw gd wll h AR cang w f fquncs dffn fm ha f gn lgh (.g. f blu lgh, vl lgh, ang lgh, c) Γ U vl blu gn yllw ang d.5 IR λ n f-spac (mc-ms) C Fall 5 Fahan Rana Cnll Unvsy Dlcc Hgh-Rflcn (HR) Cangs - I Qusn: Wha f w wan ncas h flcvy? Answ: A pdc sac f hgh ndx-lw ndx lays can b usd as an HR cang - N pas f (hgh ndx lw ndx) lays Tal N lays ach lay s qua-wavlngh hc On pd has hcnss ( λ / λ / ) Thcnss: λ Thcnss: λ C Fall 5 Fahan Rana Cnll Unvsy 8

9 Dlcc Hgh-Rflcn (HR) Cangs - II - Sa a h gh nd: Impdanc lng h gh: Nmald mpdanc: Nmald mpdanc: Acual mpdanc lng h gh: Nmald mpdanc: Nmald mpdanc: Acual mpdanc lng h gh: C Fall 5 Fahan Rana Cnll Unvsy Dlcc Hgh-Rflcn (HR) Cangs - III - Acual mpdanc lng h gh: Cnnung l hs: Acual mpdanc lng h gh: 6 Acual mpdanc lng h gh: N Acual mpdanc lng h gh: C Fall 5 Fahan Rana Cnll Unvsy 9

10 Dlcc Hgh-Rflcn (HR) Cangs - III - Acual mpdanc N lng h gh: N Rflcn Cffcn: Γ N f > Γ f < Γ Magnud f Γ can b mad abaly cls uny by: ) Chsng a lag numb N f pas f hgh ndx-lw ndx lays ) Chsng h dffnc bwn and b lag C Fall 5 Fahan Rana Cnll Unvsy Fquncy Dpndnc f HR Cangs: xampl A - Slcn Cnsd HR cang n Slcn ha s dsgnd f png gn lgh u f Slcn N On dsgns a HR cang f maxmum flcvy f gn lgh a a fquncy ω f.65x 5 ad/sc and a wavlngh f.5 mc-m n f-spac Γ U vl blu gn yllw ang d IR Qusn: Hw wll h HR cang w f fquncs dffn fm ha f gn lgh (.g. f blu lgh, vl lgh, ang lgh, c) λ n f-spac (mc-ms) C Fall 5 Fahan Rana Cnll Unvsy

11 Phnc Band Gap (PBG) Sucus A - Slcn A -dmnsnal phnc band gap (PBG) sucu Phnc band gap (PBG) sucus a sucus n whch h pmvy s pdc n spac Th sp-band In PBG sucus phns whn can bands f fquncs (calld sp-bands) cann ppaga bu a flcd ff a h sufac f h PBG sucu Γ U vl blu gn yllw ang d IR Th HR cang cnsdd n h pvus sld s an xampl f a - dmnsnal PBG sucu C Fall 5 Fahan Rana Cnll Unvsy λ n f-spac (mc-ms) C Fall 5 Fahan Rana Cnll Unvsy