Lecture contents Macroscopic Electrodynamics Propagation of EM Waves in dielectrics and metals

Transcription

1 Leure oes Marosopi lerodyamis Propagaio of M Waves i dieleris ad meals NNS 58 M Leure #4

2 Maxwell quaios Maxwell equaios desribig he ouplig of eleri ad magei fields D q ev B D J [SI] [CGS] D 4 B D 4 J B B Ieraio wih medium: i mos simple ases liear isoropi : D R B J R Polarizaio is liear fuio of eleri field Ieraio is salar, loal ad syhroous Furher i his seio he oal permeabiliy ad permiiviy will be used D B J P ; D 4 P D( r, ) ( r, ) NNS 58 M Leure #4

3 Maxwell s quaios for a Isoropi, Liear, Soure- Free, ad Lossless Medium 3 Obviously, here mus be a soure for he field somewhere. owever, we are lookig a he properies of waves i a regio far from he soure. Wave equaios for eleromagei Waves i a Simple, Soure-Free, Lossless Medium The wave equaios are o idepede. Usually we solve he eleri field wave equaio ad deermie from usig Faraday s law. NNS 58 M Leure #4

4 Propagaio of eleromagei waves i a isoropi liear, sourefree, ad lossless medium Filed vs. posiio a a fixed ime 4 Soluio: plae moohromai wave (equivale o harmoi aalysis) : ikr i e Noe: i SI he vauum osas are hose: Wih omplex waveveor (propagaio osa) i lossless medium. Serves as dispersio relaio i he medium : k Or refraive idex (i opis): The veloiy of propagaio (phase veloiy) is deermied solely by he medium: v p Ca also defie wavelegh k Srily speakig, uiform plae waves a be produed oly by soures of ifiie size. owever, poi soures reae spherial waves. Loally, a spherial wave approahes a plae wave. v p k NNS 58 M Leure #4

5 Medium wih low losses 5 Plae moohromai wave : e ikr i Wih omplex waveveor (propagaio osa) Serves as dispersio relaio i he medium : k I is oveie o irodue dieleri fuio wih real ad imagiary pars: ( ) i We a irodue he loss age of he maerial : Also omplex refraive idex (i opis): a ( ) i k xiio raio or exiio idex NNS 58 M Leure #4

6 x + (z,) Some useful relaioships (all maerial osas deped o frequey!) Waveveor a be also expressed hrough refraio ad absorpio (exiio) idexes: 6 or for = = k-veor Absorpio I his ase soluio for a plae wave alog z-direio is: e i i z z Where absorpio oeffiie: i is relaed o iesiy reduio: I I e i x Or exiio faor: Medium wih o absorpio: 4 i Sapsho of x (z,) a = e i z ad wih low absorpio: or i a z/ NNS 58 M Leure #4

7 Wave propagaio 7 Plae M wave alog z-direio i i z z x e e.. i i z z y e e.. Polarizaio Impedae of spae: {Ohm} Impedae of vauum: vauum 377 Poyig veor (ime-averaged M power flowig hrough ui area): W S Re( ) m Iesiy: I S e i z NNS 58 M Leure #4

8 leromagei sperum 8 (m) f (z) osmi radiaio -radiaio X-ray U.V. I.R Visible ligh: m viole blue gree yellow orage red (m) Radar TV - radio 8 Opial ommuiaio waveleghs NNS 58 M Leure #4

9 Medium wih ay losses (all maerial osas deped o frequey!) 9 Maxwell equaios i harmoi form i a medium wih oduio: i J i i i where i A D wave equaios will look like: I is he same as before wih subsiuio z x x k wih i k-veor i Absorpio The soluio also looks he same: r i i i r r e e e e wih is he aeuaio osa ad has uis of epers per meer (Np/m): is he phase or propagaio osa ad has uis of radias per meer (rad/m): Re Re Np i m Im Im rad i m Noe ha i geeral for a lossy medium NNS 58 M Leure #4

10 Medium wih losses Afer some log algebra: The impedae beomes omplex: i i For good dieleris: For good oduors: v p 8 v p 3 i 8 i NNS 58 M Leure #4