电磁波的传播

1、12tEJtDHf0EEEEEBtHttE20020000000002211)(1)(1111tBEBBBBHtEtB2002000002211113波动方程波动方程 002200222002tBBtEE010122222222tBcBtEcE001c)()()(0EPe)()()()()()(HBED色散色散400 tEtD5 titiexBtxBexEtxE,00222222BtBEtE002222BkBEkEk6BitBEEkiEiBEitEtDHBkiBiE0222EkEdxd，它的一个解为，它的一个解为 ikxeEE0tkxieEtxE0,tkx2k7CtkxCttxxkCtxk1k

2、dtdxv)(exp,0txkiEtxEk2kk1 vv800Ek ieEEtxkiEnEkkEkEtxkik iiEtxkiitxkiEiEiB000expexpexpkBkEEBkBEkvBE1EB92212121BEHBDEw221BEwnwnEEnEBEHES1112vwnwvS10v 瞬时值瞬时值vtxkEvwStxkEtxkEEw2cos1212cos121cos20202202v 平均值平均值数学补充：数学补充： tieftf0)(itiegtg0)()Re(21cos21)cos()cos(2*00/2000gfgftgtdtfgf)Re(21*gfgf11tieftf0)(i

3、tiegtg0)()Re(21)Re(21*gfgfgfgfnEHESBEBHDEw20*2020*21)Re(212121)Re(4112v 分离（频）谱情形分离（频）谱情形jjjjjtxkiEAtxEexp,0v 连续（频）谱情形连续（频）谱情形 dtxkiEAtxEexp,0000expexpexpEEi k xtEEi kxtEEi kxt1300BDtDHtBEEiBEiHBiE001212HHnEEnnEEnE000expexpexpnEik xEik xnEik xk xk xkx14波矢关系式：波矢关系式： xxxyyykkkkkk1kvkksinsinxxkkkksin1si

4、nkk2222211111sinsinsinsinxxkkkkknk 21sinsinn15 rrrrcv11100rrn112211221221rrrrnnn12210,n16coscoscosEEEHHHEHBE1120,E1212112sincoscossincoscos2cos2cos sinsincoscosEEEE coscoscosEEEHHH/E172cos sinsincostgEEtgEE 090tgEEtg12sinsinEE 18121221sin nccsinxxkkk121212vkkknvv v21sinxnkk2212sinnkK0yyykkk22zxkkkiK

5、00 xi k xti k xtK zEE eE ee 19221211sin2nKyEE eEnB2222xxzyk eiKekHEE ekk2222221221sinsinxzkkHEEEkknn20222122222221222122222212221221sinsin1sinsin1xknvKHiEiEin Ekkvin EiEnn yxxzzzxxzSEHE eH eH eE H eE H e *11ReRe22yxxzzzxxzSE eH eH eE H eE H e0 xi k xtKzEE ee 212*22221222*22202222122111sinReRe1221sin

6、1sin1Re1Re022zxKzSE HEiEniE Ei Eenn 212221sinsinsincos1xzkknkikn2222122122122211221coscoscossincoscoscoscoscoscoscossiniinnEeEnincossin2212ntg23EEJJJtt ttexp0衰减特征时间衰减特征时间211s17102400BDJtDHtBEHBED00HEEEiHHiE复电容率复电容率i00EiHHiEEH 25lSJElSEJlIEIURIQ2JElSQEJ耗散（耗散（Dissipation）功率密度）功率密度EJwd平均耗散功率密度平均耗散功率密度E

7、EiH20*21Re21Re21EEEEJ26i022EkEk txkitieEexEtxE0,iktxixEtxEexpexp,0 222222kiiii 2122227xxxkkkxxxikxxxk02122204122222402222222422tzizeeEE0282122221222112111211221穿透深度穿透深度21趋肤效应趋肤效应cm9 . 0cm3107 . 029EnitzizEieiEtzizitzizEiEiHzexpexp1expexp1expexp11000EniH2EniEneEniHi4exp2141EH30DHJiEEiEt EEEHHHEEBHBE0

8、0000000100HE1iHnEHiE310001HHEEHiE01EEiE 2012EEi E 002121iEEi 反射系数反射系数2ERE0203202000202022121222222121121R133,2zzxz 0k 000 xxxxxxkik1iik222222ik022222zzx 200002212121kzz00 0 2(0)2(0)22(0)22xzxzzzxkkkk 22zzxzxz134线电流密度线电流密度ff0dzJf)(0),(tzizeeyxEEtitiziztitzizfeiEeiEdzeeEdzeeEdzE22222200000)(001352222s

9、incos)(0)(220tiftifeeE2200EfzdeEEEEJw220*21)Re(2)Re(21202220022004421fzdLEdzeEdzwP20211fLPHLR100i ti tffffeIHHe36RIWd2202*21)Re(2fdRHIIRW2020202112121fffdLHLLHRLHLHWP37LC21 380, 01212BnHHnDnEEn0, 0BnHnDnEn0E0nEn39考察对象考察对象022EkE022ukuuzyxEEE, ,expE x tE xi t )()()(,zZyYxXzyxu02222222XYZkZzXYYyXZXxYZ2

10、222222111kZzZYyYXxXZzZYyYXxX2222221,1,1zyx,40yzxXxX221x1C0122XCXx01CxCxCeeX112101C21xkC0222XkXxx0, 0222222ZkZzYkYyzy zkDzkCykDykCxkDxkCzyxuzzyyxxsincossincossincos,332211zikzikyikyikxikxikzzyyxxeDeCeDeCeDeCzyxu332211,22222kkkkzyx41zyxu,zyxEEE,yE11, 0DCEy33, 0DCEy0nEn0332211zikzikyyxikxikyzzxxeDeCDik

11、CikeDeCyE22DC 12312322sin() 2cos() 2sin()8sin()cos()sin()sincossinyxyzxyzxyzEiCk xCk yiCk zCC Ck xk yk zAk xk yk z 42zkykxkAEzkykxkAEzkykxkAEzyxzzyxxzyxycossinsinsinsincossincossin3120)sin()sin()sin(0111zkykLkkAxEzyxxLxx1Lmkx32,LpkLnkzy430 E0321AkAkAkzyx321,AAA232221LpLnLmmnp321LLL1/211022121112fLL1

12、/21102212112LL1A2A03A01A02A44低频情形低频情形12UrEU高频情形高频情形0 Ebaabl dEU45l dJl dEEJ1电磁能量的传输电磁能量的传输 022EkEtzkiyxEEzexp,0,222222yxEkkyxEyxz0222222ukkuyxz),(yxuzyxEEE,46令令 )()(,yYxXyxu00222222YkYdydXkXdxdyx其中其中 2222kkkkzyxzkDykCYxkDxkCXzyxxcoscossincos2211zkDykCxkDxkCuzyxxcoscossincos2211边界条件边界条件：对对 x = 0 和和 a

13、 管壁，管壁， ，且，且 ； 0zyEE0 xEx对对 y = 0 和和 b 管壁，管壁， ，且，且 。 0zxEE0 xEy由由 x=0 和和 y=0 面上的边界条件，面上的边界条件，)exp()sin()sin()exp()cos()sin()exp()sin()cos(321zikykxkAEzikykxkAEzikykxkAEzyxzzyxyzyxx47., 3, 2, 1, 0,nmankamkyx321,AAAnm,EiH0zExykkAAA213, 0kE0zH0zEnm,00zzHE00zzEH0321AikAkAkzyx0 E4822222221zzyxkbnamkkkvknm,0zk22,bnammncac10,aavvcc22210,10,49003AEz00, 1yknm0001321xzyxEA