The far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109

Transcription

1 Th fa fl calculao: Appoa a ac oluo Pa K Novb 0h 005 B-09

2 Oul Novb 0h 005 Pa K Iouco Appoa oluo flco fo h gou ac oluo Cocluo

3 Pla wav fo Ic fl: pla wav k ( ) jk H ( ) λ λ ( ) Polaao fo η 0 0 Hooal polaao jk Vcal polaao 0 c flc c flc H H a a H Novb 0h 005 Pa K

4 Novb 0h 005 Pa K How o f h flco coffc Hooal polaao flc a wav: alo pla H H jk ( co ) ( ) η jk ( co ) ( ) ( co ) jk ( co ) ( ) ( ) 0 co jk ( ) ( co ) η 0

5 Novb 0h 005 Pa K Boua coo O h ufac: couou agal copo ( ) ( ) ( ) ( ) ( ) ( ) jk jk jk jk jk jk T k k k k k H H H η η η co co co co co co co ) )

6 Novb 0h 005 Pa K Vcal polaao ( ) V V V T k k co co co co

7 Bw agl Novb 0h 005 Pa K Fo vcall pola wav h a agl fo whch h o flc wav. Wha? I h uch a hg fo hooall pola wav?

8 Novb 0h 005 Pa K Coucv gou ω σ ω σ ω σ ω σ ω σ j j j j j H J W ca ubu h copl valu o h pvou quao. W obv ha ow boh h aplu a hphaofhflcwavachag.

9 Novb 0h 005 Pa K Wha f h c wav o pla Ta: vcal lal pol Noc: c flc ufac ( )( ) ( ) ( ) γ ψ ψ γ γ ψ γ γ ψ ψ ψ ψ γ γ ψ ρ 0 co co co co 30 co co 30 F jkil F jkil jk V jk V jk jk V jk V jk ψ

10 lav of h Novb 0h 005 Pa K Wha h agu of h ufac wav? Wha h agu of h pac wav? Wh a h copaabl?

11 Wha happ fo a hooal pol? Novb 0h 005 Pa K Wha a a w alkg abou? O a pla ppcula o h a of h pol: pac 30 jkil jk H jk O a pla paall o h a of h pol: pac 30 jkil jk V jk

12 Th ufac wav Novb 0h 005 Pa K Fo h ρ coψ F δ jkγ jk 0 : uf 30 jkilf V ψ γ δ F fo all. j δ γ fc γ ( ) ( ) [ ( γ ) γ ( j δ ) co V ψ co ψ Fo uffcl hgh coucv a low fquc F glgbl (cp fo v hallow agl) F fall apl wh ac.

13 Novb 0h 005 Pa K Appoa po fo hgh fq V lag ac bw a lva aa. Nglgbl ufac wav. H V - ( ) ( ) / co 60 co h h I h h I h h h h h h h h h h k a wh a I a a j a I a j a I I I ja ja H V λ λ

14 Novb 0h 005 Pa K Polaao clo o h gou Sufac wav A llpcall pola Hav a lgh l w h vcal (whch pla pow lo) Igog hgh o ρ uf γ 4 σ aca σ j ω 0 ω 0 j σ ω 0 Wha happ a fquc/ coucv ca?

15 Novb 0h 005 Pa K ffc of ou ah Opcal hoo h 0 a ah 0 Fo wo aa a h a h : ah ah

16 Aoal faco Novb 0h 005 Pa K Th flc fl uc bcau: Th quval hgh a ho Th flco occu ov a cuv ufac Sc h flc fl o cacl ou h c fl h wo faco pl ha h oal pac fl acuall hgh. Th aw uch o coplca fo h ufac fl. How aco h gal h?

17 Oul Novb 0h 005 Pa K Iouco Appoa oluo ac oluo Th gal quao Cocluo

18 Novb 0h 005 Pa K : Pocklgo I Dv fo pfc lcc couco U boua coo (o agal lcc fl) φ ω 0 / / ' 4 ' G G I k j jk l l

19 Novb 0h 005 Pa K Pfc agc couco Boua coo H 0 0 Igal quao ( p) T ( p) ( ' ) jk Ψ f p o S T ohw T 4 S ' Ψ' ( ) ( ) ' ' ( ' )

20 Novb 0h 005 Pa K quval ouc cu ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) jk T p T p T p T p T p T p S jk S ca Ψ ' 4 ' ' 4

21 Novb 0h 005 Pa K Splfg aupo Coa ufac av o h co of popagao pc fo h ouc cu ( ) ' ( ' ) ( ) ' ( ' ) ( ) ' ( ' ) Ia: ga call fo. a cobuo cacl ou.

22 Wha abou h cobuo? Novb 0h 005 Pa K 4 ca ( ) ( ) ( ) ( ( )) S 4 S jk jk jk jk Th appoao hol wh: W hav a clcal wav ogag fo a l ouc alog h a. o of h cobuo co fo h vc of h a of popagao (u wh h ufac coa av o h a of popagao).

23 Novb 0h 005 Pa K Go: ( ) ( ) ( ) ( ) ( ) ( ) : 0 0 Slal k k Δ Δ Δ Δ Δ Δ Δ φ φ φ

24 Novb 0h 005 Pa K Back o h gal ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) Δ ζ ζ ζ λ l jk l jk l jk jk j jk jk jk jk jk S jk ca Wha w o a ach p???

25 Novb 0h 005 Pa K po of h ogal quao ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) o back cag : If ' 4 k j j jk h h l jk f f T T l jk T T Δ Δ Δ ζ λ λ

26 Illuao of h algoh Novb 0h 005 Pa K

27 apl: a wg Novb 0h 005 Pa K

28 Pah lo ul Novb 0h 005 Pa K

29 pal ul Novb 0h 005 Pa K

30 Oul Novb 0h 005 Pa K Iouco Appoa oluo ac oluo Th gal quao Cocluo

31 Cocluo Novb 0h 005 Pa K Aupo: Sooh pfcl flcg ufac No cag No back cag Goo ag wh au a ho Fl gh o follow h la pofl!