ELEG 413 Lecture #6. Mark Mirotznik, Ph.D. Professor The University of Delaware

Transcription

1 LG 43 Lctur #6 Mrk Mirtnik, Ph.D. Prfssr Th Univrsity f Dlwr mil: mirtni@c.udl.du

2 Wv Prpgtin nd Plritin TM: Trnsvrs lctrmgntic Wvs A md is prticulr fild cnfigurtin. Fr givn lctrmgntic bundry vlu prblm, mny fild cnfigurtins tht stisfy th wv qutin, Mwll s qutins, nd bundry cnditins usully its. A TM md is n whl fild intnsitis, bth nd H, t vry pint in spc r cntind in lcl pln, rfrrd t s quiphs pln, tht is indpndnt f tim H

3 Wv Prpgtin nd Plritin Unifrm Pln Wvs If in dditin t hving plnr quiphss th fild hs qul mplitud th mplitud f th fild is th sm vr ch pln plnr surfcs thn it is clld unifrm pln wv.

4 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin y y y y y y y Fr unifrm pln wv ssum th slutin is nly functin f nd hs nly th cmpnnt f lctric fild.

5 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Fr unifrm pln wv ssum th slutin is nly functin f nd hs nly th cmpnnt f lctric fild. y H ε µ Wht bsrvtins cn w mk but th rltinship btwn nd H fr unifrm pln wvs?

6 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin y H ε µ Wht bsrvtins cn w mk but th rltinship btwn nd H fr unifrm pln wvs? Bth nd H r trvling in th sm dirctin with th sm phs r wv numbr Bth nd H r plrid in dirctins tht r rthgnl i.. 90 dgrs frm th dirctin f prpgtin nd thy r rthgnl t ch thr. 3 H hs mgnitud tht is smllr thn by r ε µ η

7 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin y H ε µ Bth nd H r trvling in th sm dirctin with th sm phs r wv numbr Bth nd H r plrid in dirctins tht r rthgnl i.. 90 dgrs frm th dirctin f prpgtin nd thy r rthgnl t ch thr. H hs mgnitud tht is smllr thn by r ε µ η Hw d I figur ut which wy H is plrid if I knw nd th dirctin f prpgtin?

8 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin y H ε µ Bth nd H r plrid in dirctins tht r rthgnl i.. 90 dgrs frm th dirctin f prpgtin nd thy r rthgnl t ch thr. Hw d I figur ut which wy H is plrid if I knw nd th dirctin f prpgtin? Which dirctin is th nrgy mving?

9 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin y H ε µ Bth nd H r plrid in dirctins tht r rthgnl i.. 90 dgrs frm th dirctin f prpgtin nd thy r rthgnl t ch thr. H S Hw d I figur ut which wy H is plrid if I knw nd th dirctin f prpgtin? Which dirctin is th nrgy mving? Th Pynting vctr S must b in th dirctin f prpgtin.g. fr this mpl. Thus crss H using th right hnd rul must pint in th dirctin f nrgy r prpgtin.

10 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin ε ο,µ ο y 0 9 y Find H

11 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin 7 4ε ο,µ ο y Find H

12 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin 4 y ε ο,6µ ο 5 y Find H

13 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint?

14 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? Cnvrt t tim dmin

15 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? Cnvrt t tim dmin { } { } t t t t t t cs, R, R, ω ω ω

16 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? Cnvrt t tim dmin, t cs ωt Which trm is th phs?

17 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? Cnvrt t tim dmin, t cs ωt Which trm is th phs? φ ωt

18 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? Cnvrt t tim dmin, t cs ωt Which trm is th phs? φ ωt W wnt t knw hw fst I must run t kp t th sm phs pint i.. cnstnt phs

19 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint?, t cs ωt φ ωt W wnt t knw hw fst I must run t kp t th sm phs pint i.. cnstnt phs ω cnstnt d dt φ t φ d φ dt [ ωt ] 0

20 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint?, t cs ωt φ ωt W wnt t knw hw fst I must run t kp t th sm phs pint i.. cnstnt phs d dt dt dt d dt [ ωt ] ω 0 v p

21 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint? d dt ω v p, t cs ωt φ ωt dt dt d dt [ ωt ] ω 0 0 v p ω v p Tru in gnrl

22 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Phs Vlcity Hw fst d I hv t run t kp t th sm phs pint?, t cs ωt v p ω Tru in gnrl ω Tru fr unifrm v p c pln wvs ω εµ εµ

23 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin nrgy nd Pwr fr Unifrm Pln Wvs y H η v m v H w w ε η µ η µ µ ε ε ε [ ] [ ] [ ] y y v H S * * η η η

24 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Grup Vlcity, t cs cs [ ω ω t ] [ ω ω t ]

25 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Grup Vlcity [ ] [ ] t t t ω ω cs cs, [ ] [ ] t t t cs cs, ω ω ω ω t ω Cnstnt

26 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Grup Vlcity, t cs cs [ ω ω t ] [ ω ω t ], t [ ω t ] cs[ ω t ] cs ω t Cnstnt d dt dt dt d dt [ ωt ] ω 0

27 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin, t Grup Vlcity [ ω t ] cs[ ω t ] cs ω t Cnstnt d dt dt dt d dt [ ωt ] ω 0 d ω v g lim ω 0 dt d dω In gnrl

28 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Grup Vlcity d ω v g lim ω 0 dt d dω In gnrl Fr pln wvs ω/c d dω c v g c Fr pln wvs

29 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Stnding Wvs

30 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Stnding Wvs

31 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Stnding Wvs

32 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Stnding Wvs

33 Unifrm Pln Wvs in Unbundd Lsslss Mdium Principl Ais Prpgtin Stnding Wvs

34 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril ω µε ωµσ 0 ωµ ωε σ 0 γ 0 whr ωε σ γ ωµ

35 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril γ 0 whr γ ωµ ωε σ Simpl pln wv slutin γ γ

36 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril γ 0 whr γ ωµ ωε σ Simpl pln wv slutin γ γ γ ± ωε σ ± α ωµ ±

37 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril 0 γ σ ωε ωµ γ whr Simpl pln wv slutin γ γ α σ ωε ωµ γ ± ± ± α α α α

38 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril γ whr γ ωµ ωε σ γ 0 Simpl pln wv slutin ωε σ α ωµ α T find α nd w slv th bv qutin.

39 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin Pln wvs trvling in lssy mtril α γ ωε σ α ωµ T find α nd w slv th bv qutin.

40 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin

41 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin

42 Unifrm Pln Wvs in Unbundd Lssy Mdium Principl Ais Prpgtin

43 mpl: Skin Dpth in S Wtr Skin Dpth, cm Frquncy, GH

44 mpl: Skin Dpth in Cppr Skin Dpth, micrns Frquncy, GH

45 mpl: Skin Dpth in Tfln Skin Dpth, mtrs Frquncy, GH