Lecture 17. Waves in Anisotropic Media

Size: px

Start display at page:

Download "Lecture 17. Waves in Anisotropic Media"

Octavia Riley
7 years ago
Views:

1 tu 17 Wavs i Aistpi Mdia I this ltu u will la: Wav ppagati i aistpi dilti mdia Wav ppagati i biaial ad uiaial mdia Bifig Quat-wav ad half-wav plats C 33 Fall 7 Faha Raa Cll Uivsit Aistpi Mdia S fa u hav b dalig with matials that ld th sam i all ditis (i.. istpi) F istpi mdia, th -fild is latd t th -fild b umb th dilti pmittivit: P Nw sid a matial mad up mluls that a asil b plaid b -filds i th -diti, but d t spd muh t -filds i th - ad -ditis, as shw i th figu -fild i th - -ditis: matial t muh plaid -v lt lud v is -fild i th - diti: matial stgl plaid C 33 Fall 7 Faha Raa Cll Uivsit 1

2 ilti Pmittivit Ts I th mst gal as, th -fild is latd t -fild thugh a dilti pmittivit ts:. What this all mas is that th -, -, ad -mpts f th -fild a latd t th -, -, ad -mpts f th -fild b a pmittivit mati: ( ) This is th mst gal wa f pstig th ffts f matial plaiati wh th matial is aistpi Th pmittivit mati is alwas smmti, i... This fllws fm phsial sidatis that hav t d with g svati ad timvsal smmt. N mdia a vilat this diti T C 33 Fall 7 Faha Raa Cll Uivsit Biaial Mdia Th dilti pmittivit mati is smmti, i.. ( ) T Th is a thm i lia algba that sas that a smmti mati a b diagalid b a suitabl hi f th basis vts (i.. b a suitabl hi f th itati f th -diat as w..t. th matial) S i th mst gal as, if hss th itati f th -diat as udiiusl, th lati btw th -fild ad -fild bms: This pmittivit mati is diagal If th diagal tis a all difft th matial is alld biaial Th hi f -diat as that sults i a diagal pmittivit mati is alld th piipal as f th matial C 33 Fall 7 Faha Raa Cll Uivsit

3 Uiaial Mdia I a uiaial mdia, tw f th diagal tis f th pmittivit mati a th sam ad is difft, f ampl: If th -fild is l alg -ais: If th -fild is l alg -ais: If th -fild is l alg -ais: ( ) ( ) ( ) F th as shw abv, -ais is alld th tadia ais, ad -ais ad -ais a alld th dia as Ma imptat matials a uiaial (.g. alit, mia, quat, t) C 33 Fall 7 Faha Raa Cll Uivsit Wav Ppagati i Aistpi Mdia - I Faada s aw: ( ) ( ) Amp s aw: v ( ) J( ) ( ) F aistpi mdia: ( ). ( ) Wav quati: ( ) ( ) ( ) (. ) ( ) ( ) Wait a miut!! Gauss aw stats that divg f -fild (t -fild) is (if th is hag dsit):... Its t bvius that th abv implis:. ( ) But. ( ) tus ut t b tu f pla wavs ppagatig i aistpi mdia C 33 Fall 7 Faha Raa Cll Uivsit 3

4 4 C 33 Fall 7 Faha Raa Cll Uivsit Wav Ppagati i Uiaial Mdia - I Th statig pit is th fllwig wav quati: Csid th fllwig uiaial mdia: Ad a pla wav plaid i th -diti ad tavlig i -diti Substitut i th wav quati ad us th pmittivit ts, t gt: S a pla wav plaid i th -diti ad tavlig i -diti is giv as: C 33 Fall 7 Faha Raa Cll Uivsit Wav Ppagati i Uiaial Mdia - II Agai sid th sam uiaial mdia: Ad a pla wav plaid i th -diti ad tavlig i -diti: Substitut i th wav quati ad us th pmittivit ts, t gt: S a pla wav plaid i th -diti ad tavlig i -diti is giv as:

5 5 C 33 Fall 7 Faha Raa Cll Uivsit Wav Ppagati i Uiaial Mdia - III A pla wav plaid i th -diti ad tavlig i -diti is giv as: A pla wav plaid i th -diti ad tavlig i -diti is giv as: S f th uiaial mdia i whih th pmittivit ts is: Wavs plaid i difft ditis (but tavlig i th sam diti) hav difft wavvts C 33 Fall 7 Faha Raa Cll Uivsit Wav Ppagati i Uiaial Mdia - IV Csid a uiaial mdia i whih th pmittivit ts is: Qusti: w ds a pla wav with bth - ad -mpts ppagat? Asw: ah mpt ppagats with its w wavvt (thi lia suppsiti) Th pla wav has sigl wavvt. Th pla wav has tw wavvts assiatd with th -mpt f th -fild ad assiatd with th -mpt f th -fild Th abv pssi will satisf th wav quati:

6 6 C 33 Fall 7 Faha Raa Cll Uivsit Uiaial Mdia ad Bifig Csid a slab f uiaial mdia with piipal as as shw: If < th th tadia ais a alld th fast ais ad th dia ais a alld th slw ais (baus th wav tavls fast if it is plaid alg th fast ais) If > th th tadia ais a alld th slw ais ad th dia ais a alld th fast ais Th phm wh wavs f difft plaiati diti tavl at difft vlitis is alld bifig C 33 Fall 7 Faha Raa Cll Uivsit Uiaial Mdia Appliatis alf-wav Plats A uiaial plat with th piipal ais idiatd At, th fild isid th plat is: Th th fild isid th plat f a is: Th fild isid th plat f is: alf-wav plats a usd t tat th plaiati f a pla wav b a abita agl h w sid tati b 9

7 7 C 33 Fall 7 Faha Raa Cll Uivsit Uiaial Mdia Appliatis alf-wav Plats A uiaial plat with th piipal ais idiatd Th fild isid th plat f is: If: K,K 1,, 1 ± ± m m π Th th fild isid th plat f is: Output plaiati i diti thgal t th iidt plaiati Plaiati tatd thugh 9-dgs C 33 Fall 7 Faha Raa Cll Uivsit alf-wav Plats: A ampl ais ad -ais a th slw as -ais is th fast ais As th wav ppagats i th plat, th -mpt f th wav lags bhid th fast -mpt f th wav i spa Wh th lag i spa is -half f a wavlgth ( a dd-multipl f it) th ttal -fild is plaid i th thgal diti (h th am half-wav plat)

8 8 C 33 Fall 7 Faha Raa Cll Uivsit alf-wav plats a usd t tat th plaiati f a pla wav b a abita agl A uiaial plat with th piipal ais idiatd Uiaial Mdia Appliatis alf-wav Plats Th utput plaiati a b tatd thugh a agl b tatig th ais f th plat w..t. th iidt plaiati C 33 Fall 7 Faha Raa Cll Uivsit Uiaial Mdia Appliatis Quat-Wav Plats Quat-wav plats a usd t tu lial plaid wavs it iulal lliptiall plaid wavs ad vi vsa A uiaial plat with th piipal ais idiatd At, th fild isid th plat is: Th fild isid th plat f a is: Th fild isid th plat f is:

9 9 C 33 Fall 7 Faha Raa Cll Uivsit Th fild isid th plat f is: If: K,K 1,, 1 ± ± m m π Th th fild isid th plat f is: ± Output plaiati is ith lft-had ight-had iula dpdig up th valu f m (i.. th thiss f th plat) Uiaial Mdia Appliatis Quat-Wav Plats Quat-wav plats a usd t tu lial plaid wavs it iulal lliptiall plaid wavs ad vi vsa A uiaial plat with th piipal ais idiatd C 33 Fall 7 Faha Raa Cll Uivsit Plim 1 Rsults

at 10 knots to avoid the hurricane, what could be the maximum CPA? 59 miles - 54 nm STEP 1 Ship s Speed Radius (e-r) 10 k - 1.0 nm every 6 minutes

at 10 knots to avoid the hurricane, what could be the maximum CPA? 59 miles - 54 nm STEP 1 Ship s Speed Radius (e-r) 10 k - 1.0 nm every 6 minutes :1 Navigatio :1 Gal 1 1 1 Rf: P, Huica You a udway o cous T ad you axiu spd is 1 kots. Th y of a huica bas 1 T, ils fo you positio. Th huica is ovig towads T at 1 kots. If you auv at 1 kots to avoid th