Question

Consider a uniform transverse electromagnetic plane wave be normally incident on an interface between region 1 and region 2, at z = 0. Let the known incident wave in region 1 be (1.20) E(1)(r) = Â Ee-ikız îkı * E")(r) у ki H*)(r) E e-ikız. (1.21) ωμι wi where kı = w M€1. Let the unknown reflected wave be (1.22) E")(r) = în Ef")eikız ku r(r) Hr)(r) = -ġ whi EX")eikiz (1.23) and the unknown transmitted wave be (1.24) E(+) (r) = À E e-ikaz k2 H+) (r) = ĝ F(t)-ikg Eo e ωμ2 (1.25) (a) Use the boundary conditions n < (E2 - E1) = 0 and nx (H2-H) = 0 to show that E%") = TEM E") = TEM (1.26) (1.27) where the reflection and transmission coefficients are T= (1.28) 12-11 12 + 1 2n2 72 +11 T= (1.29) respectively, and ni = Milei.

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Answer 1

agnetic plane wave be Consider uniform transverse eleelsoma normally incident on an infeface' between region I and region 2. at Z=0. Incident wave: -ikiz lº E" (n= sê Ele) y ki (Ů ikiz Hi (1= î k X E (V) Whi whi where ki= wfme, also c= v=e JMIEI n = Ses Milεi We get hiin (me to melk, ) Reflected Wave is (O)= relveikaz H10() --ý ki E, love ikoz €(0 WMI Medium I BM (0) i con i kız Eo 2 and transmitted wave is Elon = Ã Elle ikaz kew: 9 k E,e-ikaz Wha Medium Bey = og 5 baik2 Y

on the fields udt 7-0 , the combined field left & + ER and Bito B1 + BR must join right Eth Bř , in accordance with the boundary on the conditions EI ET V2 VI BT B, BR V. interface y 11 1 Boundary conditions are LU 6, 8, += 6,62" (u) E, SE ('') B. + 11 B2 - (iv) i Bi" ㅗ B2 씨 M2 In this case there are no componento prependiculai to surface do boundary conclition les ciú) are trivial, and we requie (ii) Eq" = Eq" i (+) (nt E (ol= E (0) Teli + ER Eolit) -(a) 5) E. 0),

and ") را gives toi (6) f ] (3) ß- - condition (iv) says (v) ㅗ u Mq which r ED EOS where Mina Mg V₂ Equation (a), (b) can be solved for outgoing amplitudes and we get (0) (t) li 2 E to litß 1+B (R) Ed Elt), TEU M2미 (RI E If - reli n-n2 ni+42 where T=1-B v2.0 itp Uztv as ß= V1/V2 if 9=140 E®=(M12) 610 ni+42 Q V2 2n also (t) co T= 2 STELUT Gatv nith (t) IB Blo? n1+12