Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 21 ECE 6340 Intermediate EM Waves 1

Reflection from Slab Notes: (2) The origin is the reference plane for T. TE z y z ii EiEi d    (1) 2

Reflection from Slab (cont.) Three methods: 1)Plane-wave bounce method (interface reflections) 2)Steady-state wave representation 3)Transverse equivalent network (TEN) 3 Find the reflection coefficient .

Method #1 Define interface plane-wave reflection and transmission coefficients: Plane-wave bounce method (interface reflections) 4

5 Interface Reflections (cont.)

Plane-Wave Bounce Diagram z  d B A C D  E y 6

Bounce Diagram (cont.) At z = 0: So we have Note that (for p an integer) 7

Bounce Diagram (cont.) Hence 8

Bounce Diagram (cont.) Hence Next, use or 9

Method # unknowns: , T, A, B Steady-State Wave Representation 4 equations: E x and H y must match at both interfaces. #1 #2 #3 Three regions y z 10 Steady-state waves

Method # 3 Transverse Equivalent Network (TEN)  z   d I V

TEN (cont.)  z  d  z   d 12

Equivalent circuit:  z  d 13 TEN (cont.)

We then have   14 TEN (cont.)

Region 2: Find the transmission coefficient T.  z   d #1 #2#3 15 TEN (cont.)

At z = 0 : Hence  z   d #1 #2 #3 16 TEN (cont.)

We then have 17  z   d #1 #2 #3 TEN (cont.)

Also Hence 18 TEN (cont.) Region 3: where

Final result: 19 TEN (cont.)  z   d #1 #2 #3