reflection standing waves

Etan is continuous E E Htan is continuous X H E H H

Reflection coefficient X E H Transmission coefficient

Reflection and transmission of a pulse signal at an interface of two different dielectrics.

impedance meter conductor

Reflection of an electromagnetic pulse from a conducting surface.

magnitude square law detector time-harmonic signal metal wall - R=-1 magnitude square law detector standing wave

Standing wave

standing wave @ different times node antinode l 

electric & magnetic fields differ in phase by p/2

Different resonances n = 1; 2; 3; ... Screen Screen Screen Screen

resonance Fabry-Perot resonator Screen L

solve for the resonant frequency application solve for the resonant frequency

two different dielectrics

applications paper ==> wood pulp & water in Sweden oleo ==> corn oil & water in Iowa curing concrete ==> [cement + water] (time) emphysema ==> lung & air metal thickness in a rolling mill

x y z qz qx qy E H r k Plane waves: not on an axis

x y z qz qx qy E H k r

reflection - two cases Einc || to surface Hinc || to surface x z z Hr Er qr Hr Er qr x x Ei Hi qi Ei Hi x qi Incident wave Incident wave

ki • r = [- k cos i ux + k sin i uz] • [x ux + y uy + z uz] = - kx cos i + kz sin i kr • r = [+ k cos r ux + k sin r uz] • [x ux + y uy + z uz] = + kx cos r + kz sin r Ei Hi Hr Er x qi qr

Ey inc = Eyi exp [- jk(-x cos i+z sin i)] E = Eo exp [j(t - k • r)] Ey inc = Eyi exp [- jk(-x cos i+z sin i)] Ey ref = Eyr exp [- jk(+x cos r+z sin r)] @ metal wall @ x = 0 -- Ey = 0 Eyr = - Eyi & r = i Ei Hi Hr Er x qi qr

Bill, could I get a job at Microsoft? Hillary taught me Basic.