This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 24 Evanescent waves and tunneling In this lecture we will explore the tunneling phenomenon associated with evanescent waves established within finitewidth regions. The multislab tunneling result to be derived in this lecture will: 1. Enhance our qualitative understanding of the frustratedFIR ex ample shown back in Lecture 19, 2. Illustrate a methodology based on transmission line analo gies to be used in forthcoming lectures on waveguides. Region 1 Region 2 Region 3 z x d E i E r E + E t E 1 2 3 Consider the threeslab geometry depicted in the margin where a TEM wave field E i = x E i e jk 1 z , accompanied by H i = y E i 1 e jk 1 z , is incident from the left in the region z < d (region 1). As a response a reflected wave E r = x E r e jk 1 z , accompanied by H r = y E r 1 e jk 1 z , is set up in the same region, as well as E + = x E + e jk 2 z , accompanied by H + = y E + 2 e jk 2 z , and E = x E e jk 2 z , accompanied by H = y E 2 e jk 2 z , 1 in the region d < z < (region 2). Finally, in region z > , we will have E t = x E t e jk 3 z , accompanied by H t = y E t 3 e jk 3 z . Our aim is to determine the amplitudes E t , E + , E , E r in terms of E i using tangential boundary conditions at z = d and z = 0 . We are in particular interested in the ratio of the transmitted power in region 3 to the incident power in region 1 as a function of slab width d as well as the refractive indices n 1 , n 2 , and n 3 , includ ing the case when n 2 is purely imaginary, the case corresponding to region 2 being in evanescent mode. Starting with the boundary at z = 0 , the continuity of tangential E and H across the boundary requires that Region 1 Region 2 Region 3 z x d E i E r E + E t E 1 2 3 E + + E = E t and E + E 2 = E t 3 . These equations can be solved for E t and E in terms of E + to obtain E t = 2 3 3 + 2 E + and E = 3 2 3 + 2 E + . 32 32 Note that we have defined a pair of coefficients representing the in teraction at z = 0 interface: a transmission coefficient 32 and a 2 reflection coefficient 32 in terms of intrinsic impedances 3 and 2 in a manner analogous to similar relations seen in our studies of...
View
Full
Document
This note was uploaded on 09/27/2011 for the course ECE 450 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Electromagnet

Click to edit the document details