Transfer Matrix Techniques for Electromagnetic Waves

Abstract

The concept of a transfer matrix is extremely simple: if we know electric and magnetic fields in the x-y plane at z=0, then we can use Maxwell’s equations at a fixed frequency to integrate the wavefield and find electric and magnetic fields in the x-y plane at z=c. In fact, if we assume that both B and D have zero divergence, we need only know two components of each field: let us say,

$$ F\left( {z = 0} \right) = \left[ {{{E}_{x}}\left( {z = 0} \right),{{E}_{y}}\left( {z = 0} \right),{{H}_{x}}\left( {z = 0} \right),{{H}_{y}}\left( {z = 0} \right)} \right] $$

((1.1))

Then,

$$ F\left( {z = c} \right) = T\left( {c,0} \right)F\left( {z = 0} \right) $$

((1.2))

defines the transfer matrix, T.