paraxial approximation

z Eq Hj  r I DL y j x

far field

E = ? E = ?

x y z   ’ x’, y’ paraxial approximation

 x y z  ’ x’, y’ 2d version of the Fourier integral

a b x y z  ’ x’, y’ uniform illumination

a = p/2 b = p/2

a = p b = p/2

a = p b = p

a = 3p b = 3p

x y z  ’ x’, y’ 2zo

The field @ z = +z0 is the Fourier transform of the field @ z = -z0 There is loss at the edges but this is very small Goubau – Schwering beam waveguide

Normal propagation for a distance 2zo S’   losses

University of Wisconsin 1958-1964 Elmer Scheibe James Beyer James Mink