1. paraxial approximation

2. z Eq Hj  r
I DL y j x

3. far field

4. E = ?
E = ?

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

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

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

10. a = p/2 b = p/2

11. a = p b = p/2

12. a = p b = p

13. a = 3p b = 3p

15. x y z  ’
x’, y’
2zo

18. 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

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

21. University of Wisconsin
Elmer Scheibe
James Beyer
James Mink