FRESNEL Quick Guide |
Open new scheme and load the input radiation from the file magnif.pls.
It is rectangular symmetry TEM_{2,0} mode which parameters can be seen
if you return back to selecting Input beam shape and choose Resonator mode. You
will see: Scale L_{0} = 1.28 cm, discretization N = 256, beam size w = 0.015 cm, wavelength 1000 nm.
Now, double click Target, switch pause "off" and set the Magnification = 8.
Running of the scheme produces the 8X magnified image (right profile in the figure above) of
the initial beam that can be compared with 8X zoomed profile of the initial beam (left profile).
Exporting the profile of the beam into Excel or other program one can compare magnification
result with analytical data for TEM_{2,0} mode.
User can now change first TEM mode index of the input radiation from 2 to 10. After running the
scheme two X-profiles for the TEM_{10,0} beam, obtained at Zoom = 8 and Magnification = 8
can be obtained for TEM_{10,0} mode as shown in the next picture.
One can see that zoomed beam exhibits only 7 maxima while the magnified beam has 11 maxima
as it should be for the mode TEM_{10,0}.
Setting Magnification = 1 and running the scheme again one can now press the "amplitude"
button to restore the TEM_{10,0}
mode amplitude distribution. The X-profiles for both zoomed and magnified beam amplitudes do
exhibit 11 extremums, as it should be. These profiles are presented below.
So there is no miracle that the Fourier interpolation restores beam shape quite correctly:
the field is defined by its amplitude and phase rather than by the energy density distribution.
It is recommended now to change the TEM mode index of the input radiation to 20. The test consisting
in the propagation of the beam to the far field zone shows that the expected precision for the
calculations with this beam is very poor. It is due to not high enough spatial frequency used to
describe the beam: the distance between sampling points used is too big and many important features
are lost. The TEM_{20,0} mode can be properly propagated and magnified using either smaller
scale (e.g. L_{0}= 0.64 cm, N= 256) or larger discretization (N=512, L_{0}= 1.28).
Try this.