FRESNEL Quick Guide

Example 3. Magnification (Fast Fourier Interpolation)

Open new scheme and load the input radiation from the file magnif.pls. It is rectangular symmetry TEM2,0 mode which parameters can be seen if you return back to selecting Input beam shape and choose Resonator mode. You will see: Scale L0 = 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 TEM2,0 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 TEM10,0 beam, obtained at Zoom = 8 and Magnification = 8 can be obtained for TEM10,0 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 TEM10,0.
Setting Magnification = 1 and running the scheme again one can now press the "amplitude" button to restore the TEM10,0 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 TEM20,0 mode can be properly propagated and magnified using either smaller scale (e.g. L0= 0.64 cm, N= 256) or larger discretization (N=512, L0= 1.28). Try this.


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