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Mode Structure of Helium-Neon Laser

The mode structure of a HeNe-laser of wavelength 633 nm is studied with a scanning Fabry-Perrot interferometer. The two laser concave mirrors have the same radius of curvature. On an oscilloscope the following image is obtained.

1- Calculate the frequency difference between TEM 004 and TEM 00q+1

2d
1
cos" (8182)'
0, 1, 4+1
0,2, q+1
0, 0, q
1, 3, q–1
2, 2, q-1
0, 1, 4
2, 3, q–1
3, 2, q–1
0, 2, 4
2, 0, q
1, 1, q
0, 3, 4
1, 2, 4
2, 1, 4
0,0, q+1
0, 5, q
:

Mode Structure of Helium-Neon Laser
The mode structure of a HeNe-laser of wavelength 633 nm is studied with a scanning
Fabry-Perrot interferometer. The two laser concave mirrors have the same radius of
curvature. On an oscilloscope the following image is obtained.
420 MHz
1- Calculate the frequency difference between TEM 00.
and TEM 004+1 •
2- Calculate the cavity length of the Fabry-Perrot interferometer.
3- Name the peak A if the peak B is the TEM 01g ·
4- Draw a picture of how the image would look like on the oscilloscope if the laser
was of type single mode frequency.
5- Calculate the curvature of the two laser mirrors based on your discussion in
questions 2 and 3.
You may find the following figure useful
2d
cos"' (g182)2
0, 0, q
1, 3, q-1
2, 2, q–1
0, 1, 4
2, 3, q–1
3, 2, q–1
0, 2, 4
2,0, 4
1, 1, 4
0, 3, q
1, 2, q
2, 1, 4
0,0, q+1
0, 5, q
0, 1, 4+1
0, 2, q+1

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