The Fabry-Perot Spectrum Analyzer produced the following plot of data from our He Ne laser.

The two peaks on the right represent the light frequencies emitted by the laser.  Clearly this laser is not monochromatic - two peaks correspond to two longitudinal modes.  Because the Fabry-Perot Spectrum Analyzer repeats the modal pattern of our laser every 2 GHz, the first and last peaks on our graph are actually the same mode.  Since we know the difference in frequency between the first and last peak, we can easily find the difference in frequency between the two separate modal peaks.  Calculating the change in frequency is also relatively simple.  As discussed in our theory section,

The following table gives the results of these calculations:

By using a polarizing lens, we found the polarization of the two modes of this laser. (We observed the peaks from the Fabry-Perot Analyzer and noted the orientation of the polarizing lens when a certain peak disappeared.) The mode with the higher frequency and intensity is vertically polarized and the mode with the lower frequency and intensity is horizontally polarized.

The next plot also shows longitudinal modes of the He-Ne Laser.  The cavity length has been changed.  Because the cavity length is larger, we expect more possible modes and thus a smaller delta frequency between modes.  By analyzing the difference between identical frequencies, we again found the difference between the two observed emitted frequencies.   

A smaller delta frequency was observed, as expected.

Again we found the polarization of these modes; the mode with the higher intensity and frequency is vertically polarized while the mode with the lower intensity and frequency is horizontally polarized.  This is in agreement with earlier results.

The following plot shows the modal structure of a commercial Uniphase Helium Neon laser. Instead of two longitudinal modes, this laser produces three modes at a much higher intensity.  We found the difference between the lower mode and the middle mode to be 441.4 MHz.  Because we do not know the cavity length, we can not compare this experimental result with calculated results.  However, we can calculate the expected cavity length - .3396m.  The entire laser casing is about .3850m so this result seems reasonable.

Again, we found the polarization of the modes.  The middle frequency is horizontally polarized while the two side frequencies are vertically polarized.

After finding that both lasers produced more than one frequency, we compared the Fabry-Perot method to the Wavemeter WA-1000 and its internal Michelson interferometer.  We thought that by using the Wavemeter, we could measure the “position” vs. time of the light, take the Fourier transform of that graph, and show the different frequencies at which the laser lased.  This is what we found the the commercial He-Ne laser:

As you can see, a single peak is produced.  There seems to be only one frequency instead of multiple frequencies as observed by the Fabry-Perot Analyzer.  We repeated this experiment with our other He-Ne laser and our results were the same:  a single peak, signifying a single frequency was found.  The precision of the Wavemeter is limited by the scanning range of its internal optics.

The following pictures are of the transverse modal patterns of our He-Ne laser.  We observed these patterns by slightly tilting the mirror at the end of the laser cavity.  We then projected the laser light onto a piece of paper several meters from the laser.  This enlarged the images of the transverse modes.  The more basic modes can be found using the equation below (see theory section). 

The other more complex modes are combinations of these simpler modes.  Some interesting patterns can be obtained.