Experimental Data

    From our experimental data, we can learn much about the mode structure of the He-Ne laser and about the scanning Fabry-Perot interferometer.   Also, we can see how changing the cavity length effects the laser output and modal structure.

    As discussed in the Theory section, the separation between longitudinal modes should be del v = c / (2L).  Transverse modes (TEM) will not necessarily be evenly spaced as their solutions involve non-linear Hermite polynomials.  As we increase cavity length increases, the distance between adjacent longitudinal modes should decrease. The Free Spectral Range, however, shouldl remain the same, as it is characteristic of the Fabry-Perot Etelon.  For our Fabry-Perot interferometer, the FSR was 2 GHz.

The first thing we observe from the Fabry-Perot data is that there are a few transverses mode for each longitudinal mode.  The closely grouped peak-pairs are TEM modes belonging to the same longitudinal mode.  Knowing that one Free Spectral Range was the separation between identical peaks, we observed that the frequency separation between peak pairs matched up with the theoretical separation between longitudinal modes.   For each data sample shown, we give the observed separation between longitudinal peaks and the theoretical prediction.

    Here, we have the cavity fixed at 46.9 cm. First, the unaltered FSR. Then, we used a hair to scatter some of the light and
remove some of the transverse modes. Weaker modes corresponding with smaller peaks can no longer achieve the threshold gain and they do not lase.  The result is three peaks, each corresponding to a longitudinal mode.  Notice that the spectrum appears to be a combination of a Gaussian and a "picket fence," as we predicted in the Theory section.

FREE SPECTRAL RANGE:   2 GHz.

Cavity Length  L= 46.9 cm.  

Frequency separation between modes:

Measured: 325.5 MHz.   Theoretical Prediction:  317.7 MHz.

Doppler width of tallest peak (HWHM):  ~ 60 MHz

Cavity Length L  = 32.9cm.

Frequency separation between modes:

Measured: 427.0 MHz.   Theoretical Prediction: 452.8 MHz.

Cavity Length = 40.5cm

Frequency separation between modes:

Measured: 366.0 MHz.   Theoretical Prediction:  367.9 MHz.

Cavity length = 51.5

Frequency separation between modes:

Measured: 273.7 MHz.   Theoretical Prediction:  289.3 MHz.

Doppler width of tallest peak (HWHM):  ~ 72 MHz.

Cavity Length = 52.3cm

Frequency separation between modes:

Measured: 268.1 MHz.   Theoretical Prediction:  284.9 MHz.

Doppler width of tallest peak (HWHM): ~ 52 MHz

Frequency Separation versus cavity length:

Now we plot the frequency separation between the modes versus cavity length.  The horizontal axis is the cavity length in centimeters, while the vertical axis is frequency separation between modes in MHz.  The separation varies inversely with length. In the first graph, we have the raw data.  In the second graph we compare the raw date with the theoretical line  v=c/2L.  The data matches up nicely with predictions, confirming that the modes (peak-pairs) we observed in the FSR were indeed longitudinal modes.

Power of Output vs. Cavity length

Here we graph ower in Watts / cm^2  versus the length of the entire laser cavity (cm).  You can see that there is a maximum length of the laser cavity.  Beyond this point, no mode is able to achieve threshold resonant gain.  For our laser, the maximum length was 54.2 cm.  The highest intensities we observed were around 2 milliwatts per square centimeter.  This data is rather scattered due to the difficulty of getting a consistent power reading for each length.  Because the intensity of the beam depends so much on the precise alignment of the mirrors, we were able to get a broad range of intensities for each cavity length.  Although we did not know the exact radius of curvature for each of our mirrors, this data indicates that the radius of curvature was about 26 cm.

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