Joseph Berg

Luwa Matthews

Modern Physics II: Laboratory Experiment I

Monday, April 12, 2010

Semi-periodic Behavior of Intensity and other Physical Properties of the He-Ne Laser

Abstract:

In this experiment, properties of the He-Ne laser such as the wavelengths of light from the anterior and side of the tube, polarization, dispersion of the laser beam, and the semi-periodic behavior of the intensity due to thermal expansion of the tube were all examined. The wavelength of the laser beam was determined to be 632.96nm, and the wavelength of major spectra lines from the side of the tube were found to be 640.5±0.03nm, 587.7±0.03nm, 614.7±0.03nm, and 610.1±0.03nm, and the dispersion was calculated to be 0.04o. The semi-periodic behavior of intensity of the laser was found to be due to the thermal expansion of the glass tube of the He-Ne Laser apparatus.

Experimental Procedure:

Angle of divergence:

To calculate the angle of divergence, the diameter of the laser point was measured using calipers at various distances from the laser apparatus. The angle of divergence was then evaluated by taking the inverse tangent of the slope of the graph of diameter against distance. This is illustrated in figure 1. The slope was 0.0012 and so the angle of divergence was calculated to be 0.039 o. Although all photons emitted are in phase with one another, the divergence of the laser beam is due to the photons’ diffraction about the atoms in the air.

Spectrum of the Light Emitted:

To measure the wavelengths of the light emitted from the sides of the laser tube, a spectrometer of detection range 600-750nm was placed at the sides of the tube. The most prominent wavelengths, that is, the ones with the highest intensities, were found to be 640.5±0.03nm, 587.7±0.03nm, 614.7±0.03nm, and 610.1±0.03nm, arranged in order of prominence. See figure 2 and 3. The uncertainty in the wavelengths reported was given by the manufacturer’s manual.

In order to find the wavelength of the laser beam the spectrometer was kept at a distance of about 2.5m from the laser apparatus. A wavelength of 632.96nm was recorded.

Brewster’s Window:

The Brewster’s window is a lens placed at the anterior of the laser apparatus. Set at an angle, its function is to allow light of a certain plane of polarization through and prevent some or all of the light in planes not perpendicular to the first plane.

When the Brewster’s window was removed, the intensity of the light was found to be higher than when it was on.

Polarization:

The laser was tested for polarization by placing a polarizer in front of the beam. On turning the polarizer through different angles, there were very visible changes in the intensity of the beam.

Semi-periodic Behavior of the Laser’s Intensity:

When taking measurements to determine the manner of polarization of the laser, periodic motion of the intensity was observed on graph of intensity versus time. This was initially thought to be evidence of circular polarization of the laser beam. But it was found that as time went on, the length of the periodic cycles of the intensity gradually increased, and an encasing semi-sinusoidal pattern, which also dwindled with time, was observed with the amplitude. See figure 4.

Upon further observation, it was found that the dwindling of the semi-periodic behavior of intensity correlated with the stabilization of the temperature of the laser tube in time (the temperature of the tube increased initially and stabilized with time). All periodic behavior was found to nearly completely fade when the temperature stabilized.

To confirm the hypothesis that this phenomenon was not simply a correlation but was actually causation by temperature, a series of tests with controlled temperature were carried out. First, the apparatus started at room temperature and a fan was put on it to slow the rise in temperature. Later in the experiment, the fan was put off, and a heat lamp was applied to the apparatus.

Initially, when the fan was applied, the lengths of the intensity cycles were relatively long eventually stabilized as the temperature stabilized as well. But when the fan was removed, periodic behavior of the intensity resumed with short wavelengths as the temperature sharply increased. Again, the temperature, and correspondingly, the periodicity in intensity were allowed to stabilize with time. Once stabilized, external heat was applied to the apparatus to resume temperature increase. And as temperature increased, the periodicity of the intensity resumed once more (the cycles were even more frequent because the temperature increased sharply). To avoid overheating the apparatus, the temperature was not allowed to reach equilibrium. See figure 4. The results of these tests vindicate the validity of this hypothesis.

The mechanism of the phenomenon in discussion is related to the thermal expansion of the laser tube. For maximum intensity, there needs to be a standing wave within the tube. Hence, every peak in the intensity cycle corresponds to a change of one half-wavelength in the tube. As the temperature changes more rapidly, the length of the tube changes proportionately and goes through more frequent changes in half-wavelengths. This explains why steeper changes in temperature

corresponds to more frequent intensity cycles. And when the temperature increases more slowly, the reverse is the case.

To verify this hypothesis quantitatively, the overall change in temperature of the tube and the corresponding number of intensity cycles (that is, the number of half wavelengths the tubes expanded through) were measured in an experiment. Using this information, the wavelength of the laser, and length of the tube, the coefficient of thermal expansion of the tube was calculated. This coefficient was found to be within the range of what is expected for glass, which is 4.0 – 5.9 m/mK [1]. This shows that thermal expansion and contraction of glass through half-wavelengths of light is responsible for the periodic behavior of the laser’s intensity.

Number of half wavelengths during temperature change (N) = 20

ΔT=12.863K

Length of tube (L) = 0.203m

Wavelength of laser (λ) = 680*10-9m

Coefficient of thermal expansion = N λLΔT

= 5.208*10-6 m/m/K

Conclusions:

The wavelength of the laser beam was determined to be 632.96nm. The wavelength of major spectra lines from the side of the tube were found to be 640.5nm,

587.7nm, 614.7nm, and 610.1nm The dispersion was calculated to be 0.039o

The semi-periodic behavior of intensity of the laser was found to be due to the thermal expansion of the glass tube of the He-Ne Laser apparatus through half-wavelengths of light.

The laser beam was found to be polarized.

References:

[1] Coefficient of Linear Expansion of Materials. Web. <http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html>.