Oscillations and Resonance in a Helium-Neon Laser

Description of the Experiment:

   This experiment was used primarily as an introduction to understanding the techniques, functions and apparatus involved in a laser. In the experiment a Melles-Griot laser tube was used to contain a few Torr of Helium and about one tenth of that pressure of Neon inside its quartz plasma discharge tube.  A transformer was used to supply the 2000 Volt potential difference across the tube.  The slightly less reflective mirror allowed a small percentage of the amplified light to pass through it and was positioned outside of the laser tube in order to permit external interference with the amplified light.  The position of the external mirror was also variable and was adjusted to produce different frequencies of amplified light.  A Burleigh-Wavemeter Jr. was used to measure the wavelength of the Helium-Neon laser's output while the Burleigh-Spectrum Analyzer and Photoamp was used to study the mode structure of the output.

Oscillations and Resonance in the Experiment:

    There are examples of resonance not only in the output of the Helium-Neon laser, but in the excitation of the gas particles themselves.  The ground state Helium atoms are excited into the metastable 2S state by free electrons which were accelerated by the 2000 Volt potential difference.  These excited Helium atoms invariably collide with the surrounding ground state Neon atoms which through a resonance effect are excited by the collision into their 3S state.  A population inversion of excited Neon atoms in their 3S state is then created and the resulting lasing transition is finally from Neon's 3S state to its 2P state.  The Neon atoms are then  re-excited into the 3S state by excited Helium atoms, a process which maintains the population inversion.  This excitation is possible because the energy level of the Neon's 3S state is very near that of Helium's 2S state.  The resonant effect that allows the Neon atom to become excited by the Helium atom is quite analogous to the classical understanding of resonance.  Consider the system of two identical tuning forks mounted on separate hollow boxes.  If one of the tuning forks is set into vibration the second one will start to vibrate at the same frequency as it receives the longitudinal sound waves from the first.  This resonant behavior will not occur if the two tuning forks have different natural frequencies of vibration.  The same principle is in effect in the excitation of Neon by excited Helium atoms and is also put to use in many other gas lasers.  If two atoms have approximately the same energy levels for various states, than if one atom is excited, the other may become excited as well through proximity or collision. 

    While this is interesting, the most striking example of resonance in this experiment is found in the output of the Helium-Neon laser.  The output of a gas laser is not perfectly monochromatic because the gas particles have various velocities as they absorb and emit photons.  Due to this Doppler effect, the emission profile of the Helium-Neon laser is not a sharp peak, but actually a Gaussian curve of frequencies.  However, the output is not the continuous distribution of frequencies that the Gaussian curve would suggest.  Only those frequencies that achieve constructive interference in the laser cavity will reach the threshold gain level.  At certain resonating frequencies then the light is reflected inside the laser cavity and forms a standing wave.  The external mirror then passes about 2% of this resonating light, which compromises the output of the laser.  These resonant effects occur at every frequency where v = (m*c) / (2*L), where L is the length between the two mirrors of the laser cavity and m is equal to 1, 2, 3, ....   The difference between these permitted frequencies is then c/2L.  So if the light in the cavity were pure white light, the output spectrum would have evenly spaced spikes separated by delta v =c/2L.  Since the gas emits light with a Gaussian shape and the laser cavity only reflects and passes light with a "picket fence" line shape, the final laser output is a combination of the two.   

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    However, since the laser cavity is not just in one-dimension the output has transverse modes as well as the longitudinal modes described above.  The frequencies of these transverse modes are a function of the width of the laser cavity just like the frequencies of the longitudinal modes are dependent upon the length L, of the laser cavity.  Since the transverse modes are described by Hermitian polynomials, the separation between the transverse modes will not be uniform as in the case of the longitudinal modes.  As it turns out there are various transverse modes for each longitudinal mode, a phenomenon that is observed in the data from the experiment.  The graph on the left of experimental data is not only demonstrative of the Gaussian and picket fence emission profile, but it depicts the transverse modes of each longitudinal mode as well.






It was possible to photograph various modal patterns by placing a fine hair inside the laser cavity to scatter some of the beam.  This interference caused all of the other frequencies except one m value to drop out.  The picture on the left depicts four different longitudinal modes that demonstrate the Gaussian and picket fence emission profile, with each longitudinal mode having two transverse modes.


To conclude, the concept of resonance was involved in both the excitation of the Neon and in the output of the Helium-Neon laser.  While we are discussing resonance on a quantum mechanical level, our understanding of resonance in this system is predominantly classical.  The excitation of Neon by Helium through a collisional transfer of energy is essentially the same process as the resonant vibration of two identical tuning forks.  The determination of the frequencies of the laser's output is also in accordance with the classical understanding of resonance.  The only permitted frequencies of emitted light are those that constructively interfere and create a standing wave inside the laser cavity, much like how a standing wave is created on a string.  Of course, this system is three dimensional and includes transverse waves as well as longitudinal waves, however, we still consider the presence of resonance in our system in a classical, linear sense.