The Helium-Neon Laser

Helium-Neon Lasers are available in a variety of sizes and shapes.  Though highly inefficient (~ 0.01 - 0.1%), they are relatively inexpensive and available for laboratory use.  The images below are of the He-Ne lasers that were used in laboratory projects.

He-He1'.jpg (20437 bytes) This is the He-Ne laser that my lab partner, Jim Nolen and I used in our Laser Lab.  Having the Mirror 2 separate from the tube allowed us to observe modal patterns of the laser's output.  The He-Ne gas of a few torr of  Helium and about one tenth that of Neon is contained in a quartz plasma tube.  Across this tube is a 2000 V potential difference.  This potential difference pulls electrons off a conductor.  Some of these electrons interact with the gas which may yield several possible outcomes which I will discuss momentarily. 

He-He2'.jpg (17415 bytes)

He-He3.jpg (9448 bytes) These are two further examples of He-Ne lasers, allowing one to see the laser is made with several designs.

As, I began to previously mention, the electrons accelerated through the plasma tube may interact with the gas.  In many cases, the electron will excite a ground-state helium atom to its 21S state.  Due to selection rules for electron transitions, this state is meta-stable, which is not only handy, but necessary for a population inversion to occur (click here to see an energy-level diagram of what's going on).  Now, some of these excited He atoms will come into contact via a collision with a ground-state neon atom. Because neon's 3S state is at an energy very close to that of the 21S state in helium, through a resonance effect, the collision will excite Ne to its 3S state.  It is from this state that the desired 6328 emission can occur.  Because helium's 21S state is meta-stable, there is an increased probability that it will encounter and excite a neon atom. 

A Neon atom excited to this 3S state may transition to ground and emit a photon. At sufficiently high pressures in the laser cavity, however, the neon atoms may undergo radiative trapping, whereby emitted photons are quickly reabsorbed by other neon atoms. So even if this excited state does decay, the photon will probably be absorbed again soon and the net result will be no change in the excited population. The Neon atoms 2p state will decay very rapidly to the 1s state. So, while electrons spend a "long time" in the 3s state due to radiative trapping, electrons spend a very short time in the 2p state because the jump down to the 1s state very quickly. This sets up a population inversion: higher population of atoms in the 3s than in the 2p. So, when stimulated emission occurs, those photons will likely find another excited atom to stimulate. Losses due to stimulation and random transitions will be counterbalanced by this population inversion.

He-Ne's Output

There is one dominant energy level transition (the one that emits the 632.8 nm emission) which is amplified in the He-Ne and we know that these transitions occur between quantized levels.  The He-Ne's output, however, is not monochromatic as might be expected.  Doppler spreading around the desired wavelength is responsible for this.  In any intro. physics text book, one can find that when an observer moves away from a light source, the frequency observed, f ', is shifted from the expected frequency, f, by the relation f'' = f (1-v/c).  Therefore, in the He-Ne gas, atoms moving at different velocities will absorb and emit photons of frequencies shifted slightly from the expected.  Thus, the output is not the expected peak in the emission profile, but actually a Gaussian  (thanks to Jim Nolen for the following sketches).

Gaussian.JPG (6730 bytes)

So, we can see that the gas has the potential to emit frequencies within that Gaussian emission profile.  This is not the case - there is not a continuous range of frequencies that can be emitted as determined by the shape/size of the cavity.  Only those frequencies that interfere constructively will reach the threshold gain level.  For this to happen, the length of the laser cavity is an integer multiple of half-wavelengths emitted.  If the light in the cavity were white light, the emission profile would show evenly-spaced spikes separated by c/2L (L = length of cavity).  It is said to look like a "picket fence."

fence.JPG (9492 bytes)

Since the gas emits light with a Gaussian line shape and the cavity permits light with a "picket fence" line-shape, the output is a combination of the two:     

 combo.JPG (8045 bytes)

The laser cavity, however, is not just one dimension.  As a result, the output includes both longitudinal modes and transverse modes (TEM modes).    The transverse modes are determined primarily by the size and curvature of the mirrors.  They are akin to TEM modes on a waveguide, yet their solutions include Hermitian polynomials and a Gaussian function and should look something like this:

H2.txtgr3.gif (1920 bytes)

For each transverse mode, there will be an associated longitudinal mode and visa versa.   Nevertheless, the frequency separation between adjacent transverse modes will not be uniform as with the longitudinal modes.

So, perhaps you would like to be able to visualize some of these modes:

See some actual data with corresponding Mathematica modeling
Check out an applet created by Jim Nolen which can demonstrate such patterns

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