Theory Behind the He-Ne Laser


Stimulated Emission

Stimulated emission occurs when an photon passes in close proximity to an atom excited to the energy of that photon (E = hf). When the photon passes, the atom emits another photon that is coherent with the incident photon, meaning that the two photons have same direction and are in phase. To see a red beam (6328 ) from the He-Ne laser, we desire a transition from the neon's 3S state to its 2P state emission.  When and if this emitted photon encounters another excited neon atom, stimulated emission occurs. 

 delE.JPG (3264 bytes)   delE3.JPG (6286 bytes)

This yields 2 coherent 6328 photons--the first bundles of laser light--to stimulate further Ne atoms.

Population Inversion

Obviously, each time an excited atom is stimulated to emit a photon, the population of excited atoms decreases by one. To get a laser beam, there must be a large number of these transitions taking place. Therefore, the key to the laser's action is population inversion: there must be more atoms in the desired excited state than in the state to which the electons transition. In the He-Ne laser, as with many gas lasers, this is accomplished by utilizing metastable states which transition to relatively short intermediate states. The process is as follows:

Across the ends of the laser tube containing the He-Ne gas, is a potential difference of about 2000 volts, which strips electrons off a conductor. Some of these electrons interact with the gas which may yield several possible outcomes.  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 metastable, 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 metastable, 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 escited 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.

Resonance

Once we achieve a population inversion and experience stimulated emissions, there must be some mechanism to increase the gain of the laser output.  Normally, this is accomplished by putting mirrors on the ends of the laser cavity. Photons emitted along the longitudinal axis of the cavity will then reflect back and forth in the cavity stimulating more emissions along this same axis.   Eventually, the gain will reach a threshold, and the gas will 'lase.'  Mirrors usually reflect about 95-99% of incident light (thus the light in the cavity is about 100 times more intense than the output).  The mirrors may be coated so that they reflect only desirable radiation. 

Output

       Though energy is quantized in electron transitions, Laser light is not truly monochromatic as one might expect.  Even if we suppress undesirable transitions (such as the 3.339 um and 1.15 um IR transitions in the He-Ne), the laser output will still not be truly monochromatic.  The primary reason for this is the phenomenon of Doppler spreading.  When we drive quickly down the street while obnoxiously blaring our car horn, the horn sounds higher pitched to a person in front of the car than it does to a person behind the car.  A similar thing happens when the source and observer of light are moving relative to each other.  If an observer moves away from a light source at v<<c, the frequency (f'') of the incoming light appears to be shifted from the expected frequency (f) according to the relation    f'' = f (1-v/c).  (This is why the spectral lines of stars moving relative to earth are either "red shifted" or "blue shifted".)   As a result, atoms at different velocities will absorb and emit photons of slightly different frequencies from the same energy line.  In a gas, atoms have a broad range of velocities, so the output peaks of a gas laser will be broadened.  We might expect the emision profile to be a sharp peak, but due to Doppler broadening it is actually Gaussian.

Gaussian.JPG (6730 bytes)

    Although the gas emits radiation that has a Gaussian lineshape, the laser cavity does not permit a continuous spread of frequencies to resonate.  Only those frequencies that achieve constructive interference in the resonator will reach the threshold gain level.  When constructive interference occurs, the length of the laser cavity will be an integral number of half-wavelengths of the resonating frequency:    L = m*wavelenth/2, where m = 1,2,3,....  We can rearrange and substitute terms to see that the permitted frequencies are v = m*c/2L.  The difference between adjacent permitted frequencies is delta v =c/2L.  If the light in the cavity were pure white light, the out put spectrum would have evenly spaced spikes separated by delta v =c/2L.  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" lineshape, the output is like 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.

Equipment

    The primary instrument we used to study the He-Ne laser was the scanning Fabry-Perot interferometer.  Like the laser cavity, the Fabry-Perot interferometer consists of 2 confocal mirrors separated by distance L.  The mirrors have a reflection coefficient of about 98%.  When an incident beam satisfies the constructive interference condition (v = mc/2L), the light resonates in the cavity.   As the intensity builds up inside the cavity the output beam builds up to nearly the intensity of the input beam.  Thus, frequencies that resonate in the cavity are passed through with little attenuation while non-resonant frequencies are eliminated.

 

 

References:

Allen, L.  Essentials of Lasers  New York:   Pergamon Press,  1969.

Allen, L and D. G. C. Jones.  Principles of Gas Lasers    London:  Butterworths, 1967.

Davis, Christopher C.  Lasers and Electro-Optics  Cambridge: Cambridge University Press,  1996.

Eberly, Joseph H. and Peter W. Milonni.  Lasers   New York: John Wiley & Sons,  1988.

Siegman, Anthony E.  Lasers  Mill Calley, California:  University Science Books,  1986.


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