How a Laser Lases

Stimulated Emission

When a photon passes very close to an atom excited to the energy of that photon (E = hv), the atom emits another photon that is coherent with the incident photon.  The two photons have exactly the same direction and are in phase.  This phenomenon is called stimulated emission. 

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

A transition from neon's 3S state to the 2P state produces a 632.8 nm photon (visibly red).  If this emitted photon encounters another Ne atom in the 3S state, stimulated emission occurs.  These two photons may then encounter more 3S Ne atoms, producing further stimulated emissions.  It is easy to see how this cascading process could produce a beam of visible red light.

Population Inversion

Each time an excited atom is stimulated to emit a photon, the population of excited atoms decreases by one. To get a laser beam, these transitions must be taking place continuously and in large numbers. The key to the laser's action is population inversion, or maintaining more Ne atoms in the desired 3S excited state than in the 2P state.  This is where the helium inside our laser comes into play.  Using a metastable state of the helium, the laser keeps up a steady supply of excited neon atoms. 

A potential difference of about 2000 Volts, which strips electrons off a conductor, is placed across the ends of the laser tube containing the He-Ne gas. Some of these electrons interact with the gas, yielding several possible outcomes.  Of importance to us, the electron may excite a ground-state helium atom to its 21S state, a metastable state.  Some of the excited He atoms will collide  with ground-state Ne atoms. The collision will excite Ne to its 3S state because of a resonance effect, since neon's 3S state has an energy very close to that of the 21S state in helium.  As noted earlier, this is the necessary initial state for production of the 632.8 nm emission.  Since helium's 21S state is metastable, a He atom in this state will remain in said state until a collision with a Ne atom occurs. 

A Ne atom excited to the 3S state may undergo a transition to its ground state and emit a photon of a wavelength other than our desired 632.8 nm. Since our laser tube is at a high pressure the Ne atoms undergo radiative trapping; 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.

Resonance

Stimulated emissions cultivated due to a population inversion alone do not produce a suitably cohesive laser beam.  To increase the gain, mirrors are placed at each end of the laser cavity.  Photons emitted along the straight line between the mirrors will bounce back and forth between them, causing more and more stimulated emissions, increasing until the threshold of emissions for our population inversion is reached.  This condition is called lasing.  The mirrors often have a slight concavity so that photons that are not precisely along the straight line will continue to reflect as well.  One mirror is not completely reflective, only 95% to 99% reflective.  The light that passes through this mirror is the projected laser beam.

Output

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 a monochromatic 632.8 nm beam.  The primary reason behind this impurity is Doppler spreading.  If an observer moves away from a light source at a high velocity (v), the frequency (f'') of the incoming light will appear shifted from the expected frequency (f), the frequency of the light in the source's reference frame, according to the relativistic relationship: f''=f(1-v/c).  Simply put, atoms at different velocities will absorb and emit photons of slightly different frequencies.  In a gas, atoms have a broad range of velocities, so the output peaks of a gas laser will be broad.  Instead of emitting light at strictly 632.8 nm, our laser emits light in a Gaussian distribution centered on 632.8 nm (where the intensity is maximized).

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The geometry of the laser cavity causes interference between different frequencies of light.  Constructive interference only occurs at specific wavelengths (modes) related proportionally to the length of the cavity (L).  L=m(wavelength)/2 where m=1,2,3...  Converting this relationship to the terminology we have been using, we have only specific permitted frequencies where v=m(c/2L).  So, the frequency separation between two adjacent modal frequencies will always be delta v=c/2L.  This phenomenon produces a "picket fence" output.

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The He-Ne gas in the laser tube is producing a Gausian, and the geometry of the laser cavity restricts the output to a "picket fence," so the actual output beam should appear to be a combination of both forms.     

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Our representation thus far has been one-dimensional, but our real-world laser is not.  As well as the longitudinal modes we have been discussing, there will be transverse modes due to the shape and size of the cavity mirrors.  The separation between these modes will not be such a simple distribution as our "picket fence."  The transverse modes are solved using Hermite polynomials, as shown below.

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There will be an associated longitudinal mode for each transverse mode and visa versa.

 

All illustrations on this page were created by Jim Nolen and Seth Carpenter.

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.

Kallard, T. Exploring Laser Light  Stony Brook NY: American Association of Physics Teachers, 1982. (Reprinted with permission from Optosonic Press 1977)

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