The Carbon Dioxide Laser

CO2.jpg (28328 bytes)

the laser Jim Nolen and Derek Kverno used in their CO2 Laser Lab

Whereas the He-Ne demonstrates an efficiency of ~ 0.01 - 0.1 %, the CO2 Laser operates with an efficiency of up to 30 %.  Continuous power levels of a few kilowatts are possible yields from a moderately-sized laser.  Thus this laser has applications in industry for cutting metals and welding.

As with all lasers, in order to operate, there must be a population inversion within the lasing medium.  Resonant scattering from excited nitrogen atoms causes the upper levels in the CO2 molecules to become populated.  The gas mixture composing a glow-discharge system consists of helium, nitrogen gas, and carbon dioxide.  A total pressure of 6-15 torr is made of   10-15% CO2 and 10-20% N2.

Of major significance to the CO2 Laser is the quantization of vibrational and rotational states of the CO2 molecule, in addition to electronic energy levels.  The CO2 molecule is a tri-atomic molecule consisting of 2 oxygen atoms covalently bonded to a central carbon atom.  The molecule has 2 stretching vibrational modes, labeled v1 and v3 and a bending mode, v2l.   l is the quantum number for vibrational angular momentum.  v1 is the number associated with the symmetrical stretching of the molecule.  v2 is that associated with bending and v3 with asymmetrical stretching (thanks to Derek Kverno for the following representation of vibrational modes).

dk-vibration.jpg (20313 bytes)

In the CO2 molecule, the individual atoms are bound by a force which acts much like that of the force due to a spring - a harmonic oscillator.  Molecules vibrate due to their lacking fixed orientations within the molecule (as seen above).  They are able to rotate and spin because they are in a gaseous state.  These states, as in electronic states, are quantized.   Transitions between vibrational energy states/levels results in photon emission in the infrared, while transitions between rotational states emit photons in the microwave region. 

Necessary mechanisms for operation of the CO2 laser, as listed by Weber (318) are:

1. Excitation of N2 vibration by electron impact
2. Transfer of vibrational energy from N2 to the nearly resonant v3 mode of CO2
3. Laser transition from v3 to v1 mode.
4. Sharing of population between  v1 and 2v2l modes and relaxation within the v2 manifold
5. The vibrational energy in the v2 manifold converted into translational energy by collisions with He

For CO2, even values of v2 and v3 along with l = 0, are symmetric.   If v3 is odd, v2 is even, and l = 0, the vibrations are asymmetric.  So, the state 00l1 (written as v1, v2l, v3) is composed of only odd-spin particles.   1000 and 0200 states, however, have only even-spin members.  Members of the same vibrational state are distributed amongst available energy levels as determined by Boltzmann statistics and are in thermal equilibrium.

An 18,000 V potential difference across the plasma causes electron collisions with N2 which excites these molecules to their lowest state.  The energy of this state is very close to the 0001 and 0002 levels in CO2 (the n=1 state of N2 excites the 0001state of CO2 and the n=2 state of N2 excites the 0002 state of CO2).   In turn, this energy is  transferred to the CO2 molecules and results in populating their upper levels. This occurs because the restoring force constant (the k, spring constant) of N2 is almost identical as that of the CO2 molecule.  The helium's presence in the gas is largely to maintain the plasma discharge, but also helps to depopulate the lower energy levels.

The following is a diagram representing some of the energy states of the CO2 molecule (thanks to Jim Nolen for this one).

jn-co2energy.jpg (15586 bytes)

0001 to 1000 and 0001 to 0200 are the most important energy level transitions allowing emissions of 10.4 um and 9.4 um respectively.   The 1000 and 0200 vibrational levels depopulate quickly.  As was earlier stated, He is not only present to maintain the plasma, but also as a depopulation mechanism.  When in one of these lower energy levels, a collision between CO2 and He atoms results in a transfer of the energy to the He atom.  The infrared transitions are relatively slower than this depopulation, thus a population inversion is the result.

Each of the vibrational modes of CO2 has an associated characteristic frequency of vibration (w) along with (as can be seen above) allowed energy levels.  These vibrational energy levels can be approximated by the quantum mechanical simple harmonic oscillator hb= h/(2pi)):

Ev=hbw0*(v+1/2), where w0 is the classical vibration frequency
w0= (k/u)^1/2

Though the modes are slightly inharmonic, the vibrational energy of CO2 can be closely approximated by:

E(n1, n2, n3) = hcw1 (n1+1/2) + hcw2 (n2+1/2) + hcw3 (n3+1/2)

In considering the rotational energy of CO2, visualize the molecule rotating about it's center of mass (the carbon atom):

dk-rotation.jpg (6821 bytes) by Derek Kverno

The rotational energy spectrum of CO2 has the same character as that for diatomic molecules and the rotational energy levels are thus approximated by:  

EJ = hcBeJ(J+1),   J = 0, 1, 2, 3, ...           

wpe32.jpg (2886 bytes)    

  where the rotational constant Be for the CO2 molecule is Be = .39 cm-1. The difference between energy levels is:

wpe31.jpg (1408 bytes)

As was previously mentioned, CO2 may be in a particular vibrational mode, but also in a rotational state.  The photon resulting from a transition has angular momentum which must be conserved.  Because of this, molecules in a particular vibrational and rotational state may transition between states only if the change in J is +1 or -1.  If the transition results in J changing by +1, the transitions are said to belong to the 'P' branch.  If J changes by -1, the transitions belong to the 'R' branch.  This results in a branched structure in the emission spectrum.

Thank to Jim and Derek for this discussion:  If the energy difference between the lowest (001) state and the lowest (100) state is E0, then the energy of the transition between the J=7 (001) state and the J=6 (100) state will be of energy:

wpe6.jpg (3189 bytes)

Likewise, transitions where the change in J is +1, the energy released will be:

wpe7.jpg (1831 bytes)

co2transition.jpg (2877 bytes)From this, there exists the possibility of transitions with energy just greater than Eo and with energy just less than Eo. Thus, there is the previously mentioned branching in the emission spectrum.  As an example of notation used, R(6) refers to the transition from the J=7 rotational state of the (001) vibrational mode to the J=6 state of the (100) mode.

The laser emission demonstrates two distinct bands, each having P and R branches.  These correspond to the series of transitions from the (001) to the (100) and from the (001) to the (020) vibrational modes.  Because the difference between adjacent rotational levels increases as J increases, the separation between emission lines in the P and R branch will increase as well.  The branches will be centered around frequency v0 (corresponding to E0).

Check out Derek Kverno's and Jim Nolen's Data page from their work with a CO2.


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References:

Eastham, Derek.  Atomic Physics of Lasers.  Philadelphia: Taylor and Francis, 1986.

Nolen, Jim and Derek Kverno used in their CO2 Laser Lab

Weber, Marvin J.  Handbook of Laser Science and Technology.  Volume II - Gas Lasers.  Boca Raton: CRC Press, Inc., 1982.