Terahertz Physics by R. A. Lewis

Author:R. A. Lewis
Language: eng
Format: epub
Publisher: Cambridge University Press

Figure 7.5 Key vibrations of the CO2 molecule.

These photon frequencies correspond to photon wavelengths of about 10 μm and 9 μm, respectively. From either the symmetric stretching or the second bending state, the system may lose further energy to end up at the first bending state of 20.0 THz frequency; from there it will readily return to the ground state.

The lasing action depends on population inversion. Normally, the lower states have a greater population than the higher states. If a higher state is occupied more than a lower state, population inversion is said to have occurred. Population inversion occurs in the CO2 laser because the upper state is rather long-lived relative to the lower states.

Rotations, as well as vibrations, play a role in the operation of the CO2 laser. We refer to rotational-vibrational or ro-vibrational transitions. So far, we have only been considering the vibrations of the CO2 molecule. If the molecule spins, then this introduces additional quantum states. The energy of the rotations is much less than the energy of the vibrational states. In this sense the rotations are a detail we have neglected so far in giving the ‘big picture’ of the operation of the CO2 laser. Figure 7.6 shows the detail of the rotational structure added on top of the vibrational structure of the CO2 molecule.

The rotational states are evenly spaced in frequency and labelled by a quantum number, usually denoted J. From details of quantum mechanics that I won’t go into, the rotational states associated with the upper level take on only the odd values J = 1, 3, 5 … ; for the lower states, the values of J are even, J = 0, 2, 4 … . Again, for reasons I won’t go into, in changing from one rotational-vibrational state to another, the value of J must go up or down by one. So starting with J = 1, the molecule might finish up with J = 0 or J = 2. The transition to the higher frequency state is labelled ‘P’ and the transition to the lower frequency state is labelled ‘R’. The J-value of the final state is given in parentheses at the end of the label. Transitions to the symmetric stretching state, of wavelength about 10 μm, are labelled ‘10’. Transitions to the bending state, of wavelength about 9 μm, are labelled ‘9’. For example, a transition starting at J = 3 and finishing at J = 2 in the symmetric stretching state is conventionally labelled ‘10R(2)’. Three other examples are given in Figure 7.6.

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