Many Oscillators with Frequency Distribution

Formally, this is a simple generalization of case (b) by changing the number of oscillators from 2 to N. Let the system be described by 

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The carbon monoxide laser normally operates at roughly twice the frequency of the CO2-laser. However, it can oscillate on several hundred lines between 4.8 and 8.4 jim [1,23]. This is due to the fact that many different vibrational levels in the deep, enharmonic potential curve of CO can be the starting point for laser emission. Under CW-condition, v=3= 2 up to v=37= 36-bands can be obtained and the frequency shift between adjacent bands is due to the anharmonicity of the CO-potential. The inversion mechanism is not as straightforward as in the CO2-laser. Usually no complete inversion for adjacent vibrational levels can be obtained and therefore only P-branch transitions do occur. Nevertheless, the wavelength region is completely covered with the rotational distribution of the vibrational bands (Fig.1.13). 

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