Consider a borad-spectrum light source with central wavelength and wavelength range , incident on a Fabry–Pérot cavity containing water vapour. Let us calculate the conditions for lasing to occur in a manner analogous to astrophysical masers.
Microwave emission, at least in gases, are most commonly due to rotational transitions. This can be modelled through the quantum rigid rotor, where the Hamiltonian is given by:
Where is the moment of inertia of the molecule. One may find that a rotational transition yields energy levels given by:
The selection rules for rotational transitions indicate that transitions may only occur between two levels of , that is, between adjacent energy levels. By the Boltzmann distribution, the population of the higher energy level versus the ground state is related by:
For lasing to occur, there must be a population inversion in the gas, which requires that . The difficulty is to create and sustain this population inversion. One method of creating the population inversion is to bring the gas to a high temperature with some energy source, also called a pump source. If, however, the gas is confined within a (metal) cavity tuned to the transition frequency of the rotational transition, then the microwave-wavelength photons will be re-absorbed and re-emitted as they travel back and forth through the cavity, resulting in lasing (in theory).
The issue is that unfortunately, known astrophysical lasers have optical path lengths of around 4 stellar radii1, which, for the Sun, is about 2. For a Fabry-Perot cavity of about a meter is size, this corresponds to somehow making the cavity well enough for the average photon to undergo several billion reflections before exiting the cavity. This is clearly absurd. Therefore, we conclude, that replicating natural astrophysical masers is not possible.