Why does a Photon interacting with an Excited Electron cause Stimulated Emission?

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Why does a Photon interacting with an Excited Electron cause Stimulated Emission?

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In broad terms, the photon interacts with the electron and is absorbed, imparting energy. The electron is not in a stable state anymore, so it tries to find a more stable state with lower energy, and that energy is emitted as another photon. The emission, therefore, was stimulated.

This has practical use in a laser (which is an acronym for Light Amplification by Stimulated Emission of Radiation). These rely on molecules with multiple states for the electrons, and the energy differences in those states determine the frequency of the laser beam. Label the electron states, from lowest energy upwards, as 1, 2, 3. If the electron was at zero temperature, it would always be in state 1. But at any higher temperature, some of them would be thermally excited to other states. If you stimulate the electrons with photons that resonate with the state 2 to state 3 transition, the electrons will no longer be in thermal equilibrium. This causes some to decay to state 1, and the state 3 to state 1 transition will produce the output beam, once it builds up as the dominant output. State 2 is repopulated by thermal interactions.