If an electron is in an excited state, it can drop down to a lower energy state and release a photon. This usually happens on its own (spontaneous emission), and is the principle behind fluorescent lamps, white Leds and so on.
However, it it can also be triggered by another photon, even if that photon is not absorbed. The photon is a disturbance in the electromagnetic field and it cam disturb the electrically charged electron enough to trigger a drop in energy level. This is called stimulated emission. Interestingly, in stimulated emission, the emitted photon gets synchronised with the incoming photon.
You don’t normally see much stimulated emission. That is because it is rare for electrons to be in an excited state. In most cases, if you do get a stimulated photon emitted, the chances are it will hit a ground state atom, and get absorbed again.
In a laser, the trick is to pump up the gain medium, so that the majority of electrons are excited, and it is rare to have electrons at ground state. This is called population inversion. In this context, the stimulated emission results in the amplification of light in the medium.
Pumping the laser medium was historically done with exceedingly bright light, using flash lamps similar to a professional photo flash. However, this is not the only way and it can be done with electrical current in semiconductor lasers or gas lasers.
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