Lasing threshold

The lasing threshold is the lowest excitation level at which a laser's output is dominated by stimulated emission rather than by spontaneous emission. Below the threshold, the laser's output power rises slowly with increasing excitation. Above threshold, the slope of power vs. excitation is orders of magnitude greater. The linewidth of the laser's emission also becomes orders of magnitude smaller above the threshold than it is below. Above the threshold, the laser is said to be lasing. The term "lasing" is a back formation from "laser," which is an acronym, not an agent noun.

The lasing threshold is reached when the optical gain of the laser medium is exactly balanced by the sum of all the losses experienced by light in one round trip of the laser's optical cavity. This can be expressed, assuming steady-state operation, as

Here ${\displaystyle R_{1}}$ and ${\displaystyle R_{2}}$ are the mirror (power) reflectivities, ${\displaystyle l}$ is the length of the gain medium, ${\displaystyle \exp(2g_{\text{threshold}}\,l)}$ is the round-trip threshold power gain, and ${\displaystyle \exp(-2\alpha l)}$ is the round trip power loss. Note that ${\displaystyle \alpha >0}$. This equation separates the losses in a laser into localised losses due to the mirrors, over which the experimenter has control, and distributed losses such as absorption and scattering. The experimenter typically has little control over the distributed losses.

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