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In this diagram, multiple emission lasing wavelengths are shown. enter image description here

What dictates which wavelength is lased? Is it random? Because this ion can be a four level or 3 level manifold due to the emissions.

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Typically in a Laser in the resonator you have optical filters that will suppress any undesired wavelengths. This is important during the startup phase. When switching the laser on, pretty much all transitions will emit light. But the filter will only allow one wavelength to resonate. Then the induced emission will amplify the emission from the selected transition.

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