= Solution
A <laser> combines pumping, an amplifying medium and optical feedback. <Stimulated emission> adds photons to an occupied optical mode; net amplification requires <population inversion> between the relevant levels after accounting for their degeneracies. Pumping through additional levels and rapid lower-level relaxation can sustain inversion; a closed <two-level system> under steady incoherent resonant pumping cannot sustain it.
An <optical resonator> selects modes and feeds light back through the gain medium. For intensity gain coefficient $g$, internal intensity loss $\alpha_i$, length $L$ and mirror intensity reflectivities $R_1,R_2$, the <round-trip laser threshold condition> is
$$
\boxed{R_1R_2e^{2(g-\alpha_i)L}=1,\qquad g_{\rm th}=\alpha_i+\frac1{2L}\log\frac1{R_1R_2}.}
$$
Above threshold, saturation limits gain and a partially transmitting mirror provides output. Typical properties are strong directionality, substantial coherence and narrow bandwidth; multiple modes and pulsed operation are possible, so perfect monochromaticity is not universal.<Fundamentals of Photonics and Quantum Electronics lecture notes by Franz X. Kärtner>[Chapter7,§§7.1–7.2 and <laser threshold>: feedback, gain and level schemes]{ref}
\Image[/past-exam-of-the-advanced-quantum-physics-course-of-the-university-of-cambridge/2014/paper-1-aqp2014-laser-principle.png]
{title=Pumping sustains gain while a resonator supplies feedback and output coupling}
{source=paper-1-aqp2014-laser-principle.py}
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