= Solution
A <laser relaxation oscillation> is the damped exchange between stored upper-level excitation and intracavity <photon number> after a small perturbation of a lasing <steady state>. Extra <photons> increase stimulated depletion of the upper level; the resulting smaller gain then reduces the <photon> population. Pumping subsequently replenishes the inversion, so the two populations overshoot their equilibrium values before damping settles them.
<Laser spiking> is the corresponding large-signal sequence of intense output pulses, often during switch-on. Excitation first accumulates while the optical field is small. Once gain exceeds loss, rapid <stimulated emission> releases this stored <energy> in a spike, depleting the inversion below threshold. Recovery can produce further spikes. This is distinct from an externally imposed <Q-switching>[Q-switching] cycle, although both draw on stored excitation.
Many solid-state gain media have upper-state lifetimes far longer than the cavity <photon lifetime>. The optical <polarization> relaxes rapidly, leaving the two slow <Laser rate equation>[rate-equation] variables of a class-B <laser>. A long-lived population reservoir and a much faster <photon> response make underdamped recovery and pronounced startup spiking common. The criterion and <frequency> follow from the <Linearization of a dynamical system>[linearization] in part c; they are not universal consequences of the word “solid-state”.
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