We discuss intrinsic relaxation rates in superconductors, and how they may be measured using nonlinear optical (terahertz) response. We consider both $s$- and $d$-wave superconductors, with and without a phenomenological (energy-dependent) damping. Intrinsic relaxation rates of interest include the Higgs mode decay rate, the quasiparticle redistribution rate ($1/T_1$), and the quasiparticle dephasing rate ($1/T_2$), where the latter two rates are zero in the pure BCS model, but nonzero in the presence of damping. Using the Anderson pseudospin formalism, we illustrate how these intrinsic relaxation rates are related to measurable quantities such as the time-dependent gap function and the nonlinear current (also known as third-harmonic generation). Hence, we show how intrinsic relaxation rates may be experimentally extracted and discuss what one may thereby learn about the underlying damping. We also discuss the effects of polarization control (i.e., nonlinear response to light polarized in different directions), which offers a useful experimental knob, especially for $d$-wave superconductors, enabling selective excitation of modes in different irreducible representations (and the readout of their corresponding relaxation rates).

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• Lifetimes & widths
• Nonlinear optics
• Superconducting gap
• Superconductors