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The discovery of superconductivity at 203K in SH$_3$ is an important steptoward higher values of $T_c$. Predictions based on state-of-the-art DFT forthe electronic structure, including one preceding experimental confirmation,showed the mechanism to be the electron-phonon interaction. This was confirmedin optical spectroscopy measurements. For photon energies between $\sim 450$and 600 meV in SH$_3$, the reflectance in the superconducting state is belowthat in its normal state. This difference decreases as $T$ approaches $T_c$.Decreasing absorption with increasing $T$ is opposite to what is expected inordinary metals. Such an anomalous behavior can be traced back to the energydependence of the superconducting density of states which is highly peaked atthe energy gap value $\Delta$ but decays back to the constant normal statevalue as energy is increased, on a scale of a few $\Delta$, or by increasing$T$ towards $T=T_c$. The process of phonon-assisted optical absorption isencoded with a knowledge of the $T$-dependence of $\Delta$, the order parameterof the superconducting state. Should the energy of the phonon involved be verylarge, of order 200 meV or more, this process offers the possibility ofobserving the closing of the superconducting order parameter with $T$ atcorrespondingly very large energies. The very recent experimental observationof a $T_c\simeq 250$ K in LaH$_{10}$ has further heightened interest in thehydrides. We compare the relevant phonon structure seen in optics with relatedfeatures in the real and imaginary part of the frequency dependent gap,quasiparticle density of states, reflectance, absorption, and opticalscattering rate. The phonon structures all carry information on the $T_c$ valueand the $T$-dependence of the order parameter, and can be used to confirm thatthe mechanism involved in superconductivity is the electron-phonon interaction.

Spectroscopic signatures of phonons in high pressure superconducting hydrides