The expression for the magnetooptical absorption of a polaron is:
Here,  is the cyclotron frequency for a rigid-band electron. The magnetooptical absorption Γ(Ω) at the frequency Ω takes the form Σ(Ω) is the so-called "memory function", which describes the dynamics of the polaron. Σ(Ω) depends also on α, β and .
In the absence of an external magnetic field () the optical absorption spectrum (3) of the polaron at weak coupling is determined by the absorption of radiation energy, which is reemitted in the form of LO phonons. At larger coupling, , the polaron can undergo transitions toward a relatively stable internal excited state called the "relaxed excited state" (RES) (see Fig. 2). The RES peak in the spectrum also has a phonon sideband, which is related to a Franck–Condon-type transition.
A comparison of the DSG results  with the optical conductivity spectra given by approximation-free numerical  and approximate analytical approaches is given in ref.
Calculations of the optical conductivity for the Fröhlich polaron performed within the Diagrammatic Quantum Monte Carlo method, see Fig. 3, fully confirm the results of the path-integral variational approach at  In the intermediate coupling regime  the low-energy behavior and the position of the maximum of the optical conductivity spectrum of ref. follow well the prediction of Devreese. There are the following qualitative differences between the two approaches in the intermediate and strong coupling regime: in ref., the dominant peak broadens and the second peak does not develop, giving instead rise to a flat shoulder in the optical conductivity spectrum at . This behavior can be attributed to the optical processes with participation of two or more phonons. The nature of the excited states of a polaron needs further study.
The application of a sufficiently strong external magnetic field allows one to satisfy the resonance condition , which {(for )} determines the polaron cyclotron resonance frequency. From this condition also the polaron cyclotron mass can be derived. Using the most accurate theoretical polaron models to evaluate , the experimental cyclotron data can be well accounted for.
Evidence for the polaron character of charge carriers in AgBr and AgCl was obtained through high-precision cyclotron resonance experiments in external magnetic fields up to 16 T. The all-coupling magneto-absorption calculated in ref., leads to the best quantitative agreement between theory and experiment for AgBr and AgCl. This quantitative interpretation of the cyclotron resonance experiment in AgBr and
AgCl by the theory of Peeters provided one of the most convincing and clearest demonstrations of Fröhlich polaron features in solids.
Experimental data on the magnetopolaron effect, obtained using far-infrared photoconductivity techniques, have been applied to study the energy spectrum of shallow donors in polar semiconductor layers of CdTe.
The polaron effect well above the LO phonon energy was studied through cyclotron resonance measurements, e. g., in II–VI semiconductors, observed in ultra-high magnetic fields. The resonant polaron effect manifests itself when the cyclotron frequency approaches the LO phonon energy in sufficiently high magnetic fields.
In the lattice models the optical conductivity is given by the formula:
Here  is the activation energy of polaron, which is of the order of polaron binding energy . This formula was derived and extensively discussed in and was tested experimentally for example in photodoped parent compounds of high temperature superconductors.