  We present Floquet theory-based predictions and electrically detected
magnetic resonance (EDMR) experiments scrutinizing the nature of two-photon
magnetic resonance shifts of charge-carrier spin states in the perdeuterated
$\pi$-conjugated polymer poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylene
vinylene] (d-MEH-PPV) under strong magnetic resonant drive conditions
(radiation amplitude $B_1$ ~ Zeeman field $B_0$). Numerical calculations show
that the two-photon resonance shift with power is nearly drive-helicity
independent. This is in contrast to the one-photon Bloch-Siegert shift that
only occurs under non-circularly polarized strong drive conditions. We
therefore treated the Floquet Hamiltonian analytically under arbitrary
amplitudes of the co- and counter-rotating components of the radiation field to
gain insight into the nature of the helicity dependence of multi-photon
resonance shifts. In addition, we tested Floquet-theory predictions
experimentally by comparing one-photon and two-photon charge-carrier spin
resonance shifts observed through room-temperature EDMR experiments on
d-MEH-PPV-based bipolar injection devices [i.e., organic light emitting diode
structures (OLEDs)]. We found that under the experimental conditions of strong,
linearly polarized drive, our observations consistently agree with theory,
irrespective of the magnitude of $B_1$, and therefore underscore the robustness
of Floquet theory in predicting nonlinear magnetic resonance behaviors.
