We find the conditions upon the amplitude and frequency of an external electromagnetic field at which the dipole moment of a Bergman-Stockman spaser oscillates in antiphase with the field. For these values of the amplitude and frequency the losses in
metal nanoparticles is exactly compensated of by gain. This shows that spasers may be used as inclusions in designing lossless metamaterials.
We demonstrate that when the frequency of the external field differs from the lasing frequency of an autonomous spaser, the spaser exhibits stochastic oscillations at low field intensity. The plasmon oscillations lock to the frequency of the external
field only when the field amplitude exceeds a threshold value. We find a region of values of the external field amplitude and the frequency detuning (the Arnold tongue) for which the spaser synchronizes with the external wave.
