  We analyze limit cycle oscillators under perturbation constructed as a
product of two signals, namely, an envelope with a period close to natural
period of an oscillator and a high-frequency carrier signal. A theory for
obtaining an envelope waveform that achieves the maximal frequency interval of
entrained oscillators is presented. The optimization problem for fixed power
and maximal allowed amplitude is solved by employing the phase reduction method
and the Pontryagin's maximum principle. We have shown that the optimal envelope
waveform is a bang-bang-type solution. Also, we have found "inversion" symmetry
that relates two signals with different powers, but the same interval of
entrained frequencies. The theoretical results are confirmed numerically on
FitzHugh-Nagumo oscillators.
