  Gravitational waves (GWs, from binary merger) interacting with super-strong
magnetic fields of the neutron star (in the same binary system), would lead to
perturbed electromagnetic waves [EMWs, in the same frequencies of these GWs,
partially in the ultra-low-frequency (ULF) band for the EMWs]. Such perturbed
ULF-EMWs are not only the signals, but also a new type of special EM
counterparts of the GWs. Here, generation of the perturbed ULF-EMWs is
investigated for the first time, and the strengths of their magnetic components
are estimated to be around 10^{-12}Tesla to 10^{-17}Tesla (in fISCO) at the
Earth for various cases [not including the influence of interstellar medium
(ISM)].The components with higher frequencies of the ULF-EMWs (e.g., especially
produced by the GWs of the post-merger stage) above 1.8kHz (typical plasma
frequency around solar system in the Milky way), could propagate through the
ISM from the source until the Earth, and the perturbed ULF-EMWs will be
reprocessed before they arrived at the Earth due to the ISM. Also, the
waveforms of the perturbed ULF-EMWs will be modified into shapes different but
related to the waveforms of the GWs, by the amplification process during the
binary mergers which could amplify the magnetic fields into 10^{12}Tesla or
even higher. Specific connection relationships between the polarizations of the
perturbed ULF-EMWs and the polarizations (tensorial and possible nontensorial)
of the GWs of binary mergers, are also addressed here. Characteristic
properties of the perturbed ULF-EMWs (which would bring us some different new
information of fundamental properties of the gravity and Universe) will be very
helpful for extracting the signals from background noise for possible
observations in the future.
