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Gravitational waves (GWs, from binary merger) interacting with super-strongmagnetic fields of the neutron star (in the same binary system), would lead toperturbed electromagnetic waves [EMWs, in the same frequencies of these GWs,partially in the ultra-low-frequency (ULF) band for the EMWs]. Such perturbedULF-EMWs are not only the signals, but also a new type of special EMcounterparts of the GWs. Here, generation of the perturbed ULF-EMWs isinvestigated for the first time, and the strengths of their magnetic componentsare estimated to be around 10^{-12}Tesla to 10^{-17}Tesla (in fISCO) at theEarth for various cases [not including the influence of interstellar medium(ISM)].The components with higher frequencies of the ULF-EMWs (e.g., especiallyproduced by the GWs of the post-merger stage) above 1.8kHz (typical plasmafrequency around solar system in the Milky way), could propagate through theISM from the source until the Earth, and the perturbed ULF-EMWs will bereprocessed before they arrived at the Earth due to the ISM. Also, thewaveforms of the perturbed ULF-EMWs will be modified into shapes different butrelated to the waveforms of the GWs, by the amplification process during thebinary mergers which could amplify the magnetic fields into 10^{12}Tesla oreven higher. Specific connection relationships between the polarizations of theperturbed ULF-EMWs and the polarizations (tensorial and possible nontensorial)of the GWs of binary mergers, are also addressed here. Characteristicproperties of the perturbed ULF-EMWs (which would bring us some different newinformation of fundamental properties of the gravity and Universe) will be veryhelpful for extracting the signals from background noise for possibleobservations in the future.

Ultra-low-frequency electromagnetic waves as signals and special  counterparts of gravitational waves (from binary mergers) having tensorial  and possible nontensorial polarizations