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The relativistic aberration of a wavevector and the corresponding Dopplershift are examined in connection with superluminal and subluminalspatiotemporally localized pulsed optical waves. The requirement of a nullDoppler shift is shown to give rise to a speed associated with the relativisticvelocity composition law of a double (two-step) Lorentz transformation. Theeffects of such a transformation are examined both in terms of four-coordinatesand in the spectral domain. It is established that a subluminal pulse reversesits direction. In addition to a change in direction, the propagation term of asuperluminal pulse becomes negative. The aberration due to a double Lorentztransformation is examined in detail for propagation invariant superluminalwaves (X wave, Bessel X wave), as well as intensity-invariant superluminal andsubluminal waves. Detailed symmetry considerations are provided for thesuperluminal focus X wave and the subluminal MacKinnon wavepacket.

Relativistic aberration and null Doppler shift within the framework of superluminal and subluminal nondiffracting waves