Abstract
We reveal relations between superluminal and subluminal spatiotemporally localized optical pulses and the phenomena of the relativistic aberration of a wavevector and the Doppler shift. It turns out that such waves are Lorentz-transformed versions of simple optical waves generated in another reference frame. The requirement of a null Doppler shift is shown to give rise to a speed associated with the relativistic velocity addition law of a double (two-step) Lorentz transformation. The effects of such a transformation are examined both in terms of four-coordinates and in the spectral domain. It is established that a subluminal pulse reverses its direction. In addition to a change in direction, the propagation term of a superluminal pulse becomes negative. The aberration due to a double Lorentz transformation is examined in detail for propagation invariant superluminal waves (X wave, Bessel X wave), as well as intensity-invariant superluminal and subluminal waves. Detailed symmetry considerations are provided for the superluminal focus X wave and the subluminal MacKinnon wavepacket.
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