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

TL;DR

This paper explores how relativistic aberration and Doppler shifts behave for superluminal and subluminal localized optical waves, revealing unique effects like direction reversal and negative propagation terms through double Lorentz transformations.

Contribution

It introduces a novel analysis of relativistic effects on superluminal and subluminal waves using double Lorentz transformations, expanding understanding of wave behavior in relativistic contexts.

Findings

Subluminal pulses reverse direction under relativistic transformations.

Superluminal pulses can exhibit negative propagation terms.

Detailed symmetry analysis of specific superluminal and subluminal waveforms.

Abstract

The relativistic aberration of a wavevector and the corresponding Doppler shift are examined in connection with superluminal and subluminal spatiotemporally localized pulsed optical waves. The requirement of a null Doppler shift is shown to give rise to a speed associated with the relativistic velocity composition 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.