Tomaschitz, R. (2009). Tachyon optics: Kirchhoff identities and superluminal Bragg diffraction, Optics Communications 282, 1710-1719, DOI: 10.1016/j.optcom.2009.01.024


Abstract (ScienceDirect, SAO/NASA ADS)

The diffraction of superluminal radiation fields in crystal lattices is studied. The negative mass-square of the tachyonic wave modes affects the modulation function of diffraction gratings and the scattering amplitude. The Bragg condition for tachyon diffraction as well as the longitudinal and transversal cross sections are derived. Scalar and vectorial Kirchhoff identities for superluminal Proca fields are obtained from Sommerfeld’s dipole functionals, in analogy to electromagnetic theory. These surface-integral representations of the tachyon potential and the tachyonic field strengths are used to calculate the asymptotic diffracted modes and the intensity ratios. The dependence of the primary and secondary intensity peaks on the tachyon mass is analyzed in the reciprocal lattice, and the conversion of transversal into longitudinal radiation by way of Bragg scattering is explained. Specifically, tachyonic spectral fits are performed to the TeV spectra of three active galactic nuclei, H2356 − 309, 1ES 1218 + 304, and 1ES 1101 − 232, obtained with the imaging atmospheric Cherenkov detectors HESS, MAGIC, and VERITAS. The curvature in the spectral maps of these blazars is shown to be intrinsic, generated by ultra-relativistic electron populations in the galactic nuclei rather than by intergalactic absorption, and is reproduced by a tachyonic cascade fit.


Keywords: Tachyon diffraction; Transversal and longitudinal polarization; Green’s function for superluminal wave propagation; Tachyonic Maxwell equations and Fraunhofer far-field approximation; Cross sections and intensity ratios of tachyonic Bragg scattering; Superluminal cascade spectra of TeV blazars

PACS classification codes: 42.25.Fx; 42.25.Ja;; 95.30.Gv


Article Outline

1. Introduction

2. Superluminal radiation fields

2.1. Proca equation with negative mass-square

2.2. Tachyonic dipole fields

2.3. Kirchhoff representation of the tachyon potential and the field strengths

3. Fraunhofer diffraction of superluminal radiation at a plane aperture

3.1. Tachyonic energy flux

3.2. Polarized superluminal modes: conversion of transversal into longitudinal tachyons by diffraction

3.3. Intensity ratios for the conversion of longitudinal into transversal radiation

4. Tachyonic Bragg scattering

4.1. Diffraction gratings: negative mass-square and Bragg condition

4.2. Tachyon diffraction in crystal lattices: transversal and longitudinal scattering cross sections

5. Tachyonic flare spectra of TeV blazars

6. Conclusion: tachyonic X-rays and Bragg spectrometers








Tachyon optics: Kirchhoff identities and superluminal Bragg diffraction



Tomaschitz, Roman



AA(Department of Physics, Hiroshima University, 1-3-1 Kagami-yama, Higashi-Hiroshima 739-8526, Japan. Tel.: +81 824 247361; fax: +81 824 240717.)



Optics Communications, Volume 282, Issue 9, p. 1710-1719.

Publication Date:






PACS Keywords:


Diffraction and scattering, Polarization, Theories of x-ray diffraction and scattering, Radiation mechanisms; polarization




Bibliographic Code:





description: Roman Tomaschitz (2009) Tachyon optics: Kirchhoff identities and superluminal Bragg diffraction, Optics Communications 282, 1710.


Keywords: tachyonic Maxwell equations, Kirchhoff identities for Proca fields with negative mass-square, Fraunhofer diffraction of superluminal radiation, Green’s function for superluminal wave propagation, tachyonic dipole fields and Sommerfeld’s dipole functionals, diffraction of tachyonic radiation fields in crystal lattices, Bragg condition for tachyon diffraction, conversion of transversal tachyons into longitudinal radiation by Bragg scattering, polarized tachyonic γ-ray cascades, tachyonic flare spectra of TeV γ-ray blazars, spectral curvature of BL Lacertae objects, H2356−309, 1ES 1218+304, 1ES 1101−232, tachyonic gamma-rays


download full-text article (PDF)           Full Text HTML


back to index