Prospective gamma-ray propagation models and comparisons to metamaterial models

Astronomical observations of gamma-ray bursts can exhibit dispersive behavior where high-energy gamma rays arrive significantly later than low-energy photons. Although the underlying mechanisms for the dispersion are not fully understood, a polynomial model has been proposed for modeling the apparent frequency-dependent photon velocity. The present work considers the impact of this dispersion model on the Helmholtz equation. The result is an extended form of the Helmholtz equation, where additional terms are used to model observed dispersion. The proposed set of equations closely resembles one type of metamaterial model, and therefore exhibits similar behavior. Comparisons are drawn between the gamma-ray models and similar metamaterial models that exhibit right-handed behavior at low frequencies and left-handed behavior at high frequencies. Finally, the overall approach provides a flexible modeling framework that can be adapted as new gamma-ray data become available.