Correlation Properties of Propagation-Invariant Fields

Abstract

In recent time, the spatially and temporally localized transfer of electromagnetic energy in linear and nonlinear media has been of increasing interest due to many possible applications. In linear media, both the exactly and nearly nondiffractive coherent fields were obtained as solutions to the Helmholtz and paraxial wave equations, respectively.¹ The concept of propagation invariance in variable-coherence optics was also introduced² and the electromagnetic model of the nondiffractive fields was proposed.³ Recently, our effort has been focused on the correlation effects of the diffraction-free fields. In particular, we derived the correlation matrix related to the wide class of non-stationary propagation-invariant fields and the general condition of the propagation invariance expressed by means of the angular spectrum of the correlation matrix. The propagation-invariant fields obtained on the basis of the scalar Bessel beams were examined as possible examples.