# Diffraction of electromagnetic waves in the gravitational field of the Sun

## TL;DR

This paper develops an exact wave-theoretical model of electromagnetic wave diffraction in the Sun's gravitational field, providing insights into the solar gravitational lens's optical properties for potential exoplanet imaging.

## Contribution

It presents a closed-form solution for EM wave diffraction in the Sun's gravitational field using the first post-Newtonian approximation, advancing the understanding of the solar gravitational lens.

## Key findings

- Derived a solution valid for all distances and angles using confluent hypergeometric functions.
- Developed a wave-theoretical description of the solar gravitational lens.
- Analyzed the optical properties of the SGL for high-resolution exoplanet imaging.

## Abstract

We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.