Plasma lens with frequency-dependent dispersion measure effects on fast radio bursts

¹ School of Physics and Electronic Engineering, Sichuan University of Science & Engineering, Zigong, 643000, China
² Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi, 830011, China
³ State Key Laboratory of Radio Astronomy and Technology, Beijing, 100101, P. R. China
⁴ Xinjiang Key Laboratory of Radio Astrophysics, 150 Science1-Street, Urumqi, 830011, China

^⋆ Corresponding author: zhouxia@xao.ac.cn

Received: 21 November 2024
Accepted: 11 August 2025

Abstract

Radio signals propagating through inhomogeneous plasma media deviate from their original paths, producing frequency-dependent magnification effects. In this paper, after reviewing the classical plasma-lensing theory, we have found a fundamental contradiction: the classical model assumes that the distribution of lensing plasma medium is related to the frequency-independent image position; however, our analysis demonstrates that both the image position (θ(ν)) and dispersion measure (DM(ν)) are inherently frequency-dependent when signals traverse a structured plasma medium. We have been able to resolve this paradox by developing a framework that explicitly incorporates frequency-dependent dispersion measures (DMs) following power-law relationships (DM ∝ ν^γ). Our analysis shows that the signal magnification decreases systematically with decreasing frequency, offering a plausible explanation for the frequency-dependent peak flux densities observed in fast radio bursts (FRBs), particularly in the case of the repeating FRB 180814.J0422+73. Our results suggest these FRBs could originate from the magnetized compact star magnetospheres. By considering these plasma-lensing effects on the sub-pulses of an FRB across different frequencies, we have the ability to more accurately investigate the intrinsic properties of FRBs via precise measurements of radio signals.