Self-modulation of fast radio bursts

ABSTRACT Fast radio bursts (FRBs) are extreme astrophysical phenomena entering the realm of non-linear optics, a field developed in laser physics. A classical non-linear effect is self-modulation. We examine the propagation of FRBs through the circumburst environment using the idealized setup of a monochromatic linearly polarized GHz wave propagating through a uniform plasma slab of density N at distance R from the source. We find that self-modulation occurs if the slab is located within a critical radius Rcrit ∼ 1017(N/102 cm−3)(L/1042 erg s−1) cm, where L is the isotropic equivalent of the FRB luminosity. Self-modulation breaks the burst into pancakes transverse to the radial direction. When R ≲ Rcrit, the transverse size of the pancakes is smaller than the Fresnel scale. The pancakes are strongly diffracted as the burst exits the slab, and interference between the pancakes produces a frequency modulation of the observed intensity with a sub-GHz bandwidth. When R ∼ Rcrit, the transverse size of the pancakes becomes comparable with the Fresnel scale, and the effect of diffraction is weaker. The observed intensity is modulated on a time-scale of 10 µm, which corresponds to the radial width of the pancakes. Our results suggest that self-modulation may cause the temporal and frequency structure observed in FRBs.

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A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽

10.3390/sym13010153 ◽

2021 ◽

Vol 13 (1) ◽

pp. 153 ◽

Cited By ~ 1

Author(s):

Christophe Humbert ◽

Thomas Noblet

Keyword(s):

Dielectric Response ◽

Structure And Properties ◽

Linear Optics ◽

Third Order ◽

Mathematical Functions ◽

Sum Frequency ◽

Non Linear Optics ◽

Non Linear ◽

Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

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