Polarizability of 2D monster and light scattering

TL;DR

This paper investigates the electrostatic properties and light scattering behavior of complex 2D structures called 'monsters', constructed via conformal mapping, and derives their polarizability and scattering cross-sections.

Contribution

It introduces a novel iterative conformal mapping method to analyze the polarizability of complex 2D objects with intricate boundaries.

Findings

Derived the polarizability of 2D monsters in external fields.

Expressed light scattering cross-section in terms of polarizability.

Analyzed structures built from conformal maps like Mandelbrot sets.

Abstract

The electrostatics of 2D system with complicated inner boundary is studied. The object which we call "monster" is built by an iterative process of multiple conformal mapping of the circle exterior. The procedure leads to the figures built from circle with branching curved cuts (i), to the multiple tangential near-round circles (ii) and the Mandelbrot map (iii). The polarizability of a monster in the homogeneous external field is found. The light scattering cross-section was expressed through the polarizability of a monster.