Minimum Scattering Superabsorbers with Dirac-Delta-Like Radiation

Scattering systems with simultaneous low radiation as well as enhanced absorption seem like a paradox, since exciting more modes to cause absorption would also accompany scattering. By exciting and engineering proper multipole modes through systematic configuration and suitable materials embedded for targeting specific functionalities, such as superscattering, superabsorption, cloaking sensors, and superdirective radiation, Ref. [1]–[3]. In this work, we alternatively address this issue by exploiting an optimization to comprehend energy distribution in scattering. The outcome is irrespective of system configuration, material parameters, and operating wavelength. We firstly define an energy function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L(a_{-N}, a_{-N+1},.., 0,..,N-1, N)=\sigma_{scs}+\lambda\sigma_{abs}$</tex> in which absorption cross section (ABS) and scattering cross section (SCS), i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma_{abs}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma_{scs}$</tex>, are involved. Here <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex> is a Lagrange multiplier and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a_{i}$</tex> is complex scattering coefficient. Then, we assume that there are total <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(2\mathrm{N}+1)$</tex> modes dominant in scattering. N ext, we derive extreme conditions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\partial L/\partial\vert a_{i}\vert =0$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\partial L/\partial\theta_{n}=0$</tex>. We could formulate a relation of minimum or maximum SCS with ABS while these all correspond to demand <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a_{i}=constant$</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$j=[-N,\ -N+1,\ ..,0,\ ..N-1,N]$</tex>, Ref. [2]. We depict these results in Fig. 1(a), displaying energy distribution for any passive scattering systems. At a constant EXT, if one could excite <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{N}$</tex> modes of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a_{i}$</tex> at will, it leads to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma_{scs}\rightarrow 0$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sigma_{abs}\rightarrow\sigma_{ext}$</tex>.