Dipole-like scattering by Rayleigh-sized particles with medium-matched real and general imaginary part of the refractive index

We explore Mie scattering by a homogeneous, spherical particle of radius much smaller than the wavelength of light and a complex refractive index. When the medium refractive index is a real number equal to the real part of the particle refractive index, the effective particle refractive index is of the form $1+i\kappa \text{.}$ In this case, scattering is caused solely by the imaginary part $\kappa$ of the particle refractive index, resembling Rayleigh scattering at small values and perfect conductor scattering at large values of $\kappa$. We employ a Mie computer program to simulate the scattering in this case; we plot the results and see that as $\kappa$ increases, the scattering of s-polarized light becomes more anisotropic, the backscattering intensity brightens while the forward scattering intensity dims. To explain our results theoretically, we explore how the Mie equations reduce for constraints of size parameter $x\ll 1$ and a refractive index of the form $m=1+i\kappa \text{,}$ though our analysis holds for arbitrary $m$ so long as $Re\left(mx\right)\ll 1\text{.}$ We find that such small particles may be described by a dipole with appropriate electric and magnetic dipole moments. Simple equations are given describing the scattering by these particles. Finally, we supplement our results with diagrams visualizing why we see the pattern found.