Non-Rayleigh limit of the Lorenz-Mie solution and suppression of the scattering by the spheres of negative refractive index

We study light scattering by spheres made of negative refractive index materials. We demonstrate that scattering efficiency of the light does not always obey the well-known Rayleigh's law $Q_{\rm sca}\sim1/\lambda^4$ for small values of size parameter, but could be wavelength independent $Q_{\rm sca}\sim const$, or even increase with the wavelength as $Q_{\rm sca}\sim\lambda^2$. In addition, it is found that spheres with radius comparable with the input wavelength may exhibit suppression of the scattering in any directions, particularly in forward one. It can be considered as analogues of Brewster's angles for spheres.