  The directionality and polarization of light show peculiar properties when
the scattering by a dielectric sphere can be described exclusively by electric
and magnetic dipolar modes. Particularly, when these modes oscillate in-phase
with equal amplitude, at the so-called first Kerker condition, the zero optical
backscattering condition emerges for non-dissipating spheres. However, the role
of absorption and optical gain in the first Kerker condition remains
unexplored. In this work, we demonstrate that either absorption or optical gain
precludes the first Kerker condition and, hence, the absence of backscattered
radiation light, regardless of the size of the particle, incident wavelength,
and incoming polarization. Finally, we derive the necessary prerequisites of
the second Kerker condition of the zero forward light scattering, finding that
optical gain is a compulsory requirement.
