  The plasmon resonance has found important application in various systems,
e.g., nanoantennas, solar panels, refractive index sensors. Unfortunately, a
few analytical solutions for such systems are known. The work aims to find a
solution for scattering by a plane electromagnetic wave on two parallel
cylinders. When their diameters and the gap between them are less than the
radiation wavelength, the quasistatic approximation is valid. We build up a
conformal transformation that maps Cartesian into bipolar orthogonal
coordinates and represent the scattered field as a decomposition by
eigenfunctions of the Laplace operator. The near-field intensity distribution
is shown to coincide with numerical calculation performed by COMSOL
Multiphysics. Green's function obtained allows one to find also higher
decomposition orders. Compared to previous studies, we treat the general case
of cylinders with different diameters and dielectric constants.
