  Optical coupling of two identical dielectric particles gives rise to bonding
and anti-bonding resonances.
  The latter is featured by significant narrowing of the resonant width and
strong enhancement of the $Q$ factor for the high index micron size particles
in subwavelength range. We consider particles shaped as spheres and disks under
coaxial illumination of dual incoherent counter propagating Bessel beams. In
the case of spheres we derive analytical expressions for the optical binding
(OB) force which decreases as $1/L^2$ for large distance $L$ between the
spheres and displays two periods of oscillations. For close distances the OB
force enormously increases in the resonant regime.
  The case of two coaxial disks owing to variation of the distance between
disks and aspect ratio of each disk is featured by extremal enhancement of the
$Q$ factor compared to the case of two spheres. In that case we demonstrate
unprecedent enhancement of the OB force up to several decades of nano Newtons.
We show that the magnitude and sign of the OB force strongly depend on the
longitudinal wave vector of the Bessel beams.
