  The tremendous progress in light scattering engineering made it feasible to
develop optical tweezers allowing capture, hold, and controllable displacement
of submicronsize particles and biological structures. However, the momentum
conservation law imposes a fundamental restriction on the optical pressure to
be repulsive in paraxial fields. Although different approaches to get around
this restriction have been proposed, they are rather sophisticated and rely on
either wavefront engineering or utilize active media. Herein, we revisit the
issue of optical forces by their analytic continuation to the complex frequency
plane and considering their behavior in transient. We show that the exponential
excitation at the complex frequency offers an intriguing ability to achieve a
pulling force for a passive resonator of any shape and composition even in the
paraxial approximation, the remarkable effect which is not reduced to the
Fourier transform. The approach is linked to the virtual gain effect when an
appropriate transient decay of the excitation signal makes it weaker than the
outgoing signal that carries away greater energy and momentum flux density. The
approach is implemented for the Fabry-Perot cavity and a high refractive index
dielectric nanoparticle, a fruitful platform for intracellular spectroscopy and
lab-on-a-chip technologies where the proposed technique may found unprecedented
capabilities.
