  High energy e$^+$e$^-$ colliders offer unique possibility for the most
general dark matter search based on the mono-photon signature. Analysis of the
energy spectrum and angular distributions of photons from the initial state
radiation can be used to search for hard processes with invisible final state
production. Most studies in the past focused on scenarios assuming heavy
mediator exchange. We notice however, that scenarios with light mediator
exchange are still not excluded by existing experimental data, if the mediator
coupling to Standard Model particles is very small. We proposed a novel
approach, where the experimental sensitivity to light mediator production is
defined in terms of both the mediator mass and mediator width. This approach is
more model independent than the approach assuming given mediator coupling
values to SM and DM particles. Summarised in this contribution are published
results of our studies concerning simulation of mono-photon events with WHIZARD
and the expected sensitivity of the International Linear Collider (ILC) and
Compact Linear Collider (CLIC) experiments to dark matter production.
