There have been experiments, but only at lower power than required for fusion. From their latest paper:
> A significant case of nonlinear deviation from classical linear physics was seen by the measurements, how the laser opened the door to the principle of nonlinearity and could be seen from the effect measured by Linlor [9] followed by others (see [7] p. 31) when irradiating solid targets with laser pulses of several ns duration. At less than one MW
power, the pulses heated the target surface to dozens of thousand °C and the emitted ions had energies of few eV as expected in the usual way following classically. When the power of the nanosecond laser pulses was exceeding a significant threshold of few MW, the ions – suddenly – had thousand times higher energies. These keV ions were separated with linear increase on the ion charge indicating that there was not a thermal equilibrium process involved.
Lasers adequate for fusion are just now becoming available.
