Theoretical basis of the diagonal scan method for determining the laser ablation threshold for femtosecond vortex pulses

In femtosecond laser micromachining, the ablation threshold is a key processing parameter that characterises the energy density required to cause ablation. Current techniques for measuring the ablation threshold such as the diameter regression and diagonal scan methods are based on the assumption of a Gaussian spatial profile, however no techniques currently exist for measuring the ablation threshold using a non-Gaussian beam shape. Here we present a formalism of the diagonal scan method for determining the ablation threshold and pulse superposition for femtosecond vortex pulses. To the authors' knowledge this is the first ablation threshold technique developed for pulses with non-Gaussian spatial profiles. Using this method, the ablation threshold can be calculated using measurement of a single feature (the maximum damage radius $\rho_{max}$), which allows investigations of ablation threshold and incubation effects to be carried out quickly and easily. Extending this method to non-Gaussian beams will allow exploration of new avenues of research, enabling characterisation of the ablation threshold and incubation behaviour for a material when ablated with femtosecond vortex pulses.