An optimized absorbing potential for ultrafast, strong-field problems

Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most strong-field observables relate to the continuum portion of the wave function, the boundaries of the grid---which act as hard walls and thus cause reflection---can substantially impact the observables. Special care thus needs to be taken. While there exist a number of attempts to solve this problem---e.g., complex absorbing potentials and masking functions, exterior complex scaling, and coordinate scaling---none of them are completely satisfactory. The first of these is arguably the most popular, but it consumes a substantial fraction of the computing resources in any given calculation. Worse, this fraction grows with the dimensionality of the problem. And, no systematic way to design such a potential has been used in the strong-field community. In this work, we address these issues and find a much better solution. By comparing with previous widely used absorbing potentials, we find a factor of 3--4 reduction in the absorption range, given the same level of absorption over a specified energy interval.