Computing light masks in neutral atom lithography

In neutral atom lithography, a collimated beam of atoms is sent through a region of standing light waves created by interfering laser beams. The intensity distribution of the light field modulates the density distribution of the atoms transversal to the beam direction. The atomic beam materializes on a substrate, and the atoms are deposited in a pattern which mimics the intensity distribution of the light. It is thus possible to create nanostructures by a suitable adjustment of the light field. While the computation of the pattern of atoms generated by any given setup of laser beams with known amplitudes and phases is straightforward, the inverse problem of deducting the appropriate amplitude and phase of each single beam to create a prescribed pattern has to our knowledge not yet been addressed.We propose a numerical method to derive these values for a fixed setup of laser beams. We consider first the general case of unrelated beam directions and then specialize to setups which induce periodic patterns. The solution of the inverse problem is a two-step process: we use Fourier techniques to compute a set of characteristic amplitude values which enter the right-hand side of a nonlinear system of equations. This system is then solved iteratively by a coordinate descent method.