Spatial and temporal symmetry breaking in nonlinear laser lithography

Symmetry breaking is ubiquitous in nonlinear systems. This is also the case for Nonlinear Laser Lithography (NLL), in which an ultrafast laser beam incident on a material surface causes the infinite fold rotational symmetry of the material surface to be broken. In the case of linear polarization, line like structures are obtained that possess 2-fold rotational symmetry. We discuss two types of NLL, one due to the formation of oxide structures (Oxidation NLL) and the other due to material ablation (Ablation NLL). The existence of both types of structures is known for many years, however, although the regularity of oxidative structures has been significantly improved by our group earlier, the same was not true for ablative structures. Here, using the technique for Oxidation NLL and the parameters for ablative structures, we were able to achieve highly regular ablative structures which we call Ablation NLL. We demonstrate the coexistence of these two NLL structures on the same surface and how a plane can be tiled using them. Furthermore, we explore the phase space of NLL and determine the regions of the phase space occupied by the two NLL structures. We also demonstrate the versatility of NLL by obtaining Oxidation and Ablation NLL structures on several metals as well as on Silicon. We also discuss temporal symmetry breaking in NLL. If the laser beam is not incident normal to the surface and is tilted towards or away from the scanning direction, it can cause the period of the NLL structures to decrease or increase respectively. One can thus discern if a video of the beam creating a pattern while scanning over the surface along a line is run forward or backward. This dependence on the scanning direction leads to temporal symmetry breaking and is reminiscent of the Doppler effect. These symmetry breakings can be important for future research in this field along with possible commercial applications, some of which we have discussed here.