Numerical modeling of nonlinear plasma formation in high-NA micromachining of transparent materials and biological cells using ultrashort laser pulses

Ultrashort laser pulses recently found extensive application in micro- and nanostructuring, in refractive surgery of the eye, and in biophotonics. Due to the high laser intensity required to induce optical breakdown, nonlinear plasma formation is generally accompanied by a number of undesired nonlinear side-effects such as self-focusing, filamentation and plasma-defocusing, seriously limiting achievable precision and reproducibility. To reduce pulse energy, enhance precision, and limit nonlinear side effects, applications of ultrashort pulses have recently evolved towards tight focusing using high numerical aperture microscope objectives. However, from the theoretical and numerical point of view generation of optical breakdown at high numerical aperture focusing was barely studied. To simulate the interaction of ultrashort laser pulses with transparent materials, a comprehensive numerical model taking into account nonlinear propagation, plasma generation as well as the pulse's interaction with the generated plasma is introduced. By omitting the widely used scalar and paraxial approximations a novel nonlinear propagation equation is derived, especially suited to meet the conditions of high numerical aperture focusing. The multiple rate equation (MRE) model is used to simultaneously calculate the generation of free electrons. Nonparaxial and vectorial diffraction theory provides initial conditions. The theoretical model derived is applied to numerically study the generation of optical breakdown plasmas, concentrating on parameters usually found in experimental applications of cell surgery. Water is used as a model substance for biological soft tissue and cellular constituents. For focusing conditions of numerical aperture NA < 0.9 generation of optical breakdown is shown to be strongly influenced by plasma defocusing, resulting in spatially distorted breakdown plasmas of expanded size. For focusing conditions of numerical aperture NA ≥ 0.9 on the other hand generation of optical breakdown is found to be almost unaffected by distortive side-effects, perfectly suited for material manipulation of highest precision.