Merging Spot Size and Pulse Number Dependence of Femtosecond Laser Ablation Thresholds: Modeling and Demonstration with High Impact Polystyrene Aida Naghilou, † Oskar Armbruster, † Markus Kitzler, ‡ and Wolfgang Kautek* ,† † Department of Physical Chemistry, University of Vienna, Wä hringer Strasse 42, A-1090 Vienna, Austria ‡ Photonics Institute, Vienna University of Technology, Gusshausstrasse 27-29, A-1040 Vienna, Austria ABSTRACT: The spot size dependence of pulse laser-induced ablation thresholds of solid materials cannot be satisfactory described by the two existing quantitative models based on defect densities and on heat accumulation. In the present study, the heat accumulation model was amended but still yielded results in contradiction to experimental observations. The existing defect model was extended to account for incubation where optically active high-density defects with a separation below the radiation wavelength are generated. The reduction of the threshold for large beam radii could be ascribed to the laser spot covering a finite number of optically active low-density defects (LDD) embedded in the matrix material. This new generic model combining the spot size and pulse number dependence of femtosecond pulse laser-induced ablation thresholds was demonstrated with high-impact polystyrene. The average distance of the optically active LDD obtained from the generic model could be confirmed by scanning electron microscopy. 1. INTRODUCTION A key characteristic of laser pulses is the fluence, which is defined as the energy per beam area. The material modification or ablation threshold fluences, F th , are commonly accepted to be controlled by a set of experimental parameters such as pulse duration, wavelength, number of pulses, and repetition rate. 1 F th is strongly affected by chemical and physical modifications in the respective materials, such as the generation of defects, conversion phases, the occurrence of segregation, preferential ablation, etc. 1−3 Laser machining and processing (cutting, drilling, laser-induced forward transfer, 3D-writing, etc.) 4−14 requires fluences above permanent modification thresholds, whereas optical and telecommunication systems 15−23 need to be irradiated below the respective thresholds to avoid damage. It has been observed that F th decreases as the beam radius, w, increases for both nanosecond 4,8,15−17,19−23 and femtosec- ond 10−12,18 pulses. Even though the dependence of F th on w has been acknowledged for decades, the mechanism of this phenomenon is still unidentified. The two existing quantitative models are based on defect densities 23−26 and on heat accumulation. 12 Both models did not comply with experimental results. 11,15 The observation that optical breakdown thresholds for silica surfaces are 2−5 times lower than for the bulk was correlated to microfractures near the surface and/or to scratches caused by polishing. Such microscopic defects may locally enhance the optical field and initiate a plasma near the defect at lower power compared to the bulk. Scaling of the modification threshold with focal spot size was discussed on the basis of stimulated Brillouin scattering (SBS), self-focusing, color center formation, material densification, impurity inclusions, as well as the differences between surface and bulk damage, plus the possibility of annealing or cumulative damage when multiple pulses are used. 27 Some authors discussed a mechanism involving the varying availability of free electrons excited from either deep or shallow donors to initiate an avalanche in a larger focal volume. 28,29 Near-surface cracks, for example introduced by polishing, can enhance the local light intensity up to 2 orders of magnitude. 30 Such enhancements may result from interference of the incident radiation with light that is totally internally reflected by cracks. The enhancement factors depend strongly on the geometry and the shape of the crack. Self-focusing in dielectrics develops over a distance on the order of the Rayleigh length, z R , when a critical power density is exceeded. 27 This may play a role in the spot size dependence of laser-induced modification thresholds. Even for lower power densities, incipient self-focusing causes the focal waist to shift and constrict, enhancing the irradiance at the waist. Self- focusing can be complicated by the presence of Kerr, electrostrictive, and thermal contributions. A contradictory observation is the decreases of the ablation rate with w for ultraviolet nanosecond pulses. 5,13,14 This effect was attributed to transient plasma and/or vapor shielding Received: July 22, 2015 Revised: August 26, 2015 Published: August 27, 2015 Article pubs.acs.org/JPCC © 2015 American Chemical Society 22992 DOI: 10.1021/acs.jpcc.5b07109 J. Phys. Chem. C 2015, 119, 22992−22998