1018 Applied Physics B – Lasers and Optics<strong>laser</strong> (λ = 800 nm). Whenever possible, the findings <strong>of</strong> the numericalsimulations are compared to experimental results.The numerical calculations yield threshold values <strong>of</strong> the irradianceabove which chemical changes in the focal region,a considerable temperature rise, and bubble formation are expectedto occur. We found two different mechanisms <strong>of</strong> bubbleformation: at repetition rates in the MHz range, fairly largelong-lasting bubbles containing non-condensable gas can beformed by plasma-mediated accumulative heating and chemicaldisintegration <strong>of</strong> biomolecules. At lower repetition rates,transient bubbles with lifetimes below 100 ns are created bythermoelastic stresses. Due to the thermoelastic origin <strong>of</strong> bubbleformation, the conversion efficiency from absorbed <strong>laser</strong>light energy into bubble energy is low, enabling the creation <strong>of</strong>spatially extremely confined disruptive effects.A comparison between experimental parameters used forcell surgery and our numerical results revealed two differentmodes <strong>of</strong> <strong>femtosecond</strong> <strong>laser</strong> <strong>nanosurgery</strong>: dissection usinglong pulse trains at MHz repetition rates is mediated byfree-electron-induced chemical decomposition (bond breaking)and not related to heating or thermoelastic stresses. Withthis dissection mode, bubble formation needs to be avoidedbecause the relatively large and long-lasting bubbles causedislocations far beyond the <strong>laser</strong> focus. By contrast, intracellulardissection at moderate (kHz) repetition rates relies onthe thermoelastically induced formation <strong>of</strong> minute transientcavities. Both modes <strong>of</strong> <strong>femtosecond</strong> <strong>laser</strong> nanoprocessing <strong>of</strong>biomaterials achieve a better precision than cell surgery usingcw irradiation.Femtosecond-<strong>laser</strong>-produced low-density plasmas arethus a versatile tool for the manipulation <strong>of</strong> transparent biologicalmedia and other transparent materials such as glass.However, they may also be a potential source <strong>of</strong> damage inmultiphoton microscopy and higher-harmonic imaging.2 Plasma formation2.1 Qualitative pictureter. Whereas the optical breakdown in gases leads to thegeneration <strong>of</strong> free electrons and ions, it must be noted thatin condensed matter electrons are either bound to a particularmolecule or they are ‘quasi-free’ if they have sufficientkinetic energy to be able to move without being capturedby local potential energy barriers. Transitions betweenbound and quasi-free states are the equivalent <strong>of</strong> ionization<strong>of</strong> molecules in gases. To describe the breakdown processin water, Sacchi [100] has proposed that water should betreated as an amorphous semiconductor and the excitation energy∆ regarded as the energy required for a transition fromthe molecular 1b 1 orbital into an excitation band (band gap6.5eV) [101–103]. We follow this approach. For simplicity,we will use the terms ‘free electrons’ and ‘ionization’ as abbreviationsfor ‘quasi-free electrons’ and ‘excitation into theconduction band’. Nonlinear absorption <strong>of</strong> liquid water actuallynot only involves ionization but also dissociation <strong>of</strong> thewater molecules [103], but in our model dissociation is neglectedto reduce the complexity <strong>of</strong> the numerical code.The photon energies at the wavelengths <strong>of</strong> 1064 nm,800 nm, 532 nm, and355 nm investigated in this study are1.17 eV, 1.56 eV, 2.34 eV, and 3.51 eV, respectively. Thismeans that the energy <strong>of</strong> six, five, three, and two photons,respectively, is required to overcome the band-gap energy∆ = 6.5eV. The excitation energy into the conductionband can be provided either by photoionization (multiphotonionization or tunneling [104, 105]) or by impact ionization[106–109]. In previous breakdown models, it was <strong>of</strong>tenassumed that a free electron could be produced as soon as∆ was exceeded either by the sum <strong>of</strong> the simultaneously absorbedphotons or by the kinetic energy <strong>of</strong> an impacting freeelectron [81, 110–112]. However, for very short <strong>laser</strong> pulseswhere breakdown occurs at large irradiance values, the bandgapenergy has to be replaced by the effective ionizationpotential to account for the oscillation energy <strong>of</strong> the electrondue to the electrical <strong>laser</strong> field. The ionization potential <strong>of</strong>individual atoms is [104]The process <strong>of</strong> plasma formation through <strong>laser</strong>inducedbreakdown in transparent biological media is schematicallydepicted in Fig. 1. It essentially consists <strong>of</strong> the formation<strong>of</strong> quasi-free electrons by an interplay <strong>of</strong> photoionizationand avalanche ionization.It has been shown experimentally that the optical breakdownthreshold in water is very similar to that in ocularand other biological media [99]. For convenience, we shalltherefore focus attention on plasma formation in pure wa-˜∆ = ∆ + e2 F 24mω 2 , (1)where ω and F denote the circular frequency and amplitude<strong>of</strong> the electrical <strong>laser</strong> field, e is the electron charge, and1/m = 1/m c + 1/m v is the exciton reduced mass that is givenbytheeffectivemassesm c <strong>of</strong> the quasi-free electron in theconduction band and m v <strong>of</strong> the hole in the valence band. Thesecond term in (1) can be neglected in nanosecond opticalFIGURE 1 Interplay <strong>of</strong> photoionization, inverse Bremsstrahlungabsorption, and impact ionization in the process<strong>of</strong> plasma formation. Recurring sequences <strong>of</strong> inverseBremsstrahlung absorption events and impact ionization leadto an avalanche growth in the number <strong>of</strong> free electrons. Therequirements to satisfy the conservation laws for energy andmomentum in impact ionization, and their consequences forplasma formation, are discussed in the text
VOGEL et al. <strong>Mechanisms</strong> <strong>of</strong> <strong>femtosecond</strong> <strong>laser</strong> <strong>nanosurgery</strong> <strong>of</strong> cells and tissues 1019breakdown, but must be considered in <strong>femtosecond</strong> opticalbreakdown where F is orders <strong>of</strong> magnitude larger.Multiphoton ionization (MPI) and tunneling are the mechanismsgoverning photoionization for different field strengthsand frequencies <strong>of</strong> the electromagnetic field. In his classicalp<strong>aper</strong> [104], Keldysh introduced a parameter γ = ω/ω tto distinguish tunneling and MPI regimes. Here 1/ω t standsfor the tunneling time through the atomic potential barrier,which is inversely proportional to the strength <strong>of</strong> the electromagneticfield. For values γ ≪ 1 as obtained with lowfrequencies and large field strengths tunneling is responsiblefor ionization, while for values γ ≫ 1 typical for optical frequenciesand moderate field strengths the probability <strong>of</strong> MPIis much higher than that <strong>of</strong> tunneling. However, <strong>femtosecond</strong>optical breakdown requires very high field strengths forwhich the tunneling time through the atomic potential barrieris extremely short, leading to values γ