Invited p aper Mechanisms of femtosecond laser nanosurgery of ...

1018 Applied Physics B – Lasers and Opticslaser (λ = 800 nm). Whenever possible, the findings of the numericalsimulations are compared to experimental results.The numerical calculations yield threshold values of the irradianceabove which chemical changes in the focal region,a considerable temperature rise, and bubble formation are expectedto occur. We found two different mechanisms of 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 of biomolecules. At lower repetition rates,transient bubbles with lifetimes below 100 ns are created bythermoelastic stresses. Due to the thermoelastic origin of bubbleformation, the conversion efficiency from absorbed laserlight energy into bubble energy is low, enabling the creation ofspatially extremely confined disruptive effects.A comparison between experimental parameters used forcell surgery and our numerical results revealed two differentmodes of femtosecond laser nanosurgery: 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 laser focus. By contrast, intracellulardissection at moderate (kHz) repetition rates relies onthe thermoelastically induced formation of minute transientcavities. Both modes of femtosecond laser nanoprocessing ofbiomaterials achieve a better precision than cell surgery usingcw irradiation.Femtosecond-laser-produced low-density plasmas arethus a versatile tool for the manipulation of transparent biologicalmedia and other transparent materials such as glass.However, they may also be a potential source of damage inmultiphoton microscopy and higher-harmonic imaging.2 Plasma formation2.1 Qualitative pictureter. Whereas the optical breakdown in gases leads to thegeneration of 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 of ionizationof 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 of liquid water actuallynot only involves ionization but also dissociation of thewater molecules [103], but in our model dissociation is neglectedto reduce the complexity of the numerical code.The photon energies at the wavelengths of 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 of 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 oftenassumed that a free electron could be produced as soon as∆ was exceeded either by the sum of the simultaneously absorbedphotons or by the kinetic energy of an impacting freeelectron [81, 110–112]. However, for very short laser pulseswhere breakdown occurs at large irradiance values, the bandgapenergy has to be replaced by the effective ionizationpotential to account for the oscillation energy of the electrondue to the electrical laser field. The ionization potential ofindividual atoms is [104]The process of plasma formation through laserinducedbreakdown in transparent biological media is schematicallydepicted in Fig. 1. It essentially consists of the formationof quasi-free electrons by an interplay of 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 amplitudeof the electrical laser field, e is the electron charge, and1/m = 1/m c + 1/m v is the exciton reduced mass that is givenbytheeffectivemassesm c of the quasi-free electron in theconduction band and m v of the hole in the valence band. Thesecond term in (1) can be neglected in nanosecond opticalFIGURE 1 Interplay of photoionization, inverse Bremsstrahlungabsorption, and impact ionization in the processof plasma formation. Recurring sequences of inverseBremsstrahlung absorption events and impact ionization leadto an avalanche growth in the number of free electrons. Therequirements to satisfy the conservation laws for energy andmomentum in impact ionization, and their consequences forplasma formation, are discussed in the text