**1. Introduction**

Femtosecond (fs) laser micromachining has been studied intensively for the past two decades. One of the advantages of using ultrashort laser pulses rather than longer pulses for laser material processing pertains to the nonthermal ablation mechanism. By considerably reducing the area of heat-affected zones, precise laser micro- and nanomachining have become feasible for fs machining. To date, fs laser micromachining has been performed on a variety of wide-

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

band-gap materials, such as polymers [1, 2], fused silica [3–6], and silicon [7–10]. However, almost all of these studies employed one-color laser pulses. More recently, coherent waveformsynthesized two-color laser pulses have been successfully used for increasing plasma generation [11], generating high harmonics [12], and producing broadband terahertz radiation [13]. By studying femtosecond laser ablation of polymethylmethacrylate (PMMA), our group demonstrated that the ablated hole areas exhibited clear modulation with a contrast of 22% by varying the relative phase between the *ω* and 2*ω* beams [14]. It was assumed that different peak intensity for the synthesized waveform was responsible for the observed phenomena. The physical mechanism was not clear.

In general, ultrafast laser ablation of dielectrics, such as PMMA, has been explained by the photochemical, photothermal, and photophysical models [15]. In the photochemical model, direct bond breaking in PMMA is achieved by exposing it to an ultrashort laser pulse for producing several reaction products, such as CO, CO2, CH4, CH3OH, and HCOOCH3. In the photothermal model, electronic excitation by picosecond laser pulses results in thermal bond breaking, leading to the formation of PMMA monomers. Among these models, the most interesting one is the photophysical one, in which both thermal and nonthermal bond breaking occur simultaneously. In thermal bond breaking, electronic excitation by ultrashort laser pulses results in ultrashort-laser-induced ionization in the picosecond (ps) and fs ranges. The three main processes of photophysical laser-induced breakdown are (i) excitation of conduction band electrons through ionization, (ii) heating of conduction band electrons through irradiation of the dielectric, and (iii) plasma energy transfer to the lattice, which causes bond breaking [16–19].

The Keldysh formalism, describing electron tunneling through a barrier created by the electric field of a laser, is often employed for modeling laser breakdown of materials by photoionization, including both multiphoton and tunneling cases. The Keldysh parameter can be expressed as the square root of the ratio between the ionization potential and twice the value of the ponderomotive potential of the laser pulse. Alternatively, it can be expressed as the ratio of tunneling frequency to the laser frequency. The tunneling time or the inverse of the tunneling frequency is given by the mean free time of an electron passing through a barrier width, *l*tunneling = *I*p/*eE*(*t, ϕ*), where *I*p is the ionization potential, *e* is the electron charge, and *E*(*t, ϕ*) is the optical field.

Depending on the laser intensity used for above-threshold ionization [20–22], two regions of photoionization exist: the tunneling ionization region [20, 23, 24] and multiphoton ionization region [25–28]. In tunneling ionization, the electric field is extremely strong. The Coulomb well can be suppressed to cause the bound electron to tunnel through the barrier and be ionized. At lower laser intensities, the electron can absorb several photons simultaneously. The electron makes the transition from the valence band to the conduction band if the total energy of the absorbed photons is greater than or equal to the band gap of the material.

The boundary between tunneling ionization and multiphoton ionization is unclear. Schumacher et al. showed that there should be a so-called intermediate region that exhibit both tunneling and multiphoton characteristics. Mazur et al., following the Keldysh formalism, estimated that the intermediate region corresponded to a Keldysh parameter *γ* ≈ 1.5 [29].

The tunneling ionization rate is a function of the electric field. It is well known that the multiphoton ionization rate can be expressed as *ϖ*mpi ∝ *σ*k*I* k, where *I* is the laser intensity and *σ*k is the multiphoton absorption coefficient for *k* photons [30]. When the ionization occurs in the intermediate region, an electron can absorb several photons and be ionized by the tunneling effect. In this regime, the ionization rate can also vary with phase of the exciting electric field. The laser intensity required, however, is considerably lower than that in the pure tunneling ionization case.

In this chapter, we present the current progress on laser ablation of polymethylmethacrylate (PMMA) by phase-controlled femtosecond two-color synthesized waveforms. Significantly, laser breakdown (ablation) of transparent materials through photoionization in the intermediate regime (Keldysh parameter *γ* ≈ 1.5) was demonstrated for the first time. The modulation of ablated hole area as well as the dependence of the ablation threshold on the relative phase between the *ω* and 2*ω* beams were observed. The data correlated closely with the theoretically predicted phase dependence of the photoionization rate using the Keldysh formalism.
