**3. Experimental methods**

According to **Figure 6**, the ionization rate is predicted to be dependent on the relative phase of the fundamental (800 nm) and second-harmonic (400 nm) beams. Further, the modulation

**Figure 6.** The total ionization rate versus laser intensity and relative phase of fundamental (*ω*) and second-harmonic

Recall that ablation by a laser with low and high intensities would fall into the regimes governed by multiphoton and tunneling ionization mechanisms, respectively. Conventionally, tunneling ionization corresponds to a regime in which the Keldysh parameter *γ* << 1. In this limit, the strength of the field is more than the value necessary to overcome the barrier. For a weaker field such that the Keldysh parameter *γ* >> 1, the main mechanism for ionization is due to the multiphoton ionization. In this regime, the electric filed strength is below the value that required for overcoming the barrier. In order to calculate the Keldysh parameter for the dualcolor case, we need to define the period of the laser *t*laser. It can be easily shown that the period of dual-color synthesized waveform by NIR (800 nm) and NUV (400 nm) beams is essentially that of the period of fundamental (*ω*) beam. Therefore, Eqs. (1) and (11) can be combined to

In the intermediate ionization regime, which is defined by *γ* ≈1.5, the ionization rate has a strong phase dependence. Likewise, the electron tunnel time now depends on the phase difference between the two colors. Note that the electric field is actually lower than the value

Ablation threshold is an important parameter for laser material processing. It is a function of the laser pulse duration, wavelength, and intensity. According to the simplified Fokker-Planck

¶ (14)

( ) ( ), *<sup>n</sup> In PI*

= +

*t* b¶

of ionization rate is more pronounced at higher laser intensities.

344 Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification

determine the ionization rate as shown in **Figure 6**.

required for electrons to overcome the barrier.

(2*ω*) laser beams.

equation [35]:

The experimental setup for laser ablation by dual-color femtosecond synthesized waveform [14] is shown schematically in **Figure 7**. The laser source was an amplified Ti: Sapphire laser system (Spitfire, Spectra Physics), which generates 70 fs laser pulses at a central wavelength of 800 nm (*λ*1) with an energy up to 1.5 mJ at 1 kHz.

As shown in **Figure 7**, we adopt an inline arrangement for phase control of the fundamental and second harmonic of the laser output. The 800-nm fs pulses were focused onto the sample surface by a single convex lens with a focal length of 300 mm. Meanwhile, the fundamental beam frequency was doubled in a 100-μm-thick type-I Beta Barium Borate (β-BBO) crystal in

**Figure 7.** Experimental setup for laser ablation of PMMA by femtosecond dual-colour synthesized waveforms. The polarizations of fundamental and second harmonic pulses were controlled by the half-wave plate. ND: neutral density filter; BBO: Barium borate; GVD: group velocity dispersion. The inset shows the reflectivity of the silicon wafer as a function of the incident angle for both polarizations.

the same beam path to generate 2*ω* pulses at 400 nm (*λ*2). Both beams were reflected from the silicon wafer at some incident angle, taking advantage of the fact that reflectivity of silicon varies with wavelengths and polarizations of the fundamental and second-harmonic beams (see the inset in **Figure 7**). We can control the intensity ratio *P*2*<sup>ω</sup>*/*Pω* of the two (collinear) beams by adjusting the incident angle. A pair of wedge prisms with controllable optical path difference was used to precisely adjust the relative time delay between the *ω* and 2*ω* pulses. We also employed a 5-mm-thick β-BBO to compensate the group velocity mismatch (GVM) of the two colors in the beam path. Besides, the *ω* and 2*ω* fields with original polarizations perpendicular to each other, were passed through a dual-color zero-order wave plate serving as a half-wave plate for 800 nm to make polarizations of the two colors parallel. Finally, the *ω* and 2*ω* pulses, overlapped in time with the same linear polarizations were focused on the sample. The spatial and temporal overlap and adjustment of the phase difference between the *ω* and 2*ω* fields were conducted using a procedure described previously [14].
