1. Introduction

Femtosecond-laser-induced ablation has been researched extensively for many years due to its tremendous application potential in solar cells [1], optical waveguides [2, 3], and microchannel fabrication [4, 5]. The ablation characteristics depend significantly on femtosecond laser parameters, such as laser fluence [6], pulse duration [7], wavelength [8], repetition rate [6], etc. For example, Jia et al. reported that threshold fluences in fused silica and calcium fluoride (CaF₂) increase with laser wavelengths from 250 to 800nm, while they keep nearly constant in the region of 800-2000nm [7].

Polarization, an important laser parameter, remarkably affects femtosecond-laser-induced ablation, especially in crystalline materials. On the one hand, optical properties of crystalline materials, after irradiation by femtosecond laser pulse, exhibit orientation dependence. For example, Gertsvolf et al. found that optical transmittance in wide band-gap crystals exhibits orientation dependence, where the effective electron mass is considered as a key factor [9]. Wang et al. discovered that third-order optical nonlinearity in a zinc oxide (ZnO) micro/nanowire shows significant dependence on the polarization angle and sample orientation [10]. On the other hand, recent studies have found that laser-induced periodic surface structures (LIPSS) also exhibit significantly crystal-orientation selectivity. For example, Lehmann et al. indicated that different spatial-frequency structures on diamond surfaces can be obtained by adjusting the polarization of an incident laser with respect to the crystal axes [11]. And in our previous work, Han et al., reported that the LIPSS in silicon (100) is much easier (or more difficult) to form when the polarization direction is along the lattice axis [011]/[$01\overline{1}$] (or [001]) [12]. Therefore, polarization-dependent ablation, especially in single crystalline materials, may open new possibilities for highly controllable laser micro/nanofabrication in the future.

This paper discusses an experiment where the ablation areas induced by a linearly polarized femtosecond laser with different polarization direction and energy were measured in cubic crystals of gallium arsenide (GaAs), zinc selenide (ZnSe), magnesium oxide (MgO), and lithium fluoride (LiF), covering a broad band-gap range of 1.46 eV~13.6 eV. Our experiments indicated that the π/2-period oscillation in ablation size with respect to the polarization direction can be found in those cubic crystals, and the oscillation can be generated or eliminated depending on the pulse fluence. The decay of the oscillation amplitude was observed in all of the cubic crystals considered with the increase of laser energy. Comparisons between the cubic crystals demonstrate that the oscillation is more robust with respect to the increase of laser energy for narrow-gapped materials over that for wide-gapped dielectrics. The orientation dependence of photoionization, including multiphoton ionization and tunneling, is selected to explain the polarization-dependent ablation, while the competition between the photoionization and avalanche ionization is responsible for the elimination of the polarization dependence.

2. Experimental set-up

In our ablation experiments, the samples with cubic structures, including GaAs<100>, ZnSe<100>, MgO<100>, and LiF<100>, were from Hefei Branch Crystal Material Technology Co., Ltd. The corresponding band-gaps were 1.46 eV, 2.8 eV, 5.37 eV, and 13.6 eV, respectively. For all ablated materials, the 10 × 10 × 0.5 mm³ samples were mechanically polished to a surface roughness of 0.5 nm Ra. The femtosecond laser ablation experimental system is depicted in Fig. 1(a). A commercial amplified 3.5 W Ti: sapphire laser (Spectra-Physics, Inc.) was employed to generate linearly femtosecond laser pulses (800 nm, 35 fs). The laser polarization was controlled by a zero-order half wave plate (HWP), and the laser beams were incident to the sample surfaces by a plano-convex lens (f = 100 mm) at ambient temperature and pressure. In our experiments, the resulting beam of radius (1/e²) were determined using a method by Liu [22] to be w₀~17μm, and the peak fluences F of pulses were determined from pulse energy accordingly. The initial pulse duration ~35 fs was stretched to ~100 fs (measured by an autocorrelator) after passing a series of lenses. And, the initial polarization orientation of incident laser is adjusted along with 010-crystal axis of samples, and the polarization angles (θ), between the laser polarization direction and 010-crystal axis of samples, could be changed by HWP, as shown in the Fig. 1(b). At a certain fluence, 20 shots per site were adopted for accurate measurement. The results measured are within a standard deviation of less than 5%. After irradiation, the ablation crater morphologies, including LIPSS, were demonstrated by scanning electronic microscope (SEM).

 

Fig. 1 (a) Schematic of femtosecond laser ablation experimental system. (b) The definition for the polarization angle, θ. E₀ is the initial incident laser polarization orientation along with 010-crystal axis of samples.

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3. Results and discussion

The polarization-dependent ablation in ZnSe by a femtosecond laser has been carefully studied. The ablation areas at polarization angles (θ) of 0°, 50°, 90°, and 140°are shown in Figs. 2(a)-2(d) (fluence 0.29J/cm²). At θ = 0°, the ablation area was about 86.63μm²; and LIPSS (periods: ~600nm, direction: //E) were observed at the edge of the ablation crater. At θ = 50°, the ablation area remarkably decreased to 25.57μm²; and the cross-grating structures (upper structure: ~700nm, //E; lower structure: ~150nm, ⊥ E) were observed (Fig. 2e partial enlarged detail). At θ = 90°, the ablation area sharply increased to 135.04μm², and LIPSS (~600nm, //E) were observed again at θ = 0°. At θ = 140°, the ablation area remarkably decreased to 24.48μm²; and the cross-grating structures were formed again at θ = 50°.

 

Fig. 2 (a)-(d) SEM images of ablation craters after irradiation with 20 femtosecond laser pulses in ZnSe at different polarization angles: (a) θ = 0°, (b) θ = 50°, (c) θ = 90°, and (d) θ = 140°, respectively. The laser fluence is 0.29J/cm². (e) The partial enlarged drawing to distinctly describe the cross-grating structure. The polarization orientation of the incident laser (E) is indicated by the arrow. (f) The normalized ablation areas as a function of polarization angle (θ) at laser fluences of 0.29J/cm², 0.33J/cm², 0.40 J/cm², 0.44 J/cm² and 0.51 J/cm², where the normalized ablation areas are ablation areas A/average ablation areas A₀. The inset image shows the cubic structure with two symmetry axes, -M and -K, at a crystal face of <100>.

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Furthermore, the normalized ablation areas (ablation areas A/average ablation areas A₀) in ZnSe, as a function of polarization angles between 0° and 180°, are shown in Fig. 2(f). The normalized ablation areas exhibited a periodic oscillation for different laser fluences [0.29J/cm², 0.33J/cm², 0.40J/cm², 0.44J/cm², and 0.51J/cm²]. The oscillation period and amplitude are defined here for a clear description of the polarization-dependent ablation areas. The oscillation period is the difference in polarization angle between adjacent peaks (polarization angles at peak values θ = 0°, 90°, and 180°) or adjacent valleys (θ = 45° and 135°), which keeps a constant value of π/2 as laser fluence increases. The oscillation amplitude is half of the normalized ablation area’s difference between peak and valley values, which decreased from 0.79, 0.25, 0.10, 0.09, to 0.05 as the laser fluence increased. In short, while its oscillation period exhibited independence of laser fluence, the normalized oscillation amplitude significantly decreased with the increase of laser fluence.

Polarization-dependent ablation has also been observed in other cubic crystalline materials, e.g., GaAs, MgO, and LiF, for femtosecond laser polarization ranging from 0° to 180°, as shown in Fig. 3. Similar patterns, as in ZnSe, including the π/2 period of polarization-dependent ablation and oscillation amplitude decreasing as laser fluence increases, are also found in GaAs, MgO, and LiF.

 

Fig. 3 The normalized ablation areas as a function of polarization angle (θ) in GaAs, ZnSe, MgO and LiF. Each of the ablation craters included 20 femtosecond pulses. The corresponding fluences were 0.12J/cm², 0.33J/cm², 0.89J/cm² and 1.75 J/cm², respectively.

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Polarization-dependent ablation is just observed in certain fluence ranges. The fluence range is defined as the fluence from when the polarization-dependent ablation appears to the fluence when the normalized amplitude is less than 0.05 (measuring error). The widths of fluence ranges are closely related to the ablated-material’s band-gap. The normalized oscillation amplitudes, as a function of fluence in GaAs, ZnSe, MgO, and LiF, are shown in Fig. 4. Here, F/F_th denotes the laser fluence divided by the ablation threshold along 010-crystal axis of samples (polarization angle: θ = 0°). For GaAs, ZnSe, MgO, and LiF, ablation thresholds (F_th) are 0.086 J/cm², 0.24 J/cm², 0.75J/cm² and 1.54J/cm², respectively. In our experiment, the fluence ranges {F_osc} in GaAs, ZnSe, MgO, and LiF, were (1-2.4)F_{th_GaAs}, (1-2.1)F_{th_ZnSe}, (1-1.4)F_{th_MgO}, and (1-1.31)F_{th_LiF}, respectively. The widths of the fluence range {F_osc} decreased approximately with the increase in the ablated-materials’ band-gaps: {F_osc(LiF)} < {F_osc(MgO)} < {F_osc(ZnSe)} < {F_osc(GaAs)}. In general, the polarization-dependent ablation was observed only in a smaller fluence range for wide band-gap material, while for narrow band-gap material, the fluence range was much wider.

 

Fig. 4 The oscillation amplitude as a function of laser fluence in GaAs, ZnSe, MgO and LiF. The direction of the arrow points to the increasing direction of the ablated-material band-gap. The ablation threshold (F_th) is defined along the crystal x axis (polarization angle: θ = 0°).

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The ablation process is closely related to carrier generation, heating, recombination, and the corresponding material phase change. In femtosecond laser ablation, carrier generation, including photoionization (PI) and avalanche ionization (AI), plays an important role [13–16]. Recent studies have shown that reduced mass (m*), determined by both the electron mass in the conduction band ($m_e^{\ast }$), and the hole mass in the valence band ($m_h^{\ast }$) [17], exhibits direction dependence in the crystal [9, 18]. Consequently, PI is significantly affected by the reduced mass which depends strongly on crystal orientation [9]. The photoionization rate as a function of laser intensity at different reduced masses for LiF and ZnSe is shown in Fig. 5, based on Keldysh’s theory. Since the photoionization rate strongly peaked at the temporal peak of the pulse, we shadowed the intensity interval around its peak value (see Fig. 5), which contributed most of the photoionization-generated free electrons. It is obvious that a small reduction in reduced mass from the <011> crystal axis (1.67m_e [18], where m_e is the free electron rest mass) to the <010> crystal axis (1.06m_e [18]) can lead to ~2 orders of magnitude growth in the photoionization rate in LiF at the mixed regime [19] between tunneling and multiphoton ionization, as shown in Fig. 5(a). Ultimately, the difference in ablation areas emerged by changing the laser polarization direction. A similar situation was also observed in ZnSe (Fig. 5(b)). The reduced electron mass along different crystal axes at a crystal face of <100> was previously unknown for ZnSe. Since the electron mass in the conduction band, independent of the crystal axis orientation, was ~0.17m_e [20], a reduced mass ($m^{*}$,$m^{*-1}=m_h^{\ast }{}^{-1}+m_e^{\ast }{}^{-1}$) of less than 0.17m_e was expected. Two values (m_e * = 0.1m_e and 0.17m_e) with small differences show that the photoionization rate was also very sensitive to the reduced electron mass, i.e., a small difference in reduced electron mass can result in a contrasted rate in nonlinear absorption. Yet, the AI, which depends strongly on the free electron heating rate and free electron kinetic energy, occurs only when free electrons become energetic enough to liberate the bound-electron via collisions [13, 21] and exhibits no crystal orientation dependence. Therefore, the oscillation of the ablation area with the polarization angle was mainly due to the PI.

 

Fig. 5 The photoionization (PI) rate as a function of laser intensity at different reduced mass (m*) in LiF (a) and ZnSe (b). The range of laser peak intensity marked with a shaded border is closely related to the laser fluences and can be calculated by $I=F/({\tau }_p\sqrt{\pi /4\ln (2)})$ [23]. The direction of the arrow points to the dominant ionization mode based on Keldysh’s PI theory.

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In general, for short pulse laser ablation, PI provides the initial free carriers known as the “seed electrons” for AI [6–8, 13, 16, 19]. In special cases, e.g., in narrow-gapped material, the PI rate alone [6, 18] can provide the critical carrier density or deposited energy density to reach the ablation threshold, as it is much stronger than the PI rate in wide-gapped material. As shown in Fig. 5, in wide-gapped dielectrics, such as LiF, the PI rate approaches ~10²⁵ - ~10²⁷ s⁻¹cm⁻³ at a laser intensity range with polarization-dependent ablation, while the PI rate in ZnSe can be as intense as ~10³⁴ s⁻¹cm⁻³. Hence, compared with ZnSe, the PI rate in wide-gapped material, such as LiF, can be easily surpassed by AI. Once AI becomes the dominant channel for free carrier generation, the polarization-dependent ablation effect, arising from the PI not AI, will tend to be masked. Therefore, with the increase of laser fluence, the polarization-dependent ablation dramatically weakens and, ultimately, tends to be eliminated when laser fluence exceeds a certain value.

The polarization-dependent ablation with π/2-period oscillation with polarization can be observed in cubic crystals, including GaAs, ZnSe, MgO, and LiF. The oscillation period is determined by crystal structure, especially the atomic arrangement on an ablated crystal face [9]. As shown in the set image in Fig. 2(f), the cubic crystal is characterized by two symmetry axes, -M and -K, at a crystal face of <100>; and they lie at an angle of π/4 to each other. Therefore, the π/2-period oscillation in ablation size is exhibited in cubic crystals.

4. Conclusions

In summary, we studied the generation and elimination of polarization-dependent ablation in cubic crystals, including GaAs, ZnSe, MgO, and LiF. The polarization-dependent ablation can be controlled by laser fluence. The polarization dependence of the ablation can be well conserved at low laser fluence, slightly above the ablation threshold for the <100> crystal face and tends to be weakened or even eliminated with the increase of fluence. While the polarization-dependence of ablation is sustained in a wide range of laser fluence for a narrow band-gap material, it is strongly suppressed with a slight augmentation of laser fluence for a wide band-gap material. The crystal orientation dependence on nonlinear absorption as a result of the anisotropic reduced mass is responsible for the generation of polarization-dependent ablation, whereas the dominance of avalanche ionization over the photoionization leads to the weakening or even the elimination of the polarization dependence.