In this article we compare the results of micromachining of fused silica and silicon with tightly focused scalar (viz., circularly and linearly polarized) and vector (viz., azimuthally and radially polarized) femtosecond laser pulses. We show that drilling with radially polarized pulses produces holes with smoother and better-delineated walls compared with the other polarizations used, whereas linearly polarized pulses can machine 20-nm wide single grooves in fused silica when the electric field of the pulse is aligned perpendicular to the cutting direction. The observed polarization-controlled micromachining is due to the formation of sub-diffraction-limited nanostructures that are optically produced in the multi-pulse irradiation regime.
©2013 Optical Society of America
Micromachining of solids using femtosecond laser pulses is influenced by such laser parameters as the magnitude and distribution of the light intensity at the workpiece, polarization state of the pulses, pulse length, pulse energy, central wavelength of the pulses, and pulse repetition rate. Among these parameters the polarization of light plays a separate and distinct role, which can be summarized as follows. The extensive experimental data suggest that in the regime of single-pulse irradiation the material modification morphology is determined by the intensity distribution inside the interaction volume and bears essentially no signature of the pulse’s polarization. In this regime the polarization affects only the threshold fluence of the laser-induced surface or bulk material modification . However, the very recent results on femtosecond laser ablation of poly-methyl methacrylate show that under certain conditions this is not true and the ablation craters produced by a single pulse become elongated along the major axis of the polarization vector for linearly and elliptically polarized pulses . On the other hand, the response of many materials to multi-pulse irradiation has long been known to depend on both the intensity and polarization of the light pulses and lead to pronounced, polarization-dependent changes in the material in the form of periodic nanostructures which tend to align themselves either perpendicular or parallel to the electric field of the light [3,4]. The nanostructures can be formed either on the surface (i.e., laser-induced periodic surface structures (LIPSS)) or inside the material. The surface phenomenon has been observed on many dielectrics , semiconductors  and metals , whereas the formation of bulk nanostructures has been reported so far only in a few transparent wide band-gap dielectrics [8,9].
There are a number of emerging applications based upon nanostructures induced by femtosecond laser pulses [10–13], even though the mechanisms that govern their formation, both at the surface and in the bulk, still remain to be ascertained [14,15]. Recently, femtosecond pulses with spatially variant states of polarization (i.e., vector pulses) have started being used to produce complex sub-wavelength nanopatterns on solid surfaces, which follow the distribution of light polarization in the pulses [16,17]. In fact, even very tightly focused vector pulses have been able to imprint nanoscale structure of their electric field in the focal region into the material .
Here, we demonstrate that the formation of nanostructures also allows one to increase the precision of micromachining with femtosecond laser pulses by purposefully arranging their polarization structure. To show this we drill and scribe fused silica (SiO2) and crystalline silicon (Si) substrates with tightly focused vector and scalar femtosecond pulses and compare the results by using scanning electron microscopy (SEM).
2. Experimental setup
The materials processing experiments were performed in ambient air using either fixed spot irradiation (i.e., drilling regime) or by moving the sample perpendicular to the laser beam propagation direction z (i.e., scribing regime) using the experimental setup that is schematically shown in Fig. 1. The linearly polarized output beam of a femtosecond Ti:sapphire amplifier with a central wavelength of λ = 775 nm is first spatially filtered. In order to synthesize femtosecond vector pulses, i.e., radially and azimuthally polarized pulses, we start with converting the output linearly polarized pulses into single-charge circularly polarized vortex pulses by using the step phase mask M followed by the quarter-wave plate λ ∕4 and ensure that the polarity and the handedness of the vortex pulses are of opposite signs (Fig. 1) . Then we let the vortex pulses propagate along the optical axis of the uniaxial crystal CR which is placed between the negative lens L1 and the positive lens L2. Radially and azimuthally polarized fields are eigenmodes of any c-cut uniaxial crystal, with their waists being axially shifted with respect to each other due to double refraction in the crystal . The azimuthally and radially polarized pulses can therefore be discriminated with the pinhole P by shifting it together with L2 along the z axis (Fig. 1). A detailed description of this method can be found elsewhere .
Scalar pulses are generated using the same optical setup by simply removing M and CR from the optical path in the case of circularly polarized pulses and by additionally replacing λ ∕4 with the half-wave plate λ ∕2 in the case of linearly polarized pulses (Fig. 1). The half-wave plate is required to vary the orientation of the electric field vector in the xy-plane, whereas the handedness of the circularly polarized pulses is changed with λ ∕4. After P, the pulses are re-collimated and directed to the microscope objective O. The negative corrector lens C is placed in front of O to compensate for spherical aberration, which is introduced when finite conjugate distance optics (i.e., O) is used for focusing collimated beams. The pulse duration before O is:200 fs (FWHM) in all the cases based on collinear autocorrelation measurements.
3. Results and discussion
Under our experimental conditions (see captions to Fig. 2), micromachining of SiO2 is evidently influenced by the formation of nanostructures. In the drilling regime (Fig. 2, left-hand panels), the nanostructures self-organize exactly perpendicular to the dominant local electric field component in the focal region , except for circular polarization (i.e., Fig. 2(c)), in which case they form a chiral, propeller-like pattern whose handedness follows the handedness of the light [12,19]. The boreholes and grooves produced with azimuthally and radially polarized pulses (i.e., Figs. 2(a) and 2(b)) are significantly larger and wider than their counterparts produced using circularly and linearly polarized pulses (i.e., Figs. 2(c)-2(e)). This happens because the fundamental TEM00 scalar laser mode (i.e., the common Gaussian beam) can generally be focused tighter than higher order transverse laser modes, including the ring-shaped radially and azimuthally polarized TEM01* vector mode. The 1/e2 radius of the TEM00 scalar modes is nominally 21/2 times smaller than the spot size of the TEM01* vector modes, defined in the latter case as the radius at which the intensity drops to 1/e2 of the intensity of the outermost peak [20,21]. In order to keep the peak intensity at the sample approximately constant, the pulse energy in our experiments, in accordance with , was e times higher for the vector pulses than for the scalar pulses. The same applies to the micromachining of Si shown in Fig. 3. Strictly speaking, this approach is valid only for azimuthally polarized pulses which, no matter how tightly they are focused, preserve their original ring-shaped transverse intensity distribution in the focal plane . The total electric field of azimuthally polarized pulses in the focal region always remains purely transverse. This is also true of weakly focused radially polarized pulses. As the focusing becomes tighter, the electric field of these pulses in the focal region attains a noticeable longitudinal component (i.e., z-component), which can exceed the magnitude of the transverse component at focusing angles approaching 1 radian. For strongly apodized radially polarized light pulses  or continuous wave beams  the longitudinal electric field component can be much stronger than the transverse component. We estimate that in our experiments the two components were of approximately equal strength.
The layout of the nanostructures affects the borehole morphology in two ways. First, it determines the cross-sectional shape of the borehole. For instance, drilling with linearly polarized pulses results in strongly elongated boreholes, whereas boreholes produced with azimuthally, radially and circularly polarized pulses preserve the axial symmetry of the beam. Secondly, the smoothness of the borehole wall depends on whether the nanostructures grow parallel or at an angle to the wall. In this respect, radially polarized pulses, which create cylindrically shaped nanostructures arranged coaxially with the walls, offer an advantage over azimuthally, circularly and linearly polarized pulses. In the scribing regime, however, it is linearly polarized pulses with the electric field vector oriented perpendicular to the cutting direction that give the best results as the nanostructures in this case are aligned along the grooves and do not disrupt their walls (Fig. 2(e), middle panel). When the light intensity is kept close to the nanostructure formation threshold (Fig. 2(e), right-hand panel), such pulses can produce solitary 20 nm-wide grooves (Fig. 2(e), bottom image), whereas low intensity pulses with the other states of polarization presented in Fig. 2 generate irregular, much wider nanostructure patterns.
Micromachining of Si (Fig. 3) exhibits similar trends. Specifically, drilling with radially polarized pulses produces deeper and smoother boreholes, whereas scribing with linearly polarized pulses with the electric field vector oriented perpendicular to the cutting direction results in smoother, narrower and deeper grooves. In the case of Si, however, light-induced nanostructures are not present in all the SEM images shown in Fig. 3 and their role in explaining the observed results can be revealed only by analyzing the full set of the laser-processed samples. Low spatial frequency LIPSS with a period of ~450 nm are formed in the scribing regime using linear polarization (Fig. 3(d)), whereas sub-wavelength high spatial frequency LIPSS having a period of ~100 nm are produced in the drilling regime with azimuthal and circular polarizations (Figs. 3(a) and 3(c)). In the scribing regime, the transition from uniform ablation to the formation of well-defined nanostructures is observed only for the linear polarization oriented perpendicular to the cutting direction Fig. 3(f). Such a transition is clearly seen in the right-hand portion of the ablation line in Fig. 3(f) where the pulse energy is kept below the nanostructure formation threshold. A similar phenomenon involving the evolution of material modification from being uniform to one consisting of ellipsoidal ablated/modified regions was reported both on the surface and inside SiO2 samples in  and . This evolutionary development is in agreement with the predictions of the nanoplasmonics model  according to which polarization-dependent ablation or bulk modification of solids results from the local field enhancement during the interaction of the laser pulse with the plasma produced by its leading edge. For undercritical plasma density the enhancement is expected to occur perpendicular to the light’s polarization direction, whereas for overcritical plasma density it should coincide with this direction [2,25]. A faster ionization rate taking place in the regions with an enhanced electric field leads to an asymmetric plasma density profile and, assuming that the energy transfer from electrons to the lattice is localized and coincides with the shape of the plasma, to the elongation of ablated/modified regions either parallel or perpendicular to the polarization [2,25]. As the laser focus is moved continuously, order is imposed in the newly exposed material by the modes of the plasma grating seeded by the existing nanostructures  and polarization dependence of the whole ablation process is therefore preserved.
The formation of nanostructures is essentially a multi-pulse laser irradiation process involving such phenomena as memory in nonlinear ionization  and optical erasure [19,26]. Any material that undergoes such major transformations is expected to have quite different properties compared with its original state. A crystalline material, for instance, can become amorphous , which may explain why the formation of LIPSS is insensitive to the orientation of the semiconductor crystals relative to the polarization of the incident pulses .
It is also instructive to compare our results with those from other studies on the role of the beam polarization in femtosecond laser materials processing. It was found earlier that for a wide range of experimental conditions the beam polarization does influence the cutting or drilling rate, kerf width, borehole geometry, and edge quality [28–31]. The overall phenomenon is interpreted in terms of polarization-dependent reflection/absorption of the laser light on the walls and bottoms of the grooves or boreholes, which is described by the Fresnel equations [28,29]. Linearly polarized laser pulses are hence absorbed differently depending on the cutting direction [29,30], whereas the absorption of vector pulses whose polarization distribution possesses cylindrical symmetry becomes independent of the cutting direction . Interestingly, similar to our findings, laser cutting of semiconductors with linearly polarized femtosecond pulses in  and  also produced deeper grooves with straighter edges when the pulses were polarized perpendicular to the cutting direction and inhomogeneous kerf development was observed when the polarization was aligned along the cutting direction. The experiments in the above references, however, were conducted with weakly focused laser pulses and usually at light intensities well above the ablation threshold. Under such conditions, the sheer geometric scale of laser machining easily obscures the fine morphology of the hole or groove walls and, as a consequence, the contribution of the concomitant nanostructures to the material removal process .
In our experiments, in order to perform nanoscale laser machining of SiO2 and Si substrates, we have used very tightly focused femtosecond pulses with the light intensity close to the ablation threshold of these materials. In this regime, the formation of polarization-sensitive nanostructures plays a dominant role in determining the morphology as well as the ultimate precision of laser-micromachined features. As a result, drilling with radially polarized femtosecond pulses produces the best results as far as the quality of the boreholes is concerned, whereas linearly polarized pulses with the electric vector oriented perpendicular to the cutting direction are best suited for micromachining of grooves. Taking into account the widely different properties of the substrates used in our experiments, we anticipate that femtosecond laser micromachining of other materials will maintain these trends.
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