Truncated Gaussian-Bessel beams for short-pulse processing of small-aspect-ratio micro-channels in dielectrics.

In order to control the length of micro-channels ablated at the surface of dielectrics, we use annular filtering apertures for tailoring the depth of focus of micrometric Gaussian-Bessel beams. We identify experimentally and numerically the appropriate beam truncation that promotes a smooth axial distribution of intensity with a small elongation, suitable for processing micro-channels of small aspect ratio. Single-shot channel fabrication is demonstrated on the front surface of a fused silica sample, with sub-micron diameter, high-quality opening, and depth of few micrometers, using 1 ps low-energy (< 0.45 µJ) pulse. Finally, we realize 10 × 10 matrices of densely packed channels with aspect ratio ~5 and a spatial period down to 1.5 μm, as a prospective demonstration of direct laser fabrication of 2D photonic-crystal structures.


Introduction
Bessel beams have attracted great attention since firstly demonstrated by Durnin [1]. Such beams can maintain their transverse shape invariant over quite long propagation distance, denoted as "diffraction-free". Moreover, they have the capability to reconstruct themselves behind a small obstacle, exhibiting high robustness during propagation [2]. These features make Bessel beams attractive in the field of super-resolution imaging [3], optical manipulation [4,5], and laser machining [6][7][8][9][10]. In the context of deep drilling with ultrafast laser pulse in transparent materials, zero-order Bessel beam shows its decisive advantages over Gaussian beam, that can be summarized in terms of penetration geometry, nonlinear robustness and interaction phenomenology [11,12]. In particular, a Bessel beam overcomes to certain extent the transient surface plasma screening effects that limit Gaussian beam applicability to depths of hundreds of nanometers [13], since it permits extended penetration of the laser pulse inside the bulk material. Ultrahigh aspect ratio (depth/diameter) channels exceeding 1200:1 have been reported [14] by using femtosecond (fs) micro-Bessel beams. Juxtaposing several nanochannels has proven its efficiency for cutting or cleaving transparent samples [15].
Bessel-beams have also been considered as interesting tools for the fabrication of photonic-crystal structures [16]. In this context, the characteristic dimensions of the fabricated channels or holes are critical. For instance, in integrated optics, 2D photonic crystal structures providing novel optical functions like super-prism, negative diffraction/refraction [17] or photonic band gap [18,19] are usually composed by a block of periodically arranged holes. Typically, these holes are desired to have taper-free profiles, hundreds of nanometers in diameter and a few micrometers in depth. Despite the effectiveness of short-pulse-duration Gaussian-Bessel beams for drilling high aspect ratio channels, it is quite challenging to precisely manipulate the characteristics of the fabricated holes and to access diverse aspect ratios. In our previous work [20], we demonstrated the front-surface fabrication of moderate aspect ratio micro-channels in fused silica by Gaussian-Bessel laser pulse of picosecond (ps) duration. High quality taper-free channels with excellent cylindrical shape, mean diameter of ~1.2 µm and length of ~40 μm were fabricated. However, further downscaling of the spatial characteristics of these channels is still required.
Fabricating taper-free channels (from the front surface) with aspect ratio of a few units is challenging. Highly focused Gaussian beams are not well suited to this aim, because: (i) strong absorption of the beam in the first hundred(s) of nanometers of the material may drastically limit the accessible depth, so the crater profile does not replicate the beam profile [13], and (ii) considering a radial energy relaxation profile, a Gaussian-Bessel beam is prone to reduce channel tapering with respect to Gaussian beam, and also to avoid non-uniform crater profiles observed in the literature [21]. However, it is not straightforward for a Gaussian-Bessel beam to directly fabricate channels with aspect ratio of a few units. This requires dedicated engineering of the beam. Shaping the spatial phase and/or the amplitude was shown to be effective in tailoring the intensity distribution. For instance, the side lobes of a conventional Bessel beam can be eliminated by introducing a specially designed binary phase plate in the beam path before the axicon [22]. Beam filtering at the Fourier plane of a 4f optical system with a stopper and aperture efficiently suppresses the undesired axial modulation [23]. The axial intensity profile can also be customized: by using spatial light modulators that enable to engineer the beam propagation, on-axis intensities with uniform, increasing/decreasing [24,25] or length-tunable profiles [26] have been demonstrated. In the present work, we use a simple and convenient solution -near-field filtering with an annular slit -to tailor the depth of focus (DOF) of the Gaussian-Bessel beam, and we show the interests of this technique to machine short-length microchannels on the front-surface of transparent dielectric materials.
The paper is organized as follows. First, we generate and characterize a truncated Gaussian-Bessel (TGB) beam that preserves the merit of Bessel beams and has about one quarter the DOF of the initial Gaussian-Bessel beam. To support our development, we analyze numerically the influence of the annular slit width on the spatial beam distribution. Then we use our customized TGB beam to perform single-shot ablation experiments on the front surface of a fused silica sample at different pulse energy and for the two pulse durations of 25 fs and 1 ps. The geometrical characteristics of the ablated channels are characterized by optical microscopy and scanning electron microscopy. Finally, we demonstrate that under proper processing conditions, arrays of non-through channels matching the requirements for the fabrication of photonic integrated circuits (submicron opening size, aspect ratio < 10, repeatability with high accuracy) are accessible.

Generation and characterization of a short-DOF beam by truncation of a Gaussian-Bessel beam
The experiment is performed with the beam line 5A (1 mJ, 100 Hz, 25 fs, linearly polarized, 800 nm) of the Ti:Sapphire ASUR laser platform (Applications des Sources Ultra-Rapides) of LP3 laboratory. The schematic of the beam shaping setup is shown in Fig. 1(a). It basically consists of an axicon (Altechna, 1-APX-2-H254-P, n = 1.45, nominal base angle = 1°) providing a first Bessel region, and a 4f demagnification optical system (with a factor of 50) made of a lens (f 1 = 500 mm) and a microscope objective (20 ×, NA = 0.4, f 2 = 10 mm, Mitutoyo NIR, working distance 20 mm) to get a second Bessel region (with half conical angle of 21.4° in air) adapted for micromachining. The setup and characteristics of the optical elements used are the same as in [20] except that here we further tailor the beam by inserting specially designed annular apertures in the beam path, just after the axicon. These annular apertures are home made by laser peeling treatment on metal-coated (600 nm thick copper film) glass sli 3. To achieve accumulated a is further var experiments promising res channel fabric is precisely po via a motoriz in the single s  mpact on aracterize e beam is mm) on a nning and d stacking arison, the Note here for easier does not l near the axicon tip apex, which leads to the typical horn-shape at the beginning of the Gaussian-Bessel beam and the intensity oscillations along the propagation axis [24,27]. The mean size of the central lobe of the beam is estimated as ~840 nm and DOF ~80 μm at full width at half maximum (FWHM).
A straightforward technique to achieve a Bessel beam with shorter DOF is to truncate the incident Gaussian beam with a circular aperture [28]. However, in view of keeping away the undesired effects from the imperfect apex of the axicon, that induce intensity modulations along the propagation axis, we additionally block the central area of the beam. To this aim, we thus place an annular aperture, with width of 420 μm and mean radius of 1185 µm to perform beam truncation just next to the axicon. The insertion energy loss of the annular slit was measured to be relatively high, approximately 86%, but this is not detrimental for the present experiments since we dispose of a large reserve of energy. The TGB beam is shown in Fig. 1(c). The size of the central lobe is slightly increased (~970 nm at FWHM), and interestingly a slight inverse tapering profile of the beam is observed. These effects come from the fact that the slit truncation causes wave diffraction. Finally, the TGB beam obtained here not only clearly shows a shorter DOF, from ~80 μm (Gaussian-Bessel beam) to ~20 μm, but also it has a smoother axial intensity profile and a better stability of beam distribution than the initial Gaussian-Bessel beam in practice. Figure 1(d) plots the normalized axial intensities of these two beams, and shows their relative axial positioning.

Simulation of the truncated Gaussian-Bessel beam
In this section, the propagation of the truncated beam is simulated, in order to justify our choice of the appropriate annular slit width, and to identify the limitations of this method to get the shortest uniform DOF. The simulation is performed only in the first Bessel region due to the paraxial conditions required by the scalar Fresnel diffraction theory. However, the beam propagation in the second Bessel region is closely related to the first region through the 4f system taking into account its image relay function (with a demagnification factor of 50 and 2500, respectively in transversal and axial directions).

Modeling of propagation
Free wave propagation can be described according to the Fresnel diffraction integral [29]: , h x y is the convolution kernel containing the quadratic phase term [29]: Discretizing the two terms in Eq.

U m n and ( )
, h m n , and making use of the convolution theorem, the above-mentioned convolution calculations can be switched to two Fourier transforms and one inverse Fourier transform (see Eq. (3)). The reason of this mathematical treatment is to improve the computing speed thanks to the fast Fourier transform (FFT) algorithm.   nt a divergent mitation of this cording to the e Fig. 2(a) is the We chose this xperimental re axicon, which Z = 70 mm to 4 he normalized arried out in t of the beam ar at three typica ig. 2(c) to con tal result. For oth simulation a DOF of the ed annular ape One can clearly the slit width rmalized accor of these image beam (full be ot of Fig. 3(a)

Characte
For compariso each case, the as 30 nJ at low by a single sh influence.
As shown objective (Nik When irradiat 25 fs pulse d middle image and same ene pulse. As the a single hole 25 fs case, a energy is appl as 28 μm can lobes is also v  Fig. 4, the kon, LV-UEPI ting with energ uration, a foot e of Fig. 2(c

Channel
The character size of the ch channels is ex and high orde nted to reveal the comes from the to er characterize Fig. 5). The c ce was coated w JSM-6390). Ei e evolution of in Fig. 4  The two a which a singl length of the ablation. We when 25 fs pu the subject of pulses underg inherent facili absorption, st from the ener [33]. In our c ral hole, counti is choice is th for both pulse volution upon ote that, for the n the center. , but the coun he present wo s not constant o e, we use the m evolutions of t lotted as a func d 6(b). 6 ons below arding the for deep accessed ributed to ed that ps due to the nonlinear eam away ic sample n a more stationary way and waste less energy than fs pulses before the laser pulse deposits its energy in the material in the intense central core volume. Note that it has been shown that Bessel beams with low cone angle are more vulnerable to nonlinearities [32]. Increasing the latter could be a route for reducing the limitation observed with ultrashort (25 fs) pulses. Finally, Bhuyan et al. [34] reported that, at low cone angle of 7° in fused silica, chirping laser pulses from fs to ps regime can be an effective strategy to fight against the poor stability of nonlinear Bessel beams, and to improve the energy deposition efficiency for bulk material modification, which is in support of our experimental result. Similar conclusions were also obtained by Garzillo et al. [35] in a different glassy material (BK7).
The most interesting range for short-length channel processing (1 ps case, E < 0.5 µJ) is plotted in Fig. 6(c), regrouping the evolution of channel diameter and length. It clearly shows that small aspect ratios, in the range of ~5, with sub-micrometric opening diameter, can be obtained using 1 ps pulses of low energy. The shortest channel length could approach the level of one micron with the lowest energy applied here of 0.28 μJ. Moreover, comparing the in-depth transverse profiles at different depths (using for example the case of energy of 0.36 µJ in Fig. 4), we observe that the diameter of the channel does not vary significantly, in agreement with previous experiments and dedicated analysis [20]. Using post-mortem polishing procedure, it is possible to further decrease the aspect ratio by removing calibrated thicknesses of matter at the sample surface, as also demonstrated in [20]. This way, taper-free holes with even smaller aspect ratio (in the range 1-5) and diameter opening below the upper wavelength of visible range are reachable when small-energy 1 ps pulses are used.

Processing of matrices of channels
Finally, to highlight the interest of the tailored short TGB laser pulses and their flexibility for single step direct writing of two-dimensional photonic crystal structures, we fabricated square matrices of 10 × 10 channels with spatial pitch of respectively 5 μm, 3 μm, and 1.5 μm (see Figs. 7(a)-7(c)). They are processed sequentially by using single pulses of 1 ps duration and 0.36 μJ energy, corresponding to channel dimensions of 680 nm in diameter and 3.6 µm in length (see Fig. 6(c), which is used as a look-up table). We chose these parameters on the basis of the results shown above.
The obtained matrices show densely-packed channels, that are regular in terms of morphology, with little residual side effects (such as bump, melted zone, etc.) around the opening of every channel. Indeed, the surrounding affected zone is << 100 nm (much below the inter-channel spacing, even in the 1.5 µm case). Fluctuations in the separation of channels are observed, which is mainly attributed to the limitations of the translation stage. Note the pollutants on surface become more apparent when smaller separations are applied due to the increasing density of residues. Air-blowing or liquid immersion strategies can be considered during the laser ablation for improvement in future works.
To confirm the void nature of the channels in bulk, the sample surface is repeatedly polished, metalized and characterized by SEM. As an example, we show in Fig. 7(d) the sample surface of the 5 µm pitch matrix when 0.5 μm material thickness is removed by polishing away. The filling of the channels (see the white spots in SEM) is attributed to post processing polishing substances. Indeed, these fillings have been identified as CeO 2 from Energy Dispersive Spectroscopy (EDS) coming from 2.5 μm CeO 2 powder used for sample polishing, see Fig. 7(e). The dark spots in Si image (Fig. 7(f)) explicitly indicate the lack of a-SiO 2 , thus confirming the void formed there.

Conclusio
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