Introduction

Colloidal particle lens arrays (or contact particle lens arrays, CPLAs) proved to be a convenient tool for laser nanostructuring of materials [1–8]. The monolayer of dielectric micro- or nanospheres placed right on the surface acts as an array of near-field lenses that focus the laser radiation into the multitude of distinct spots, allowing formation of many structures in a single stage. Examination of the effect of the powerful femtosecond laser radiation on transparent materials mediated by the CPLA near-field focusing mask reveals new aspects of fundamentals of laser-matter interactions. At the same time, nanostructured surfaces can be employed for numerous applications in photonics and bio-medicine [8]. High focusing ability of microspheres in combination with high nonlinearity of the material response to irradiation by the femtosecond pulses provides an opportunity for fine-structuring of the material surfaces. On the contrary, multiple rescatterings of the laser light within the array of spheres [9–12] can diminish the advantages of the considered setup.

In this work, we study nanostructuring of polymethylmethacrylate (PMMA) and glass substrates using a Ti:Sapphire laser facility delivering single pulses of 50 fs duration at a millijoule energy level. CPLA composed of micrometer-sized polystyrene (PS) spheres is employed as a near-field focusing tool. The goal of this paper is to show the advantages for nanostructuring of conversion of some part of the laser energy to the second harmonic by a nonlinear crystal placed into the femtosecond beam. Recently, efforts to provide a more efficient modification of materials by optimization of the femtosecond pulse shape typically via spectral phase modulation have been reported [13–15]. The idea is that the more powerful front part of the pulse efficiently promotes seed electrons by multi-photon ionization, while the following tail could be effective in the impact ionization process. In this communication, we would like to draw attention to the importance of optimization of the frequency spectrum of a pulse by harmonic generation. The second harmonic can also be a powerful tool for generation of seed electrons [16]. We show below that the second harmonic (SH) has additional advantages over the fundamental frequency (FF) when CPLA is used as a focusing device and that simple conversion of even a small amount of pulse energy into the second harmonic can change the result of the modification.

Theoretical considerations

In this section, we consider several reasons why conversion of some part of the beam energy into the second harmonic could be useful for the CPLA-mediated nano-structure formation.

For the laser intensity level more than 10¹² W/cm² and a short pulse duration of about 50 fs, any modification of a material that is linearly transparent at the wavelength of the irradiation is caused by ionization (or electron excitation from the valence to the conduction band). For such a short pulse length, either multiple photon or tunnel ionization mechanism dominates, depending on the value of the adiabatic (Keldysh) parameter, ${\gamma }_A$ [17]. If ${\gamma }_A>>1$, then the direct transition from the ground state to the conduction band can be interpreted as a multi-photon transition with rate given by $W_{\omega }\propto I_{\omega }^K$. For the typical cases described below, the value of ${\gamma }_A^{}=1$ corresponds to the intensity$I\approx {10}^{14}W/c{m}^2$. Here, the ionization rates at FF and at SH can be estimated as

For the intensity levels below 10¹⁴ W/cm², one can estimate from Eqs. (1) that conversion of a few percent of the initial pulse energy into the second harmonic can significantly increase the multi-photon ionization rate (see [16] for detail). When the intensity approaches the value at which ${\gamma }_A\cong 1$, the difference between W_ω and W_2ω becomes less pronounced. Nevertheless, we can conclude that at the same laser intensities not exceeding $I\approx {10}^{14}W/c{m}^2$, ionization is more efficient at SH than at FF. Combined effect of FF and SH, as is shown in [16], can be more effective than that of FF and SH applied separately because the seed electrons generated by SH can be multiplied by the impact ionization process promoted by FF. Thus, when some part of the laser energy is converted into SH, one can expect a lower modification threshold.

When the laser light is focused by means of a spherical microlens, the strong field maximum is formed beneath the sphere. The smaller wavelength of SH compared to FF allows the microlens to focus the light into a smaller spot. Indeed, FDTD calculation of the field intensity distribution on glass surface beneath the polystyrene sphere (our experimental conditions) shows that irradiation at SH results in about a factor of 1.9 smaller focal spot compared to FF. This ratio roughly matches the ratio of wavelengths. This calculation was performed for a sphere of 1 μm diameter. The plane wave approximation was used for the wide slowly converging beam employed in the experiment. The wavelength at FF is 800 nm. The refractive indices of PS and glass are 1.59 and 1.46, respectively. The widths were calculated as Gaussian fit of the intensity distribution in the substrate near its surface in the direction matching the incident wave polarization. MEEP parallel code [19] was used for the calculations.

As is seen from Eq. (1), the multi-photon absorption order at FF is twice that at SH. However, the ionization rate profile provided by SH is still a factor of $1.9/\sqrt{2}\approx 1.3$ narrower than the one provided by FF. Even with allowance for the different orders of the multi-photon absorption processes, SH is advantageous over FF for the localized material modification.

When CPLAs are employed for the laser beam focusing, coupling of the spherical modes of the constituent microspheres results in multiple cross scatterings of light within the array. Thus, the spherical particles in the closely packed arrays do not act as independent microlenses. Some of the practically important coupling effects can be understood by using a simplified concept of the “effective medium” formed for a spherical particle within the array by its environment, including other spheres and the substrate [12]. Such a medium with the refractive index $n>1$ weakens the focusing ability of a spherical lens. However, this deteriorative effect may be different at the FF and SH wavelengths. To illustrate this, we calculated and compared the field distributions in the setup described above and in the modified setup, where the sphere was surrounded by six similar neighbors, forming a planar, closely packed, hexagonally symmetric cluster. For both the SH and the FF, the presence of the neighbors results in a smaller enhancement and a weaker localization of the field beneath the central sphere. The local maximum of the field intensity at the substrate surface is degraded by a factor of 2.4 at FF and only by a factor of 1.9 at SH. Due to the neighbors, the width of the intensity maximum is increased by a factor of 1.4 at FF and by a factor of 1.2 at SH.

Thus, calculations show that the CPLA focusing systems provide a better field localization at SH than at FF. As was argued above, conversion of only a small fraction of the beam energy into SH can significantly lower the modification threshold. This also means that even if the major part of the energy remains in FF, the localization of the modification process would be governed by SH at near-threshold fluences. Thus, more localized structures can be obtained, which is observed experimentally.

Experimental

Polystyrene spheres (Sigma-Aldrich Co.) with about 1-μm diameter (standard deviation <0.1 μm) were deposited on both the PMMA (JSC DOS) and the glass plate (microscope slides by ApexLab Co.) substrates. A suspension with selected concentration of microspheres was prepared in order to obtain a monolayer after draining a drop of the suspension on an oblique substrate. The angle of the incline was adjusted for the best result. Finally, monolayers comprising well-arranged, closely packed hexagonal arrays of microspheres were obtained. Imperfections in obtained arrays rely on the size dispersion of the deposited spheres. Each of the closely packed domains had hundreds of particles. We used diffraction of the CW laser beam on the deposited array for rapid control of prepared samples. Hexagonal diffraction pattern indicated the well-arranged areas which were suitable for the further laser processing.

In our experiments, we used the Titanium Sapphire laser system Spitfire-Pro (Spectra Physics Co.) in a single-shot regime. The pulse duration was 50 fs, the energy of a single pulse was 1.7 mJ, the central wavelength was 800 nm, and the beam diameter was 7 mm. A flat-convex lens with a focal length of 15 cm was used for the beam focusing. We studied the formation of periodic pit and hillock (hole and bump) nano-structures in different irradiation regimes. The samples were irradiated by single femtosecond pulses of fundamental frequency (FF), of the second harmonic (SH), or by bi-chromatic FF + SH pulses. A thin (100 μm) BBO crystal (oee or II type) was used for the SH generation with a maximal integral efficiency of 5%. Crystal orientation was varied for the efficiency (phase matching) adjustment. The crystal was placed after the lens to avoid space separation of the FF and SH pulses [20]. A blue glass filter (absorbance A₄₀₀<0.02, A₈₀₀>20, 3 mm thick) was used for the SH selection. The fluence was changed by moving the sample along the axis of the focused beam, keeping it far from the air breakdown area. In what follows, when speaking about the fluence of a bi-color pulse, we assume the fluence of FF alone before matching the BBO orientation.

Atomic force microscope “Solver Pro” (NT-MDT) was used for the substrate surface analysis. The best-resolution and clear pictures were successfully obtained by the intermittent contact-mode scanning technique.

When the fluence of the laser pulse is increased above a certain threshold level (threshold intensity is about 5x10¹¹W/cm² for SH + FF and 10¹² W/cm² for FF), the spheres are eliminated from the substrate within the irradiated area. This process is similar to the cleaning phenomenon [21]. When increasing the fluence up to fifteen percent from the cleaning threshold, we obtain well-defined structures. They are ablation craters on PMMA substrates and swelling bumps on glass substrates (see Fig. 1). For glass substrates, the elimination threshold, and correspondingly the fluence of the structure formation, are almost twofold lower in the case of irradiation by an FF + SH combination compared to the sole FF. For PMMA substrates, this difference proves to be even more pronounced.

 

Fig. 1 Typical AFM picture of obtained structures on the surface of PMMA (a) and glass (b) substrate after irradiation by FF + SH.

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In both cases, the fluence of the structure formation for the FF + SH irradiation is significantly smaller than the fluence of cleaning for irradiation by the FF alone.

The addition of SH results in more localized structures both on glass and PMMA substrates, allowing one to reach an ablation-pit radius of about 100 nm. This is seen in Fig. 2 showing typical substrate profiles after the irradiation for fluences close to the threshold. The statistics presented in Fig. 2(c) show that the widths of the craters created as a result of PMMA irradiation by either the FF + SH or the sole SH are close to each other and smaller than for the sole FF.

 

Fig. 2 Profiles of the ablation pits on PMMA (a) and the swelling hillocks on glass (b) after the irradiation by either FF or SH + FF. The SH + FF diagram (b) is multiplied by 10. Full width at half maximum (FWHM) of the structures is indicated. Statistics (c) of FWHM of ablation craters on PMMA for the minimal sufficient energies of laser pulses. 20 surface profiles are averaged for calculating the standard deviations for each of the cases: FF, FF + SH, and SH.

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When filtering out the FF radiation and keeping the SH alone, the structures appear only if the sample is shifted closer to the focus of the beam relative to the position at which the FF + SH structuring occurs. The shift provides an SH fluence that is an order of magnitude higher than that in the FF + SH beam taking into account the attenuation by the filter. This means that FF radiation in a bi-color beam significantly contributes to the modification process.

Discussion

Typical profiles of ablation craters at the threshold fluences are shown in Fig. 2(a). Under these conditions, though the FF + SH profile is smaller in both longitudinal and radial directions, irradiation by both the FF + SH and the sole FF creates ablation craters of comparable volumes. The case is different with the glass irradiation. The threshold for the sphere removal by SH + FF radiation is almost two times lower than by FF. However, for the fluence levels close to threshold, the height of the structures obtained with FF + SH is an order of magnitude lower than the height of the structures obtained with a sole FF. The explanation relies on the different physical mechanisms of the sphere elimination and the hump formation.

Figure 3(a) shows calculated longitudinal distributions of the multi-photon ionization rates within the substrate provided by irradiation of the sphere within the cluster by either FF or SH. It is seen that the ionization rate profile at FF has two pronounced maxima, the first of which is at the surface and the second is about 3 μm deeper in the substrate. The first maximum is responsible for the sphere elimination, which is governed by the thermo-mechanical shock resulted from the sudden near-surface material heating. The height of a swelling hump, as it follows from the simplest relaxation model [22], is determined by the integral heating within the whole light penetration layer. In view of this, the ionization (and thus the heating) in both maxima are related to the hump formation.

 

Fig. 3 Normalized longitudinal ionization rate distribution within the substrate (glass) just below the sphere (polystyrene, d = 1μm). The blue curve shows SH (two-photon ionization) and the red curve, FF (four-photon ionization). a) The sphere is surrounded by 18 neighbors; b) single sphere.

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The addition of SH bursts the ionization efficiency near the surface, thus halving the sphere removal threshold. However, SH does not have any pronounced maximum within the layer of the in-depth FF absorption. A twofold decrease in FF energy at the threshold results in a 16-fold decrease in the ionization rate at the second maximum with allowance for the fourth order of muti-photon absorption at FF. Contribution of the in-depth heat to the swelling is reduced accordingly. This explains the phenomenon of the smaller swelling humps in the case of irradiation by bi-chromatic laser pulses. It is important that the explanation comes from the consideration of the cross-scattering effects in CPLA arrays. As is seen in Fig. 3(b), the single-sphere setup does not provide any in-depth field maximum, which is important for the model. The ‘long focus’ phenomenon provided by CPLA is studied in [12].

Conversion of a part of the energy of the fundamental frequency into the second harmonic beyond the focusing lens precludes spatial separation of the SH and FF signals. If the BBO crystal were located before the lens, the FF pulse would go first and the SH pulse behind. Our calculations of temporal intensity distributions of the fundamental frequency and of the second harmonic within a bi-chromatic pulse at the output of a BBO crystal taking into account the dispersion of group velocity shows that in this case both pulses (FF and SH) propagate together. It is clear, however, that for a more efficient use of the bi-chromatic pulses, the SH pulse should be the leading one. Corresponding calculations showing the optimal time distance between the pulses and respective experimental implementation will be the subject of our next paper.

Conclusions

Experimentally, we demonstrate accurate 100-nm pit and hillock structures resulting from irradiation of the closely packed arrays of polystyrene micrometer-sized spheres deposited on polymethylmethacrylate and glass substrates by powerful laser pulses of 50 fs duration from a Titanium Sapphire laser system.

We discuss the advantages of using the second harmonic over the fundamental frequency. These include the higher sensitivity of the material, the tighter localization of the modification, and the reduced effect of light rescattering within an array of spheres.

It is shown that conversion of about 5 percent of the laser pulse energy into the second harmonic provides a decrease in the modification threshold and a change in the morphology of obtained structures. The results indicate that for the near-threshold fluences, the localization of the modification process is governed by SH, resulting in production of finer structures.