1. Introduction

Optical near-fields in the vicinity of metal or dielectric microstructures upon external illumination display complex patterns that can be used for nanoscale imprinting on substrate surfaces.[1, 2, 3, 4] This is a promising concept for nanoprocessing large regular patterns, for example by arranging colloidal particles to form closed-packed layers that act as a mask. This approach has been used with different types of surfaces and for various particle materials and shapes.[5, 6, 7, 8, 9, 10] Engineered structures exploiting the focal points of the colloids become realizable in practice by angular beam scanning[11]. It is generally known that the resulting patterns not only correspond to a linear superposition of the optical near-fields of the single particles, but also that particle interaction and mutliple scattering effects become important for touching particles in a colloidal monolayer.[12] Recent FDTD simulations for periodic boundary conditions in a Si particle monolayer have been used to identify optimum particle array and irradiation parameters for maximum field enhancement at the substrate surface near the contact point with the particle. [13] Moreover, collective effects in the resulting 2D photonic crystal produce a wealth of features, beyond a single region of field enhancement as typically reported and exploited, which enlarge the suite of achievable imprinting structures. In this combined experiment-theory study, we address the optical near-fields imprinted by colloidal particle arrays to gain insight into the underlying mechanisms of pattern formation.

2. Experiments

We use chalcogenide phase-change substrates to record and subsequently image the near-field light intensity with subwavelength resolution.[14] Upon irradiation with short laser pulses, a change from the crystalline to the amorphous phase is induced in regions where the local intensity is large enough, effectively mapping complex intensity patterns for varying illumination conditions with great detail.[15, 16, 17] The phase transition induced is also accompanied by a change in material density, topography, and electric conductivity, which makes scanning electron microscopy (SEM) a suitable high-resolution read-out technique.[18] We have applied this method to study the near-field distributions of 2D hexagonally arranged arrays of polystyrene (PS) spheres (n_PS = 1.58, κ = 0.003 at λ = 800nm) as a function of several experimental parameters, as illustrated in Fig. 1(a). The substrates consist of 40-nm-thick, face-centered-cubic (fcc) polycrystalline Ge₂Sb₅Te₅ (GST) films [15, 16, 17] sputter-deposited on Si [001] wafers covered by a 10-nm-thick amorphous SiO₂ buffer layer (Numonyx, Italy). The complex index of refraction (n + iκ) of these materials at the experimental laser wavelength (800nm) is 5.72 + 4.09i for fcc-GST[19], 4.74 + 1.45i for amorphous GST[19], 1.453 + 0i for amorphous SiO₂, and 3.69 + 0.006i for Si. Closed-packed monolayers of spherical PS particles (diameters 817nm and 1704nm, Microparticles GmbH, polydispersity 2.6%) were self-assembled on a water surface and then deposited onto the substrate. Given their large Mie parameter $\frac{2\pi }{\lambda }\frac{n_{\text{PS}}d}{2}\gg 1$, each particle produces collimating lensing, involving the participation of many multipoles up to a high order.

 

Fig. 1 (a) Hexagonal lattice of polystyrene spheres with an underlying calculated near-field pattern, which is imprinted into a GST substrate. The calculation details are as in (d) (see below). The incident light is p-polarized and has wave vector along a nearest-neighbors bond direction (ϕ = 0°). (b) Dispersion diagram showing the reflection coefficient |r| of a closed-packed monolayer of polystyrene spheres on an fcc GST planar substrate. (c)–(e) Near-field associated with specific points in the dispersion diagram for a = 817 nm (see corresponding symbols in (b)). Wavelengths and angles of incidence used: (c) λ = 409 nm, θ = 40.8°; (d) λ = 799 nm, θ = 52.2°; (e) λ = 925 nm, θ = 30.0°.

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Laser irradiation of the particle covered films was performed in air using a regeneratively amplified Ti:sapphire laser system operating at 800nm central wavelength with a pulse duration of 350ps. The laser beam was focused onto the sample at an angle of incidence θ = 52.2° to a measured elliptical spot size of 270 × 150 μm² (1/e² diameter). A single pulse was selected from a 100Hz pulse train by means of an electromechanical shutter to irradiate the targeted area. The sample was mounted on a motorized 3D translation stage and observed with a home-built microscope for in-situ control. Subsequent to laser irradiaton, the particles were removed with a scotch tape in order to access the patterns because the laser irradiation at the fluences required for imprinting the near-field patterns did not lead to removal of the particles. Additionally, images were taken using a Gemini Ultra Plus field emission scanning electron microscope (SEM) operated at 5kV and yielding 5nm spatial resolution.

3. Results and interpretation

We performed multiple scattering calculations using a layer-KKR approach[20, 21, 22, 23] for periodic particle arrays, which are converged with respect to both the number of multipoles used for each sphere and the number or reciprocal lattice vectors in the layer-substrate coupling. Fig. 1(b) shows the calculated band diagram for a hexagonal PS sphere monolayer on crystalline GST. The upper triangular region above the light line ( $k=\frac{\omega }{c}{n}_{\text{PS}}\equiv k_{\Vert }$) allows us to identify configurations of particle diameter a (equal to the lattice spacing in the closed-packed structures), incident wavelength $\lambda =\frac{2\pi }{k}$, and incidence angle (related to the parallel wave vector through k_‖ = k sinθ) associated with resonant optical modes, where high local field enhancement is expected. Incidentally, the kinematical small-particle bands given by |k_‖ − G_nm| = k, where G_nm runs over reciprocal lattice vectors (superimposed curves in Fig. 1(b)), differ from the numerical bands due to inter-particle interaction (see Supporting Information (SI) for more details).

The remarkable diversity in the near-field distribution patterns at the GST-air interface for selected points of the band diagram (see Fig. 1(c)–(e)) clearly illustrates the large sensitivity of the imprinted structures to geometrical and illumination parameters. This allows a rich variety of patterns to be created that display the periodicity of the colloidal monolayer mask. Notice that the change in the particle size-to-wavelength ratio of the patterns shown in Fig. 1 varies the complexity of the near-fields. The near-field intensity is given as the ratio of the intensity I directly beneath the GST surface normalized by the intensity of the incident field I₀. This indicates the absorbed field intensity that produces phase-change nanoimprinting.

In Fig. 2 we compare simulations for fixed azimuthal sample orientation and increasing angles of p-polarized light incidence. The imprinted intensity drops with increasing angle of incidence, but it acquires a more complex structure, presumably due to the involvement of a richer structure of modes, as observed in the dispersion diagram of Fig. 1(b) with increasing k_‖.

 

Fig. 2 Imprinted near-field intensity calculated for increasing angles of incidence with fixed azimuthal sample lattice rotation ϕ = 21°, particle size a = 1730 nm, and p-polarized light of wavelength λ = 900 nm. Gray circles signal particle positions. The maximum of intensity beneath the GST-air interface is given in each figure, while the color scale is normalized as indicated in the lower color bar. The imprinted intensity drops for increasing inclination.

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Additionally, pattern complexity is influenced by the incident-light polarization, see Fig. 3. From here on, light is considered to be coming from the left in all figures. The upper panels show measured SEM images of structures created with a single laser pulse at an angle of incidence of 52.2°. The dark spots at position II in Fig. 3(a) can also be found in regions that were not irradiated, and thus, they are not associated with light irradiation effects (see SI, Fig. 2). They can only be detected with the inlens detector, indicating they are small modifications of the GST surface that result from adsorbants deposited at the PS spheres contact region. They are therefore suitable to determine the position during illumination of the spheres even after their removal. In contrast, the dark regions with a brighter circle inside (position I) are a direct result of irradiation. By comparison with optical micrographs, the observed modifications of the GST film can be attributed to amorphization of the otherwise crystalline film (outer ring) and ablation (enclosed by the bright rim). [18] A relevant parameter is the lattice orientation angle ϕ relative to the light incidence direction (see inset of Fig. 3(c)). Regions of similar orientation ϕ were selected in Fig. 3, so the main differences between panels (a) and (b) is the light polarization (s and p, respectively). While displaying only a simple elliptically shaped maximum at I for s polarization, the imprint is more complex for p polarization. Beside the main maximum at IV, which is still well pronounced, several less intense features are revealed (see III), including an auxiliary maximum at the contact point V, which can not be observed for s polarization. The remarkable modifications observed in the spatial patterns when the light polarization is changed can be traced back to the involvement of several array modes for any given light frequency and direction of incidence. Their excitation strongly depends on the orientation and amplitude of the in-plane electric field vector of the incoming light, see Fig. 1 (b). Essentially, different polarizations couple with different strengths to these modes, thus producing different spatial patterns. The same arguments apply to the variations on the produced patterns with the angle of incidence (Fig. 2) and the lattice rotation that we discuss in the following.

 

Fig. 3 Influence of incident light polarization on the imprinted near-field for λ = 799 nm, a = 1704 nm, and θ = 52.2°. Gray circles in the calculated graphs indicate the sphere-substrate contact points. Measured SEM images (a,b) are compared with theory (c,d) for the following parameters: (a),(c) s-polarization, and lattice rotation ϕ = 22.3° (see inset to (c)); (b),(d) p-polarization, ϕ = 20.6°.

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The lower panels in Fig. 3 depict our corresponding calculations with grey circles superimposed to indicate the positions of contact points. The agreement between theory and experiment is good. In particular, the occurence of multiple local maxima as well as their detailed shape and position depending on the laser polarization is well reproduced in the calculations. As indicated in Fig. 1(c), the number of near-field maxima is not limited by the number of particles and can exceed it.

The dependence on the lattice orientation relative to the projected light incidence direction (angle ϕ) is discussed in Fig. 4. The left (right) side corresponds to ϕ = 41° (ϕ = 23°). Symmetry is reduced with respect to the horizontal axis and significant differences between both of them are observable in the detailed shape of the position of the near-field maxima relative to the spheres.

 

Fig. 4 Influence of lattice rotation ϕ on the imprinted near-field for a = 817 nm and p-polarized light incident with λ = 799 nm and θ = 52.2°. Gray circles signal contact points in the calculated images. Measured SEM images (a,b) (acquired with a sideways detector that is insensitive to the contact-point surface modifications) are compared with theory (c,d) for ϕ = 41° in (a,c) and ϕ = 23° in (b,d).

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We want to emphasize that the intensity pattern produced by a colloidal monolayer cannot be described by a simple superposition of patterns produced by single spheres, without considering particle interactions. To demonstrate this, we have performed an experiment using conditions for imprinting a relatively simple pattern (Fig. 5(a)), which we compare with calculations both for the multiple scattering method noted above (Fig. 5(c)), as well as with a simple superposition of the scattered field of each individual particle[14] (single scattering, Fig. 5(d)). The latter was carried out for a hexagonal lattice of 11 × 11 particles, neglecting collective effects such as multiple scattering from neighboring particles. This superposition model does not reproduce the position of the dominant intensity maxima, which are predicted to lie much closer to the contact points than found experimentally. At the same time, the multiple scattering model predicts a distance between maxima and contact points that is in agreement with experiment. Notice that the contact points are more pronounced here than in Fig. 3, presumably as a result of slightly varying conditions during sample preparation. Furthermore, the intensity maxima calculated with the superposition model display considerably different shapes and amplitudes with respect to those measured in Fig. 5(a) or calculated with the full model. This demonstrates that the patterns produced cannot be explained by simple interference of incoming and scattered light because each particle reacts to significant field contributions originating in scattering from its neighbors. The experimental conditions in Figs. 3 and 5 are very similar, with only a small variation in both lattice rotation and particle size. However, the imprinted patterns look different, thus emphasizing the sensitivity small parameter changes.

 

Fig. 5 (a) Observation of an imprinted pattern imaged with a SEM inlens mode detector. The sample and illumination parameters are λ = 799 nm, a = 1730 nm, θ = 52.2°, p-polarization, and ϕ = 26.4°. The single lattice defect is marked by an arrow. No perturbation in the imprinted near-field pattern is observed. (b) Optical microscopy image of a different, larger region of the same monolayer before irradiation, showing the presence of single defects (vacancies). (c) Multiple- scattering calculation of the corresponding full lattice (no defect). (d) Simple superposition model.

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A remarkable feature can be observed in Fig. 5(a): the absence of a single contact point (at the position marked by a dashed circle), indicating that the particle at this position might have been missing in the monolayer during illumination. Such lattice defects in form of vacancies are frequently observed in colloidal monolayers, as shown in Fig. 5(b). Despite this defect, the imprinted pattern in Fig. 5(a) features the corresponding main maximum next to the defect, just as if there was no defect. We speculate that the strong collective interaction between the particles might render the optical response of the monolayer robust against the presence of lattice defects, featuring collective photonic crystal-like properties. Yet, we cannot exclude the possibility that the defect was not a vacancy but a particle slightly elevated above the substrate, thus not forming a contact point but contributing in a slightly different way to the optical response. Nonetheless, both explanations imply that the imprinted patterns are not too sensitive to small displacements and structural defects of the colloids. Further analysis of the degree of tolerance against monolayer defects is still needed.

4. Conclusion

In conclusion, we have experimentally imaged the complex optical near-fields of colloidal monolayers by imprinting them on thin GST films. The measured intensity distributions are in excellent agreement with electromagnetic simulations. This simple yet effective concept is well suited for nanostructuring and mapping arbitrary intensity distributions with high spatial resolution, which can be implemented directly for large scale fabrication on other substrates. The imprinted near-fields inherit the full translational invariance from the colloidal monolayer. At the same time, by studying the influence of various setup parameters, we conclude that the detailed near-field distribution is not only determined by the particle arrangement but also strongly depends on light polarization and angle of incidence. In particular, the number of near-field maxima is not limited by the number of particles and can be increased by the proper choice of illumination conditions. The orientation of the lattice with respect to the light incidence direction is found to have a significant impact on the near-field distribution, thus providing an additional degree of freedom to tailor patterned imprinted structures.