1. Introduction

During the last decade, the formation of laser-induced periodic surface structures (LIPSS, ripples) upon irradiation with femtosecond (fs) laser pulses has gained new attraction (see the review articles [1–5]). For strong absorbing materials such as silicon, typically so-called low-spatial-frequency LIPSS (LSFL) are observed with periods Λ close to the irradiation wavelength λ and with an orientation perpendicular to the laser beam polarization [1,6]. These LSFL are generated by interference of the incident laser radiation with a surface electromagnetic wave (SEW), generated at the rough surface, which might include the excitation of surface plasmon polaritons (SPPs) [3,7,8].

While there are numerous publications on “static experiments” reporting parametric dependencies of the LIPSS characteristics on irradiation wavelength, fluence, number of pulses per spot, polarization, environment, etc. (see the references in [1–5]), the temporal evolution of the formation of LIPSS has been studied much less. Currently, the dynamics of LIPSS is investigated in three complementary approaches, i.e., (i) by pump-probe diffraction [9–11], (ii) by pump-probe imaging [12,13], or (iii) in distributed energy deposition experiments by means of temporally shaped pulse sequences [14–25].

For the latter case, the formation of fs-LIPSS on silicon surfaces has already been studied in double-fs-pulse experiments of varying delays Δt in the picosecond range, using Ti:sapphire laser radiation at 800 nm wavelength [17,18,21]. A characteristic decay of the LSFL rippled area A_LSFL has been observed for increasing Δt [18], while the LSFL period Λ_LSFL ~λ is almost independent on the delay [17]. Later, using an SPP based theoretical model, the delay dependence of the LSFL area was quantitatively analyzed in numerical simulations [20]. That approach allowed us to identify the Auger recombination process as the dominant inter-pulse carrier relaxation mechanism accounting for the decrease of A_LSFL on the timescale of ~10 ps [24].

Most of the double-pulse experiments on fs-LIPSS formation were performed at the same irradiation wavelength. Only very few studies employ synchronized irradiations at different wavelengths [22,23,25]. As an additional parameter, the polarization state was manipulated (rotated by 90°) within the irradiation sequence [14,22]. Recent experiments with fused silica, using parallel [23] or cross-polarized [25] two-color (UV: 400 nm & IR: 800 nm) double-fs-pulse sequences for irradiation, revealed a sharp transition of the LIPSS morphologies from UV-LSFL (Λ_LSFL,UV ~400 to 500 nm) to IR-LSFL (Λ_LSFL,IR ~600 to 800 nm) when crossing the zero delay. These experiments evidenced that, for fused silica, the first pulse of the double-pulse sequence dominates the energy deposition into the material and always determines the orientation of the LSFL [23,25]. These findings are in good agreement with recent two-color pump-probe experiments of Mouskeftaras et al. [26].

In this work, we extend these experiments on fused silica and our previous single-color studies on silicon [17,18] by using both, parallel and cross-polarized two-color double-fs-pulses for the generation of LIPSS on single-crystalline silicon wafer surfaces. This approach provides an additional and independent test of the validity of SPP-based models for the formation of fs-LIPSS on silicon.

2. Experimental

A commercial regenerative Ti:sapphire fs-laser system (Spectra Physics, Spitfire) was operated at 250 Hz to generate linearly polarized laser pulses of τ = 50 fs duration at a center wavelength of λ = 800 nm. The laser pulse energy E was measured by a pyroelectric detector (Molectron/Coherent, 3Σ, J25LP-3A). An electromechanical shutter allowed the selection of a desired number of laser pulses. These single-fs-pulses were transformed into double-fs-pulse sequences by a conventional Mach-Zehnder interferometer (N_DPS: number of double-pulse sequences).

Figure 1 provides a schematic of the experimental setup. The femtosecond (fs) laser beam was divided by a beam splitter (BS) into two parts. In one of the interferometer arms [“UV (ultraviolet) arm”, UVA], a barium borate (BBO) crystal was inserted for frequency conversion (λ_UVA = 400 nm). The polarization direction of the resulting second harmonic radiation (UVA) is rotated by 90° with respect to the fundamental radiation [λ_IRA = 800 nm in the “IR (infrared) arm”, IRA]. A computer-controlled motorized translation stage in the UVA allowed the change of the interferometer arm length, resulting in cross-polarized double-fs-pulse sequences with two different wavelengths and a variable delay. Optionally, a half-wave plate was inserted to the UVA to generate parallel polarized double-pulse sequences.

 

Fig. 1 Mach-Zehnder interferometer based experimental setup for the generation of double-fs-pulse irradiation sequences with two different wavelengths (400 and 800 nm) and parallel or crossed polarizations. Abbreviations: BS: beam splitter, BBO: barium borate crystal for frequency conversion, DM: dichroic mirror, λ/2: optional half-wave plate, ∆x: spatial translation, ∆t: temporal delay, c: speed of light.

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The temporal delay Δt between the two pulses was systematically varied between –10 and + 10 ps, with a resolution better than ~0.15 ps [23]. For negative delays, the IR laser pulse arrives at the sample surface prior to the UV laser pulse, while for positive delays the order of arrival of the two pulses is reversed. After passing a beam combining dichroic mirror (DM), the collinear double-pulse sequences were focused normally onto the surface of a single-side polished silicon wafer of ~400 µm thickness [(111) crystal orientation, n-doped, Werk für Fernsehelektronik, Berlin, Germany]. The samples were positioned in the focal plane of a spherical dielectric mirror with f = 75 mm focal length. All irradiation experiments were performed in ambient air. For both wavelengths, the resulting Gaussian beam radii (1/e²) were determined in single-pulse experiments using a method by Liu [27] to be w_0,UV ~10 µm and w_0,IR ~18 µm. The same method was used to quantify at both wavelengths the ablation threshold fluences (F_th,UV and F_th,IR) of silicon upon irradiation with the corresponding number of single-pulses (N_SPS) for comparison. In the following we refer to the peak fluences F_0,UV and F_0,IR, which were determined from E accordingly. The pulse energy E was individually controlled for each interferometer arm. For that purpose, an attenuator consisting of a half-wave plate (for the corresponding wavelength) in combination with a linear polarizer, was utilized (not shown in Fig. 1).

Scanning electron microscopy (SEM) was performed to characterize the laser-generated surface morphologies. Based on the corresponding micrographs, one- and two-dimensional Fourier transforms (FT) revealed the most frequent period and the period range of the LIPSS, respectively.

3. Results and discussions

Figure 2 shows a series of SEM micrographs of a silicon surface after laser irradiation by a constant number of two-color double-pulse sequences (N_DPS = 10). The different columns [Figs. 2(a)-2(d)] represent the surface morphologies for varying double-pulse delays between −6.66 ps ≤ Δt ≤ + 6.66 ps. The double arrows in Fig. 2(a) indicate the orientation of the polarization of both pulses (IR: red arrows and UV: blue arrows) arriving to the sample for parallel (upper row) and cross-polarized (lower row) pulse sequences. The peak fluence for each wavelength was chosen below the respective ablation threshold, i.e., F_0,IR = 0.5 × F_th,IR(10) = 0.12 J/cm² and F_0,UV = 0.7 × F_th,UV(10) = 0.08 J/cm². Hence, only the joint action of both pulses modifies the surface permanently.

 

Fig. 2 Scanning electron micrographs (13.4 × 13.4 µm²) of the surface of silicon after irradiation by N_DPS = 10 two-color double-fs-pulse sequences at four different delays [(a): Δt = −6.66 ps, (b): Δt = −0.06 ps, (c): Δt = + 0.06 ps, (d): Δt = + 6.66 ps]. The fluence of both pulses (IR/UV) was kept below the corresponding damage threshold [IR: F_0,IR = 0.5 × F_th,IR(10), UV: F_0,UV = 0.7 × F_th,UV(10)]. The red and blue double arrows in (a) indicate the orientation of the polarization of both pulses (IR and UV) for parallel (upper row) and cross-polarized (lower row) sequences.

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For a negative delay of Δt = −6.66 ps [see Fig. 2(a)], IR-LSFL with an orientation perpendicular to the polarization of the IR-pulse (always vertical) were observed for both, parallel or cross polarized double-pulse sequences. Here, the IR-pulse arrived first to the sample, as indicated by the curly brackets below the figure. The corresponding periods Λ_LSFL,IR ~750 nm are close to the IR laser wavelength of 800 nm. In silicon, an LSFL orientation perpendicular to the polarization and a periodicity close to the laser wavelength is well known for 800 nm fs-laser irradiation [1,8,28]. Consequently, the first (IR-)pulse determines the spatial characteristic of the LIPSS here. At the given delay, the second (UV) pulse does not affect the LIPSS morphology.

On the other hand, for a very small negative delay of Δt = −0.06 ps [Fig. 2(b)], predominantly UV-LSFL with periods around Λ_LSFL,UV ~450 nm cover the center of the ablation spot. These UV-LSFL are oriented horizontally after irradiation with parallel polarized double-pulses (upper row), while their orientation is vertical after irradiation with cross polarized double-pulses (lower row). Hence, these LSFL are aligned perpendicular to the polarization direction of the UV-pulse in both cases. Additional experiments with UV single-pulse sequences (results not shown here for brevity) confirmed this characteristic behavior for UV-LSFL on silicon (period close to the UV-wavelength and an orientation perpendicular to the polarization). Thus, the UV-pulse dominates the LIPSS morphology here, regardless its arrival at the surface shortly after the IR-pulse.

The irradiation spots for the corresponding positive delay of Δt = + 0.06 ps are displayed in Fig. 2(c). In this case, the UV-pulse arrived first as indicated by the curly brackets below the figure. IR-LSFL with periods of Λ_LSFL,IR ~700 nm dominate the morphologies and cover the central area of the irradiated spot. Some UV-LSFL are present but much less pronounced and appear only in the outer region of the spots. For both cases (parallel or crossed polarization) they are oriented perpendicular to the polarization direction of the UV-pulse. Their periods around Λ_LSFL,UV ~420 nm almost coincide with the UV-wavelength. For larger positive delays of Δt = + 6.66 ps [Fig. 2(d)], again solely IR-LSFL with periods around Λ_LSFL,IR ~720 nm are observed always perpendicular to the polarization of the IR-pulse.

The SEM images depicted in Fig. 2 clearly indicate the dominance of the IR-pulse for absolute delay values |Δt| > 2 ps, independent on the order of arrival of the UV- and the IR-pulse to the sample surface. For absolute delays smaller than |Δt| ≤ 2 ps, both the UV- and IR-pulse contribute to the resulting surface morphologies, where UV-LSFL as well as IR-LSFL coexist. Moreover, the experiments using either parallel or cross-polarized pulse sequences allow a clear identification of the LIPSS type and the associated wavelengths. This is exemplified in the delay range |Δt| ≤ 2 ps, where a rotation of the UV-LSFL by 90° is observed between the two cases [compare the upper and the lower row of Figs. 2(b) and 2(c)].

3.1 LIPSS periods

For a more detailed investigation and quantification of the LSFL periods, the SEM images obtained at different delays were subjected to one- (1D-FT) and two-dimensional (2D-FT) Fourier transforms. The characteristic peaks in the 1D-FT, which were evaluated in the direction perpendicular to the corresponding LSFL orientation, provided the most frequent LSFL period. In addition, an evaluation of the peaks in the 2D-FT of the SEM images revealed the complete signature of the LSFL in the Fourier space and allowed the determination of an upper and a lower limit of Λ_LSFL, and can be visualized by error bars.

Figure 3 displays the LSFL periods quantified for the cross-polarized two-color double-pulse experiment in the delay range Δt between −8 and + 8 ps. The data were evaluated by 1D-/2D-FT analyses of a full series of 13.4 × 13.4 µm² sized SEM images with identical irradiation parameters (N_DPS = 10, F_0,IR = 0.5 × F_th,IR /F_0,UV = 0.7 × F_th,UV) - as for the four examples given in Fig. 2 (lower row). The periods of the IR-LSFL (Fig. 3, red full circles) are almost constant between 680 and 750 nm over the entire delay range −6.66 ≤ Δt ≤ + 6.66 ps, regardless the order of arrival of the UV- and IR-pulses. UV-LSFL coexist with the IR-LSFL only for −2 < Δt < + 2 ps and, again, exhibit constant periods close to the UV laser wavelength (Λ_LSFL~390 to 450 nm, Fig. 3, open blue circles).

 

Fig. 3 LSFL period Λ_LSFL upon irradiation with N_DPS = 10 double-pulse sequences for a fixed peak fluence ratio between the IR- and the UV-pulses [IR: F_0,IR = 0.5 × F_th,IR(10), UV: F_0,UV = 0.7 × F_th,UV(10)] obtained by Fourier-analyses (1D/2D) as a function of the double-pulse delay Δt. The full circles indicate the most frequent period obtained from the (1D) power spectral density while the error bars visualize the entire period range deduced by 2D-Fourier transform of the SEM images.

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This behavior of delay-independent LSFL periods (even crossing the zero delay) is significantly different from the case of fused silica irradiated under similar sub-threshold conditions. For that dielectric material, a characteristic step-like change from values close to the IR-LSFL periodicities to that of UV-LSFL periodicities was observed upon crossing the zero-delay for changes in Δt of less than 0.1 ps [25]. In other words, while in fused silica the first pulse arriving to the surface always determines the LSFL periods and also their orientations, the situation for silicon is more complex, indicating that different mechanisms are causing the LSFL in both materials.

3.2 LIPSS covered areas

Apart from the LSFL spatial periods, the rippled surface areas were evaluated from the same series of SEM images (N_DPS = 10, F_0,IR = 0.5 × F_th,IR /F_0,UV = 0.7 × F_th,UV). Figure 4 shows the LSFL area A_LSFL for the cross-polarized two-color double-pulse experiment performed in the delay range Δt between −8 and + 8 ps. For negative delays (IR-pulse arrives first), the rippled area varies between 20 and 35 µm². A step-like increase of A_LSFL can be seen at Δt = 0 ps, while for positive delays (UV-pulse arrives first) the rippled area is between 55 and 75 µm².

 

Fig. 4 LSFL rippled area A_LSFL upon irradiation with N_DPS = 10 double-pulse sequences for a fixed peak fluence ratio between the IR- and the UV-pulses [IR: F_0,IR = 0.5 × F_th,IR(10), UV: F_0,UV = 0.7 × F_th,UV(10)] obtained from SEM images as a function of the double-pulse delay Δt.

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The changes in the rippled area, different by a factor of more than two between positive or negative double-pulse delays, clearly evidences that the wavelength of the first pulse arriving to the sample plays a crucial role in the LSFL formation – even if this is not directly manifested in the delay dependence of their spatial periods (previously shown in Fig. 3).

3.3 Two-color plasmonic model of LSFL on silicon

For a detailed understanding of the fs-LIPSS on silicon upon polarization controlled two-color double-pulse irradiation, the differences in the optical properties of silicon at the two different wavelengths (400 & 800 nm) and the plasmonic origin of these nanostructures must be considered. As listed in Table 1, the optical constants (n: refractive index, k: extinction coefficient), accounting for the dielectric permittivity ε_Si = (n + i k)², are significantly different here. This arises from the physical nature of the optical absorption process and particularly manifests in widely varying values for the optical penetration depths [1/α = λ/(4 × π × k)]. At 800 nm wavelength the optical absorption is mediated via phonons as an indirect transition, while at 400 nm wavelength electrons can be directly promoted from the valence band into the conduction band without the involvement of phonons. While the 800 nm (IR-) radiation penetrates at low intensities approx. 10 µm into the silicon wafer material, the 400 nm (UV) radiation is absorbed within a sample depth of ~80 nm only. Hence, for the generation of a large number of conduction band electrons at the surface using a two-color double-pulse sequence under sub-threshold conditions, it is beneficial when the UV-pulse arrives first, as the following IR-pulse can then be efficiently absorbed in a shallow superficial layer by the carriers generated by the UV-radiation in direct transition. In contrast, when the IR-pulse arrives first, its energy is deposited via indirect transitions in a two orders of magnitude larger depth and only a shallow superficial part of these carriers can absorb additional photons from the UV-pulse. As a consequence, for a fixed sub-ablation IR/UV peak fluence ratio, considerably higher carrier densities can be achieved when the UV-pulse arrives prior to the IR-pulse. The effect may be even stronger if the transient increase of the absorption coefficient by the laser-generated carriers is considered [29].

Table 1. Optical properties [n: refractive index, k: extinction coefficient] of single-crystalline silicon (c-Si) at the IR and UV laser wavelengths. Data taken from [30]. The optical penetration depth (1/α) was calculated from the absorption coefficient α = 4 × π × k/λ.

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Recently, we have shown in numerical simulations of double-fs-pulse irradiated silicon, that the LSFL rippled area can be associated with the laser-induced “SPP-active area”, which is determined by two criteria [20,24]:

(Criterion I) a number density threshold of laser-excited electrons in the conduction band has to be exceeded (N_e ≥ N_th^SPP) to turn the semiconductor silicon transiently into a metallic state, which allows for SPP excitation at the air/silicon interface [ℜe{ε_Si*(N_e)} < −1], and

(Criterion II) the incident laser pulse and electromagnetic field of the laser-excited SPPs have to interfere temporally, which most efficiently occurs during the maximum of intensity of the laser pulses.

This interference between the laser radiation and the electromagnetic field of the SPP spatially modulates the energy deposited to the laser-excited electronic system. After electron-phonon interaction and carrier relaxation in the ps-range [20], this leads to a modulated material removal from the surface via ablation. The induced “SPP-active area”, thus, is a prerequisite for the LSFL formation. Following that idea and additionally considering the spatially Gaussian fluence profiles of the focussed (IR/UV) laser beams, it becomes clear that the increased electron density (due to the arrival of the UV pulse prior to the IR pulse) also directly affects the size of the “SPP-active areas”.

Based on this discussion and the observations related to Figs. 1 to 4, an SPP-based fs-LIPSS formation scenario is proposed here for the two-color double-pulse irradiation of silicon. It is sketched in Fig. 5 and outlined in detail in the following. The key element in understanding the diversity of the different LIPSS morphologies and their delay dependence lies in the fact that the carrier density threshold for SPP excitation N_th^SPP strongly depends on the laser wavelength. This can already be seen within the frame of a Drude model for the optical constants of the fs-laser-excited silicon (for details see [8,20,29]). Based on that Drude model, and using the condition ℜe{ε_Si*(N_th^SPP)} = −1, the wavelength dependence of the electron density threshold can then explicitly be written as

 

Fig. 5 Schematic of SPP-based LIPSS formation upon two-color double-pulse irradiation of silicon. In each sub-figure (a)-(d) the lower graph visualizes the temporal intensity (I) arriving at the sample surface. The upper graph shows the corresponding electron density (N_e). Note that I is scaled linearly while N_e is scaled logarithmically. The wavelength dependent threshold densities for SPP excitation (N_th^SPP) are indicated by red (800 nm) and blue (400 nm) horizontal dashed lines. The hatched circles mark the moment of interference between the laser beam radiation and the laser-generated SPP (red: 800 nm, blue: 400 nm).

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where m_e* = 1.64 × 10⁻³¹ kg denotes the effective optical electron mass [31], ε₀ is the dielectric permittivity of the vacuum, ε_Si(λ) is the dielectric permittivity of the non-excited silicon, e is the electron charge, c is the vacuum speed of light, and ν⁻¹ = 1.1 × 10⁻¹⁵ s represents the carrier collision time in fs-laser-excited silicon [31]. This choice of a constant carrier collision time can be justified by the excellent agreement of the Drude model calculations with the time-resolved experimental data presented by Sokolowski-Tinten et al. in [31]. From the refractive index data given by Palik in [30] (see Table 1), the dielectric permittivities of the non-excited silicon are calculated as ε_Si(400 nm) = [5.567 + i 0.386]² = 30.84 + i 4.298 and ε_Si(800 nm) = [3.693 + i 0.006]² = 13.64 + i 0.048. Using Eq. (1), carrier density threshold values of N_th^SPP(400 nm) = 4.1 × 10²² cm⁻³ and N_th^SPP(800 nm) = 5.3 × 10²¹ cm⁻³ are obtained. Hence, the carrier density threshold for SPP excitation is almost one order of magnitude larger for the UV-wavelength when compared to the IR-wavelength.

The four scenarios sketched in Figs. 5(a)-5(d) all directly correspond to the surface morphologies previously shown in Figs. 2(a)-2(d). The two carrier density thresholds N_th^SPP at 800 nm and 400 nm wavelengths are schematically indicated as dotted horizontal (red and blue) lines in all sub-figures. Each sub-figure displays the temporal intensity distribution of the double-pulse sequence (lower graph, white background) along with the associated dynamics of the electron density at the sample surface (upper graph, gray background). While the intensity is drawn in a linear scale, the electron density N_e is sketched in a logarithmic scale here to consider the two very different density thresholds. Moreover, it should be underlined that the abscissa always displays the time t elapsed at the sample surface and does not represent the interpulse delay Δt. The zero value of time (t = 0) is defined here by the arrival of the intensity maximum of the first pulse hitting the surface since it initiates the whole subsequent carrier dynamics.

For large negative delays [Δt ≤ −2 ps, Fig. 5(a)] the IR-pulse arrives first and generates an electron density N_e ≥ N_th^SPP(800 nm), which allows the excitation of SPP at the IR-wavelength [Criterion I]. During the pulse intensity maximum, interference with the SPP field [Criterion II] spatially modulates the deposited energy with an IR-LSFL pattern (this process is indicated by a horizontally hatched red circle in the graph). Subsequently, N_e starts to decrease via relaxation processes such as Auger recombination, carrier diffusion, etc [24]. The second (UV-)pulse of the sequence increases again the electron density. As the threshold density for SPP excitation at 400 nm wavelength is almost one order of magnitude larger than at 800 nm, the maximum electron density created by the UV-pulse does not exceed N_th^SPP(400 nm). Consequently, the second (UV-)pulse may “amplify” (reinforce) the carrier density pattern seeded by the first IR-pulse, but causes no additional spatial modulation of the deposited energy via plasmonic effects. As a result, after energy relaxation (electron-phonon coupling) and ablation, the silicon surface exhibits solely the LSFL pattern initially imprinted by the IR-pulse, as it can be seen in Fig. 2(a).

For small negative delays [-2 ps ≤ Δt ≤ 0 ps, Fig. 5(b)], again, the first pulse can excite SPP at 800 nm wavelength. Since the electron density does not significantly decrease between the arrival of the IR- and the directly following UV-pulse, the latter one can then drive the electron density above the threshold for SPP excitation at 400 nm wavelength N_th^SPP(400 nm). Via interference with the SPP fields, the UV-LSFL pattern (indicated by a vertically hatched blue circle in the graph) is imprinted into the carrier density distribution and finally into the surface topography [see Fig. 2(b)]. As the pulses at both wavelengths were capable to excite SPPs, the signatures of both processes are visible as coexisting IR-LSFL and UV-LSFL in Figs. 2(b) and 3. However, as the UV-pulse arrived later at the surface, its UV-LSFL pattern clearly dominates the surface morphologies here [see Fig. 2(b)].

For small positive delays [0 ps ≤ Δt ≤ + 2 ps, Fig. 5(c)], the UV-pulse arrives prior to the IR-pulse. As already mentioned, significantly higher carrier densities can be achieved when the UV-pulse arrives prior to the IR-pulse. The UV laser pulse induced electron density N_e exceeds the SPP excitation threshold at 400 nm N_th^SPP(400 nm) and, via interference with the laser pulse, the UV-LSFL pattern is imprinted to the carrier distribution at the surface. The following IR-pulse already interacts with a quasi free-electron plasma of a density more than ten times the SPP threshold value at 800 nm wavelength N_th^SPP(800 nm). As a consequence of the spatially Gaussian beam profile, a large surface area is then “SPP-active” for the second pulse and IR-LSFL dominate the surface morphologies [see Fig. 2(c)]. Simultaneously, significantly enlarged LSFL areas are observed in the corresponding delay regime of Fig. 4, when compared to the negative delay range.

For large positive delays [Δt ≥ + 2 ps, Fig. 5(d)], the first UV-pulse generates an ample sized SPP-active area at 400 nm wavelength. A significant part of the electrons excited by the first pulse have already relaxed when the second (IR-)pulse arrives more than one picosecond later to the surface. This IR-pulse can still excite SPPs at 800 nm wavelength [N_e,max ≥ N_th^SPP(800 nm)] and imprints the associated interference pattern to the surface. As the IR-pulse arrives clearly after the UV-pulse and generates a large SPP-active area, the IR-LSFL then dominate the surface morphologies [see Fig. 2(d)].

In summary, the proposed two-color plasmonic LIPSS model successfully explains all essential experimental observations, i.e., (i) the dominance of the UV-LSFL in the small negative delay range (−2 ps ≤ Δt ≤ 0 ps) as well as the dominance of the IR-LSFL for all other delays up to ± 6.66 ps (Fig. 2), (ii) the partial coexistence of the IR-/UV-LSFL and the independence of their periods on Δt (Fig. 3), and (iii) the significantly increased LSFL rippled area for positive delays, when compared to negative delays (Fig. 4).

4. Conclusions

Multiple (N_DPS = 10) two-color sequences of parallel or cross-polarized double-fs-pulses (τ = 50 fs, λ = 400 & 800 nm) were used for the irradiation of single-crystalline silicon surfaces under sub-ablation conditions, where only the joint action of both pulses leads to the generation of LIPSS. Upon systematically varying the delay Δt of the two fs-pulses between −8 ps and + 8 ps, a diversity of the appearance of two types of LIPSS (IR-LSFL and UV-LSFL) was observed. This behavior is significantly different from that for dielectric materials (fused silica) where always the first pulse determined the LSFL period and their orientation [23,25]. Fourier-analyses of the LIPSS morphologies on silicon revealed almost constant periods for each LIPSS type (IR-LSFL: 680 to 750 nm, UV-LSFL: 390 to 450 nm) as well as their coexistence for |Δt| < 2 ps. In contrast to the periods, the LIPSS covered areas show a strong dependence on Δt, manifesting in an approximately twice enlarged rippled area for positive delays when compared to negative values. All these experimental observations were successfully explained by an extension of our single-color plasmonic model of LSFL formation upon double-fs-pulse irradiation of silicon [20,24]. As a key element, it takes into consideration the wavelength dependent critical carrier density required for the excitation of SPPs. These two-color experiments further confirm the importance of the ultrafast energy deposition to the silicon surface for LIPSS (LSFL) formation and additionally evidence their plasmonic origin.