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Laser induced periodic surface structures (LIPSS or ripples) were generated on single crystal germanium after irradiation with multiple 3 µm femtosecond laser pulses at a 45° angle of incidence. High and low spatial frequency LIPSS (HSFL and LSFL, respectively) were observed for both s- and p-polarized light. The measured LSFL period for p-polarized light was consistent with the currently established LIPSS origination model of coupling between surface plasmon polaritons (SPP) and the incident laser pulses. A vector model of SPP coupling is introduced to explain the formation of s-polarized LSFL away from the center of the damage spot. Additionally, a new method is proposed to determine the SPP propagation length from the decay in ripple depth. This is used along with the measured LSFL period to estimate the average electron density and Drude collision time of the laser-excited surface. Finally, full-wave electromagnetic simulations are used to corroborate these results while simultaneously offering insight into the nature of LSFL formation.
© 2015 Optical Society of America
1. Introduction
Femtosecond laser induced periodic surface structures (LIPSS) have been actively investigated over two decades and are now gaining further interest due to the broad industrial applications in surface modifications such as solar cells [1], colorization [2], waveguides [3], surface enhanced Raman scattering [4] and many other applications. LIPSSs may form on metals, semiconductors, and insulators but exhibit quite different characteristics (e.g. ripple periodicity and orientation) depending on the laser parameters, experimental environments, and material properties. They are typically classified by two distinct categories according to the scale of ripple period: low spatial frequency LIPSS (LSFL, period > λ/2) and high spatial frequency LIPSS (HSFL, period < λ/2) [5]. Recently, under femtosecond laser irradiation at 800 nm, both LSFL and HSFL formation have been reported on the surface of silicon [6, 7]. However, there have been few publications investigating LIPSS formation on germanium, another key semiconductor like silicon, and, to the best of our knowledge, none in the mid-IR region. Strong field physics at mid-IR region has also generated great interest because of its ponderomotive scaling [8] and promise of new sources of high harmonic generation [9], supercontinuum generation [10], nanoplasmonics [11], etc. Current trends in laser technology is also advancing rapidly in intense field mid-IR sources [12] to enable physical understanding of strong field phenomena in this exciting regime.
Because of the wide transmission window and high third-harmonic optical nonlinearity [13,14], germanium gained recent interest as a promising linear and nonlinear optical material in the mid to far-infrared (IR) region (3–16 µm). In this region, germanium is transparent and behaves like a ‘high band-gap’ semiconductor. LIPSS formation in such a material is strongly dependent on its modified optical properties under laser excitation, as seen in double-femtosecond-laser-pulse experiments performed by Rohloff et. al [15]. The high carrier mobility of germanium also gives it potential as a low-loss, plasmonic metamaterial in the infrared regime [16]. Another aspect to consider is that even within relatively modest intensity range of 1012 – 1013 W/cm2 at surface is enough to induce strong field effects in a solid like Ge, because significant number of electrons would have enough energy to overcome electron affinity (∼7 eV). Finally, since plasma critical density is proportional to the square of the frequency of incident light, surface plasmon coupling in the presence of mid-IR light becomes important at much lower free electron densities.
Though there have been some studies of LIPSS formation at oblique incidence with s-polarized light [17–19], they are limited. It is expected that LIPSS (LSFL or HSFL) can be generated on the germanium surface under femtosecond laser irradiation at oblique incidence with fluence close to or above the ablation threshold [20, 21]. Considering the increased absorptance that LIPSS can cause [22], understanding their formation is also important for the study of multi-pulse, femtosecond laser damage, which is crucial for current and future laser technology development in mid IR and beyond. Here we report, for the first time, a study of femtosecond LIPSS generation at mid-IR frequencies in germanium. In particular, LSFL generation under laser irradiation at oblique incidence is studied, for both the s- and p-polarized cases.
2. Experimental setup
The experiment was performed using the output of a KTA-based optical parametric amplifier (OPA) tuned to a central wavelength of 3 µm with a pulse duration of 90 fs and repetition rate of 1 kHz. The OPA is pumped by a Ti:Sapphire based laser system producing 3 mJ TEM00 pulses at 792 nm central wavelength with a pulse duration of 80 fs at 1 kHz repetition rate, which consists of a regenerative amplifier and a double-pass, liquid nitrogen cooled booster amplifier. The pulse duration of the mid-IR OPA output is confirmed by an intensity calibration measurement described below. White light continuum generation is used to provide a signal with a wavelength range of 970–1100 nm, measured using a 1D array optical spectrometer (Ocean Optics, USB4000-NIR). The idler therefore has a wavelength range of 2800–4200 nm. Measurement of the pump and signal spectra allowed for the determination of the idler’s central wavelength to within 5%.
The intensity of the output was calibrated by measuring the photoelectron spectrum of xenon irradiated with pulses at a central wavelength of 3.6 µm (Fig. 1(a)) [23]. The spectrum can be explained as follows: a bound electron undergoing tunnel ionization enters the continuum at a certain phase ωt0 with respect to the laser field. Treating the electron classically after tunneling and assuming it is at rest, it will oscillate in the presence of the laser field with a velocity given by where the first term is the quiver motion and the second term is the drift motion. It is this drift energy that is detected in the photoelectron spectrum and, without further scattering with the ion core, it cannot exceed 2Up where is the ponderomotive energy. With ionic-rescattering, however, electrons can acquire energies in excess of 2Up with a much flatter energy distribution [24]. The point at which the energy distribution abruptly changes can therefore be used to determine the ponderomotive energy and, consequently, the output intensity. This point was found to be at 180 eV, corresponding to an output intensity of 7.5×1013 W/cm2. Together with the measurement of the pulse energy and the focal spot size within the xenon, the pulse duration for the mid-IR pulses was determined to be approximately the same as that of the pump (90 fs). Though the calibration was performed at 3.6 µm, dispersion within the KTA crystal is negligible and the pulse duration at 3 µm is not significantly altered.
Fig. 1 (a) Laser intensity estimation via photoelectron spectroscopy in xenon irradiated with 3.6 µm wavelength pulses. In the strong field limit, typical photoelectron spectra recorded along the laser polarization exhibit two well-known regions [23]. At first, starting at low energies, the electron yield decreases sharply, followed by an abrupt transition into a long, extended plateau. The physical origins of the two regions are well understood (see text for details). The sharp transition between the two regions (dashed green vertical line) occurs at twice the ponderomotive energy UP. Using the definition , the intensity is readily estimated to be 7.5 × 1013 W/cm2. (b) Focal spot of the 3.0 µm beam used in the LIPSS generation setup. Imaged with 10.2× magnification using a mid-IR camera, which was mounted sideways. As a result, vertical and horizontal profiles in this image correspond to horizontal and vertical profiles respectively, in actual experiment.
The setup for LIPSS generation follows a slight variation of the setup described in [25] by Poole et al. A zero-order half-wave plate was used in conjunction with a thin-film polarizer and a pellicle beamsplitter (30% transmission) to adjust the output pulse energy. The number of pulses was selected using a Uniblitz mechanical shutter, allowing as few as one pulse to be selected from the 1 kHz laser beam reliably. Depending on the desired polarization, this beam could then be sent through an additional half-wave plate before being focused onto the sample surface at 45° incidence by a 100 mm focal length, plano-convex CaF2 lens mounted on a translation stage. The position of this lens was adjusted to maximize the fluence on the sample. The sample was positioned on a four-way stage system to allow for tip-tilt adjustment, and translation of the sample along vertical and horizontal axes (oriented at 45° with respect to the laser axis). Surface modification was observed in-situ using a 10x infinity conjugate microscope objective (Mitutoyo 378-803-3) with the image relayed onto a 14-bit camera (Point Grey FF MV-03M2M-CS) using a 200 mm achromatic tube lens. Determining on-sample fluence required an accurate measurement of the energy per pulse as well as the beam waist. The former was achieved by using a 1 mm thick silicon window as a small-percentage pickoff optic to send light to a calibrated photodiode. The latter was achieved by imaging the focal spot onto an infrared beam profiling camera (DataRay, WinCamD-FIR2-16-HR) using a second CaF2 lens and a magnification of 10.2× (Fig. 1(a)).
A series of shots were taken on a double-sided polished n-type Ge optical window (<111> orientation and resistivity of 10 – 40Ω/cm with corresponding carrier concentration of ∼ 1013 –1014 cm−3), each shot varying in fluence and number of pulses. After irradiation, the sample was translated by 200 – 500 µm, depending on the size of the damage spot to ensure that a debris-free surface was used for each exposure. Damage spots were then examined under a scanning electron microscope (FEI Helios Nanolab 600 Dual Beam) and an interferometric depth profiler (Wyko NT9100 by Veeco) to analyze laser induced surface modification.
3. Results and discussion
After irradiation with mid-IR femtosecond laser pulses, both LSFL and HSFL were formed on Ge when the laser fluence (reported here as beam normal fluence) was above the damage threshold at various pulse numbers (3 – 10,000 shots) [20]. LIPSS formation was determined by imaging the damage spots using scanning electron microscopy (FEI Helios Nanolab 600 Dual Beam) and an interferometric depth profiler (Wyko Profiler NT9100). The LSFL were observed in the center of the laser spot area with a period-to-wavelength ratio of Λ/λ = 0.47 – 0.61 with orientation perpendicular to the laser beam polarization. HSFL were observed with Λ/λ = 0.17–0.30 at both the center and periphery of the damage spots. The orientation of HSFL was always found to be parallel to the incident laser beam polarization.
3.1. P-polarized LSFL
At fluences marginally higher than damage threshold (measured in our previous work to be 0.25 ± 0.05J/cm2 for 100 pulses [20]), only HSFLs tend to form; whereas, at 0.43J/cm2, LSFL form at the central region with orientation perpendicular to laser polarization. This type of LSFL formation is widely accepted to be due to phase matching between the wavevector of surface-bound electromagnetic waves (surface plasmon polaritons or SPPs) and that of the incident laser light [26]. Excitation of these SPPs requires an enhancement of the incident light’s in-plane wavevector k‖. This can be achieved by scattering the light off a grating structure and creating various diffracted orders, increasing or decreasing its in-plane wavevector by integer multiples of the grating wavevector G. Because a rough surface can be considered a superposition of many gratings with different spatial frequencies, surface modification due to an initial pulse can enhance SPP excitation for subsequent pulses. Interference between these SPPs and the incident laser will produce ripples with periods determined by the phase-matching condition [26]
where θ is the angle of incidence and k0 and ks are the laser and SPP wavevectors, respectively. Using the real part of ks from the familiar dispersion relation [27], the SPP wavelength λs and the corresponding ripple period Λ are found to be where ε′ is the real part of the permittivity of the surface ε = ε′ + iε″ and εd is the permittivity of the surrounding medium (in this case, air with εd ≈ 1). Here it is assumed that |ε′| > ε″ where ε″ is the imaginary part of the surface’s permittivity.It is these ripples that correspond to the observed LSFL. As they form, SPPs are able to be excited more efficiently to create stronger electric fields which modify the surface. The Fourier component of the initially rough surface that matches this condition for Λ would therefore be selected and reinforced with each pulse. Depending on how light is incident upon the target, SPPs can propagate in the forward (along k‖) or backward (opposite to k‖) direction, and at normal incidence, they are identical. Figure 2 shows SEM images of a germanium damage site formed using p-polarized light at a 45° angle of incidence and a wavelength of 3.0 µm. LSFL and HSFL coexist in close proximity with LSFL aligned perpendicular to the polarization (white arrow) and HSFL aligned parallel to the polarization. In Fig. 2, the LSFL feature extends towards the left of figure, opposite of the incoming light’s wavevector. Curvatures of LSFL are most likely caused by angular divergence of SPPs in the SPP propagation direction. Figure 3 shows the depth profile of the same spot, obtained from Wyko profiler.
Fig. 2 SEM image of germanium damage site. 100 pulses, 0.43J/cm2, 3.0 µm wavelength, p-polarized, 45° AOI, ΛLSFL = 1.6 ± 0.1 µm, ΛHSFL = 0.9 ± 0.1 µm.
Fig. 3 (a) Image of same damage site with Wyko depth profiler, showing the depth of the ripples. (b) Lineout starting from the right end of the red line in (a) and proceeding to the right, showing periodic structure.
Based on this model of LSFL formation from SPP excitation, the LSFL period is largely dependent on the material’s permittivity after laser excitation. Using the Drude model [26], this can be written as , where εc is the dielectric constant of the material without laser excitation, ωp is the plasma frequency, and τ is the Drude collision time. The plasma frequency itself, , is dependent on the electron density ne and the effective mass m*. Here, the optical effective mass from standard textbooks (see e.g. [28] by Wang) is used. For germanium, this yields 0.081me where me is the electron mass.
Additionally, the length over which the ripples extend yields an estimate of the SPP propagation length, defined to be the distance over which the SPP intensity has decayed by a factor of 1/e. This length can be written as
Measurement of LSFL period along with the SPP propagation length may therefore yield knowledge of the average electron density and Drude collision time for the LIPSS region. Using the observed LSFL period, two values of allowed ε′ can be obtained: the forward propagating solution (+ sign) with −1 diffractive order, yielding −1.18, and the backward propagating solution (- sign) with +1 order, yielding −3.75. The next subsection presents evidence that the backward propagating solution dominates. This solution is therefore selected for further analysis here.
Using the method of determining SPP propagation length Ls described in [26] by Huang et al, the value of 55 µm was obtained. This yields a value of 0.077 for ε″ for the backward-propagating case. Together with the value of ε′, this yields an electron density ne of 1.99×1020 cm−3 and a Drude collision time τ of 493 fs. This value for the collision time is unrealistically large and leads us to believe that this method of determining Ls is not valid (the collision frequency is typically on the order of the plasma frequency, i.e. τ ∼ 1 fs [29, 30]). Physically, it should be expected that the extent of the ripples should exceed Ls as SPP coupling is not localized to one region of the damage spot. Instead, we believe that a better measure of Ls would be found by examining the decay in ripple depth near the edge of the damage spot. For this particular spot, we examine an LSFL decay region at about 38 µm surface distance away from the peak of focus (Fig. 4(a) 15 µm mark),which corresponds to ∼ 26.87 µm off from peak intensity along beam normal, with a Gaussian waist radius, w0 = 44 ± 1 µm. If it is assumed that the ripple depth is determined by the intensity of the SPP, then the decay of the former can be attributed to the decay of the latter. Since the SPP decay length is defined in terms of the field intensity (as opposed to the field), a typical 1/e propagation distance could then be determined by fitting the data to an exponentially decaying sinusoidal function, giving a value of 4.3 ± 0.3 µm. Although the estimated ∼36% laser intensity fall-off over this 10 µm surface distance plotted in Fig. 4(b) does not fit with the 90% decreas of LIPSS depth measured over the same distance, it may play a role affecting this analysis. This solution to Ls corresponds to the same average electron density of 1.99 × 1020 cm−3, but a significantly shorter average Drude collision time of 32fs, and the overall average permittivity is found to be ε = −3.75 + 0.98i. The Drude collision time obtained is still large compared to prediction from plasma frequency argument above; however, within this framework, a τ of 1 fs results in an SPP decay length of Ls = 134 nm, which is unrealistically small, given LSFL periods of 1.6–3.2 µm has been observed in the current experiment. This points towards limitation of the Drude model based LSFL framework, and suggests that further theoretical and experimental work is necessary for a complete understanding of this process.
Fig. 4 (a) Wyko depth profiler image of same 100-pulse damage spot near periphery with line-out. The contrast has been adjusted to emphasize the ripples. (b) Lineout starting from the right end of the red line in (a) corresponding to 0 distance and proceeding to the left in (a) as distance increases. Variation in ripple depth exhibits an exponential decay with a 1/e decay length of 4.3 ± 0.3 µm.
3.2. S-polarized LSFL
An interesting aspect of oblique incidence laser-solid interaction is that it breaks the symmetry of interaction and allows a different type of SPP phase matching, causing different LIPSS patterns (see Fig. 5). By changing the polarization of the incident mid-IR pulses, the orientation of the SPP wavevector on germanium can be controlled. In contrast to the p-polarized case, there is a large asymmetry of the LSFL with respect to the damage site in the s-polarized case, suggesting that SPP propagation is toward the right (see inset arrows showing direction of k‖, ks, and LSFL wavevector G). Also to be noted is that it required much higher fluences in the s-polarized case to create LIPSS, most likely because of the lower Fresnel absorption. Additionally, with s-polarized light, no E field component naturally exists normal to the unperturbed surface to support SPPs. Significant roughening of the surface by high fluence shots are therefore required so that fields of subsequent pulses can have strong components normal to the roughened surface. Depth profile of the same spot in Fig. 6 shows LSFL with significantly larger depth compared to p-polarization case (see Fig. 3).
Fig. 5 SEM image of germanium damage site. 100 pulses, 0.84J/cm2, 3.0 µm wavelength, s-polarized, 45° AOI, ΛLSFL = 3.2 ± 0.15 µm, ΛHSFL = 1.0 ± 0.15 µm. Though the polarization has been rotated 90 degrees from that of the p-polarized case, the LIPSS orientation with respect to laser polarization is maintained. Inset: diagram showing the SPP wavevectors with respect to the laser wave vector k‖ and the grating vectors. With s-polarized light, SPPs must have a wave vector component along k‖, ensuring they propagate from the left to the right of the image.
Fig. 6 (a) Image of same damage site with Wyco profiler, showing the depth of the ripples. (b) Lineout starting from the top end of the red line in (a) and proceeding to the bottom, showing the periodic structure.
In the s-polarized case, the LSFL period Λ does not match the period which would be naively predicted by a forward-propagating solution to (2), using the Λ and ε′ with the error bar obtained from p-polarization case. Instead, it is necessary to consider the vector nature of the momentum equation shown in inset of Fig. 5 with k‖ ⊥ G, and
Applying these conditions yields the following expression for the period of s-polarized LSFL:
This results in a period of Λs−pol = 3.23 ± 0.2 µm, when ε′ = −3.75 obtained from the backward propagating solution above is used, which is consistent with the 3.2 ± 0.15 µm period of LSFL measured in the s-polarization case in Fig. 5. Using the ε′ = −1.18 obtained from forward propagating solution in (5) yields Λs−pol = 1.2 ± 0.1 µm, which is much smaller than the observed period. This along with the observed LSFL curvatures suggests that backward propagating SPPs dominate in the p-polarized case. If the measured value of Λs−pol is used along with the value for Ls from the p-polarized case, the values of ne and τ are found to be 1.97 × 1020 cm−3 and 34 fs, respectively.
Another interesting feature of the s-polarized case is the fact that there are no LSFL in the center of the damage spot, despite the higher local fluence in this region. Instead, they are observed to form exclusively on one side in a region with significantly lower fluence (as much as 50% lower). This is also observed to some extent in the p-polarized case, where LSFL extend further on one side of the damage spot. One possible explanation for this is that SPPs formed at the center of the damage are able to propagate with little absorption initially. These SPPs must carry a significant amount of laser energy that they then deposit upon entering a region with high absorption, due to the change in ε″ over either time or space. This deposition of energy manifests itself as LSFL formation. This hypothesis is supported by the fact that the LSFL are observed to form only on one side of the damage spot. Because of the phase-matching condition given by (4), SPPs require a wavevector component along the laser wavevector k‖ (see inset of Fig. 5). This ensures that the SPPs propagate toward only one side of the damage spot, which is consistently the same side in which LSFL are observed to form.
3.3. Simulation results
In order to study the interaction of the laser pulse with the surface grating structure, finite element method (FEM) full-wave electromagnetic simulations were performed using the commercial software package Comsol (see [25] by Poole et al for more details). The model assumed a sinusoidal top layer of laser-excited metal-like germanium (1.0 µm thick) residing on the non-excited germanium substrate (see inset of Fig. 7(a)), which at these wavelengths resembles a dielectric insulator. This allowed for an air-‘metal’ interface at which SPPs could potentially be excited. The incoming laser beam was modeled as a plane wave with an angle of incidence of 45° and a 3 µm wavelength. Both s- and p-polarizations were simulated. These simulations were two dimensional, with the the incoming light wavevector projection on the air-‘metal’ surface normal to the grooves in the p-polarized case or parallel to the grooves in the s-polarized case. The simulation domain consisted of one sine undulation within periodic boundary conditions, with a perfectly matched layer used to terminate it in the other dimension. The period of this sinusodal grating was varied to determine resonances where the incoming laser pulse would couple to the SPP, as manifested by peaks in absorptance. It is assumed that surface periodic structures would form at the resonant period due to the strongest surface modification resulting from energy transferred into the surface.
Fig. 7 (a) Inset: simplified diagram of the simulation model. Light is incident on a germanium surface with a 1.0 µm thick, laser-excited layer and a sinusoidal surface. (a) Outset: results from FEM simulations of 3.0 µm wavelength, p-polarized light incident on the laser-excited germanium with a permittivity of ε = −3.75+0.98i (determined from LSFL measurements). The period of the sinusoidal surface was varied to determine resonances in absorptance. The resonance occurs at the observed LSFL period. The groove depth of the sinusoidal surface was also varied to determine its effect on the resonant period. No significant effect is observed, though the peak absorptance shows a continual increase with groove depth until ~ 200 nm at which point it begins to decrease. (b) S-polarized case: resonance occurs near the observed LSFL period, though a shift with groove depth is noticeable. Additionally, as the groove depth increases up to 500 nm, the absorptance increases, suggesting that the energy deposition rate increases as each pulse deepens the grooves further.
It is to be noted that the model presented here does not attempt to capture any dynamical effect, like the effect of high ponderomotive energy (5 - 10 eV, assuming meff = me) acquired by the electrons during the interaction, or how the band structure of Ge may be modified by these highly excited electrons.
3.3.1. P-polarized case
The permittivity of the laser-excited germanium was set to ε = −3.75+0.98i, as determined by the previous section. Figure 7(a) shows the absorptance of incident p-polarized light as a function of the sinusoidal surface’s period. The resonant period was found to match the observed LSFL period. The depth of the periodic grooves was also varied, showing little effect on the resonant period. It did, however, change the value of the peak absorptance. As the groove depth is increased, the absorptance also increases until ~ 200 nm, at which point it begins to decrease again. This suggests that the amount of laser energy absorbed by the first few pulses is relatively low. As each pulse deepens the grooves further, the amount of energy absorbed increases and the rate of ablation increase. Beyond a groove depth of ~ 200 nm, however, the ablation rate decreases with each pulse due to the decreasing absorptance.
It should be noted that the LSFL period in Fig. 4 (near the edge of the damage spot in Fig. 2) is approximately 1900 nm, larger than that measured at the center. One might expect this to be attributable to a lower electron density in regions of lower laser fluence. However, this would only result in a greater (less negative) permittivity, which in turn would result in a shorter LSFL period (Eq. (2)). Another possible cause is the decrease in ripple depth to tens of nanometers. This was shown by Huang et. al. to result in an increase in LSFL period at normal incidence [26]. However, our simulation results here show that there is no change in period with groove depth at a 45° angle of incidence, in direct contrast with the normal incidence results of Huang et. al. At normal incidence, the increase in groove depth modifies the SPP dispersion relation in such a way that a larger grating period is necessary to satisfy phase-matching. With p-polarized light at a 45° angle of incidence, however, the modification to the dispersion relation is very small and no appreciable shift in grating period is necessary.
Instead, it is necessary to examine the assumptions made in the derivation of the expression for the LSFL period. This expression relies on the standard dispersion relation for SPPs, which assumes a semi-infinite metallic medium (laser-excited germanium) adjacent to a semi-infinite dielectric (air). However, when near the periphery of the damage spot, the excited layer may be too thin to be approximated as infinite. In this case, it becomes necessary to use the dispersion relation for a thin metal film between two dielectrics (see Eq. 7 in [31] by Burke et al). Here, the top dielectric layer would be air, the metal film would be laser-excited germanium, and the bottom dielectric layer would be unexcited germanium. From this dispersion relation, it can be seen that decreasing the thickness of the metal film results in an decrease in the SPP wavevector. This corresponds to a smaller grating vector needed for phase-matching and, consequently, a larger grating period. A detailed study on the effects of varying the excited layer thickness will be presented in future work.
3.3.2. S-polarized case
For simulations using s-polarized light, the permittivity of the laser-excited germanium was set to the same value as in the p-polarized case, ε = −3.75+0.98i. Similar to the p-polarized case, Fig. 7(b) shows the absorptance of incident s-polarized light as a function of the sinusoidal surface’s period. Again, the resonant period was found to match the observed LSFL period. Variation in the groove depth was found to produce a slight blueshift in the resonance period. This is because there is no component of the incident light’s wavevector along the grating wavevector (and thus no propagating Bloch wave), leading to the same behavior as at normal incidence for any angle. Interestingly, while an increase in groove depth led to a decrease in absorptance after 200 nm in the p-polarized case, absorptance continued to increase until 500 nm in the s-polarized case. This helps explain why such a large amount of material is ablated in the s-polarized case: as each pulse removes material and reinforces the grating structure, the amount of energy absorbed by subsequent pulses increases. This leads to an increasing rate of ablation with each pulse. Another reason for large groove depth/material removal (~3 times that of p-polarization case) could be the high ponderomotive energy of the surface electrons (~10 eV), which would instantly overcome electron affinity, resulting in strong charge separation field to pull some of the Ge ions from surface non-thermally. Experiments and simulations are being prepared to study this possible effect in detail.
4. Conclusion
LIPSS generation studies with mid-IR light at oblique incidence opens up a rich arena of phenomena which are inaccessible to normal incidence studies. In this paper, LIPSS formation was demonstrated on germanium using 90 fs laser pulses at a central wavelength of 3.0 µm and a 45° angle of incidence. The corresponding photon energy (0.34 eV) is below the indirect band gap of germanium (0.67 eV), making the sample transparent to the incident light. Both HSFL and LSFL were observed to form using both s- and p-polarized light. Orientation of either type of LIPSS was dependent on polarization of light, and LSFL preferentially forming towards SPP propagation direction. Measurement of the LSFL period and the decay in ripple depth for p-polarized LSFL allowed for a measurement of the permittivity of the laser-excited germanium. From this permittivity, the electron density and Drude collision time were obtained. A generalized expression for the phase-matching condition of SPPs was used to derive an expression for the period of s-polarized LSFL. The prediction of periods obtained thus was consistent with experimentally measured values. These s-polarized LSFL were also observed to form exclusively on one side of the damage spot and resulted in greater material removal than any other region, including the center. This asymmetrical ablation is believed to be due to the requirement that SPPs induced by s-polarized light are required to propagate with a wavevector component along k‖, restricting their influence on the surface to one side of the damage spot. This discovery may be significant in designing future opto-plasmonic devices in the mid to far-IR region. Finally, full-wave electromagnetic simulations were used with the measured permittivity to determine the absorptance and reflectance for different grating periods and groove depths. The results of these simulations show a resonance at the observed LSFL period for both s- and p-polarized light. Additionally, they show that, for s-polarized light, the absorptance increases with groove depth until at least 500 nm, compared with 200 nm for p-polarized light. This would allow for greater amounts of energy to be absorbed in the LSFL region, with the amount of energy absorbed with each pulse increasing as the grooves deepen. With more absorption comes more ablation, which offers an explanation for the large amount of material removal in a region of relatively lower fluence.
Acknowledgments
This work was supported by the Air Force Office of Scientific Research, USA under grant no. FA9550-12-1-0454 and FA9550-12-1-0047 as well as the Air Force Research Laboratory, USA grant no. FA-9451-14-1-0351. The DiMauro group acknowledges support from NSF grant PHY-1304218. Urszula B. Szafruga acknowledges support from the NSF Graduate Research Fellowship grant no. DGE-1343012.
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