Ultrabroadband suppression of mid-infrared reflection losses of a layered semiconductor by nanopatterning with a focused ion beam

Moth-eye structures are patterned onto gallium selenide surfaces with sub-micrometer precision. In this way, Fresnel reflection losses are suppressed to below one percent within an ultrabroad optical bandwidth from 15 to 65 THz. We tune the geometry by rigorous coupled-wave analysis. Subsequently, ablation with a Ga ion beam serves to write optimized structures in areas covering 30 by 30 μm. The benefits are demonstrated via optical rectification of femtosecond laser pulses under tight focusing, resulting in emission of phase-stable transients in the mid-infrared. We analyze the performance of antireflection coating directly in the time domain by ultrabroadband electro-optic sampling. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Emission of phase-stable mid-infrared transients results from optical rectification [1] or ultrafast transport processes [2] driven by few-femtosecond laser pulses. Subsequently, ultrabroadband electro-optic sampling provides direct time-domain access to the electric field traces [2,3]. Owing to its high second-order nonlinearity, strong birefringence and wide transmission window, the layered semiconductor GaSe has found widespread application in this context both as an emitter [4] and detector [5,6]. Over the last two decades, these technologies have enabled timeand phase-resolved mid-infrared spectroscopy of condensed matter, solid-state nanostructures, gases and even biological systems [7][8][9][10][11][12][13][14]. More recently, the control of time-resolved fields in this spectral range has become a cornerstone of the emerging area of time-domain quantum electrodynamics. Interest in this subject has been sparked by the first direct detection of the vacuum fluctuations of the electromagnetic field [15,16]. An increasing body of related studies in both experiment and theory [17][18][19][20][21][22][23] is working towards exploring the quantum properties of light with subcycle resolution. Such nonclassical states may be generated via nonlinear interaction of intense femtosecond pulses with dielectric nonlinear media. However, in order to examine their quantum character and to harness it for metrology or spectroscopy, it is of paramount importance to preserve the purity of the nonclassical state while propagating it across the surface of a nonlinear element. Any losses result in admixture of uncorrelated vacuum fluctuations, as typically modelled by the open port of a beamsplitter [24]. The crystals employed for generating and detecting these states are non-resonant in the relevant spectral regions and therefore, reflections at their surfaces constitute the largest threat to quantum applications. For typical specimens, these Fresnel losses can eliminate almost half the field amplitude between emitter and detector, constituting a major challenge for achieving a full quantum tomography in the time domain [25]. In addition, another challenge created by the interface between material and air/vacuum are the echoes spawned by multiple reflections inside the crystal. This effect becomes especially harmful when filtering in the time domain is performed to isolate relevant contributions, as typically observed in many studies based on field-resolved spectroscopy [26]. Overlap of the echo of an intense pulse with the signal of interest may severely deteriorate the information content. A conventional solution to both problems, i.e. losses and delayed replicas, is provided by antireflection (AR) coatings on the exit and entrance facets of nonlinear elements. However, such coatings are of limited bandwidth and efficiency especially in the mid infrared. In addition, they induce unwanted spectral phases on ultrashort pulses. They also may be challenging to deposit on some important nonlinear materials with two-dimensional layering such as GaSe due to adhesion problems on atomically flat surfaces with strongly different thermal expansion coefficients [27]. An alternative method was recently applied to GaSe surfaces [28]: AR microstructures fabricated by single-pulse femtosecond laser ablation.
In this paper, we present broadband and highly efficient suppression of reflection losses even of cumbersome nonlinear crystals with van-der-Waals-bound layered character: nanostructuring of the surface with a focused-ion beam (FIB) to establish a moth-eye structure [29]. Here, the steplike transition of the linear refractive index at the interface GaSe/air is circumvented. Instead, the effective index experienced by the incident electromagnetic wave changes continuously along the longitudinal direction. As a consequence, Fresnel losses are minimized. This strategy is especially advantageous for the small spot sizes of mid-infrared ultrashort pulses typically employed in the context of time-domain quantum optics. It turns out that our approach suppresses reflections on the GaSe-air interface by orders of magnitude without adding any noticeable spectral phase, therefore preserving the pure quantum character of the emitted transients. Furthermore, FIB milling provides a resolution enabling even smaller structures for application in the near-infrared and visible spectral range. The details of the sample preparation process are discussed in Section 2 and a rigorous theoretical model for the reflection properties of the resulting nanopatterns is presented in Section 3. Section 4 introduces the femtosecond optical setup for characterizing the moth-eye strucutures and demonstrates their compatibility with ultrasensitive time-domain spectroscopy. It also compares our experimental data with the numerical simulations and with results from recent literature.

Manufacturing
Bulk GaSe exhibits a two-dimensional structure of hexagonal atomic trilayers bound by vander-Waals forces, allowing cleaveage only along the (001) planes. While this fact enables the exfoliation of extremely thin samples approaching the few-layer limit [30], it also complicates processing with macroscopic cutting or polishing techniques. To the best of our knowledge, the sole method beyond growth and exfoliation demonstrated to date is cutting or microstructuring via laser ablation [28,31]. Here, we demonstrate that nanostructuring of the surface of a material as anisotropic as GaSe with a resolution substantially below 1 µm is readily possible with FIB. This finding enables us to create moth-eye structures on the surface of a highly efficient layered material for nonlinear optics. The specific dimensions of the structures are determined to allow for strong suppression of reflections of mid-infrared radiation.
We employ a Zeiss Neon 40EsB system equipped with a beam of Ga + ions for nanopatterning and a scanning-electron microscope (SEM) for simultaneous process control. Beyond the superior spatial resolution provided by the ion beam, Ga + ions also offer the advantage of not introducing additional chemical elements which could act as impurities in the material. At the same time, maximum energy transfer to the Ga atoms of the compound is ensured. The penetration depth of implanted Ga + ions is estimated to be 20 nm under our conditions with state-of-the-art stopping and range of ions in matter (SRIM) software. Note that this length scale is much smaller as compared to both the thickness of our nonlinear-optical crystal and thickness of the moths-eye coatings as well as to the mid-infrared wavelengths we are dealing with. Consequently, we do not expect significant influences of the FIB milling process on the performance of the structures. A schematic arrangement of the two beams is represented in Fig. 1(a). Ga + ions are accelerated to 30 keV and focussed onto the GaSe surface for precise ablation. A nanopatterning and visualization engine extends the capabilities of beam guidance, enabling the production of complex structures on a relatively large surface. Essential for patterning moth-eye structures into a GaSe crystal are an adapted milling strategy and a high-resolution ion beam. We achieved the best results employing an ion current of 500 pA corresponding to a beam diameter of approximately 50 nm. During the process, the ion beam is scanned over the sample with 10.000 repetitions to create the desired shapes. We also take into account the nonlinearity between exposure time and milling depth, resulting in an adjusted lateral dose as displayed in Fig. 1(b). Mechanical drift of the sample position inevitably occurs throughout this process. Therefore, it is crucial to implement an efficient strategy for drift compensation. To this end, markers are written into the substrate with the ion beam in the immediate vicinity of the projected writing field before the actual processing. These markers are recorded every 240 s during the patterning and the drift of the sample is corrected. Figure 1(c) clearly demonstrates the precise and high-resolution processing of the GaSe crystal enabled by the Ga + ion beam. To the best of our knowledge, no other technique has so far demonstrated comparable performance in three-dimensional nanopatterning of the surface of a layered material like GaSe. Figure 1(d) displays the entire pattern of a dimension of 30 by 30 µm which took 2 hours of FIB processing time.

Simulation
To tailor the reflection and transmission properties of the moth-eye structure in the mid infrared, we apply rigorous coupled-wave analysis (RCWA) [32][33][34] exploiting the modeling code GD-Calc (Grating Diffraction Calculator, KJ Innovation, U.S.). Figure 2(a) displays a segment of the periodic geometry underlying numerical simulation. It consists of a two-dimensional array of micro-sized pyramids located on top of the crystal surface. Along the optical propagation axis (indicated by the wave vector k THz and z axis in Fig. 2(a)), the grating structure is split into 32 horizontal slices resulting in staircase-shaped edges. In each layer, the lateral periodicity of the dielectric function is modelled by a Fourier series. Additionally, we apply a Sellmeier equation in order to account for the linear dispersion of GaSe [35]. The RCWA algorithm then solves the Helmholtz equation in each sublayer for plane monochromatic waves under normal incidence while considering the electromagnetic boundary conditions. This step is repeated multiple times with varying wavelengths to map out the frequency dependence of the grating properties. In this way, we obtain the total Fresnel coefficients of the moth-eye structure for both s-and p-polarized inputs. However, since the period of the array is equal in both lateral directions (x-and y-axis), the overall reflection and transmission is independent of polarization. In order to find the maximum suppression of reflections at the GaSe surface, we now vary the geometrical properties of the structure, i.e. its period d and the height h of the pyramids. Figure 2(b) features a cross section of the structure along the x-z-plane where those quantities are defined. The opening angle α of the pyramids is unambiguously given by α = arctan(d/2h). Figure 2(c) then depicts the amplitude reflection coefficient inferred from RCWA as a function of h and optical frequency. The periodicity is fixed at d = 2 µm. These results demonstrate that the higher the structures the lower the Fresnel reflection coefficient. Tendentially, the sharper the pyramids are, the smoother the spatial transition of the refractive index becomes, thus resulting in a better performance of the anti-reflection coating. Note that the nanolithographic fabrication process of the gratings developed here limits the aspect ratio h:d to approximately 3:1. In addition, deep etching into the bulk GaSe crystal reduces its effective thickness and consequently the converted power during nonlinear-optical interactions. Thus, we choose a realistic height parameter of h = 5 µm.
In the next step, we also vary the periodicity of the grating. Figure 2(d) shows the calculated amplitude reflection coefficient with respect to the geometric parameters d (periodicity) and h (height) at a frequency of 33 THz. Blue and red colors indicate low and high reflection coefficients, respectively. Obviously, the total reflection is only weakly affected by the grating period. The transmitted intensity, in turn, is split into multiple diffraction maxima if the lateral separation exceeds the wavelength of the multi-terahertz radiation. The normalized intensity contained within higher diffraction orders, i.e., within all interference maxima except for the zero-order peak, after transmission through the moth-eye structure is depicted in Fig. 2(e). These results clearly demonstrate that the lower the distance between the pyramids, the higher the cut-off frequency ν cut at which diffraction to higher-order maxima starts to play a role (white dashed line). For d = 2 µm, we find ν cut = 55 THz, explaining also the minor discontinuity in the data of Fig. 2(c).
To summarize the results of the RCWA simulations presented in Figs. 2(c-e), our choice of h = 5 µm and d = 2 µm represents a good trade-off between high-quality structuring and minimum Fresnel losses for an ultrabroadband frequency band centered at 33 THz (see also white markers in Figs. 2(c) and 2(d)).

Characterization setup and results
We now proceed to demonstrate the viability of these considerations by exploiting a nanostructured sample as a generation crystal (GX) for coherent and phase-locked mid-infrared pulses. The experimental setup is depicted in Fig. 3(a). It is based on a modelocked Er:fiber oscillator and two femtosecond Er:fiber amplifiers [36]. The output of both branches is spectrally broadened in separate highly nonlinear fibers to achieve pulse durations of 10 fs. The pump branch (green solid line, repetition rate of f rep = 20 MHz) is centered at 1550 nm. The center of the probe spectrum (blue, f rep = 40 MHz) is located at a wavelength of 1200 nm. In the time-domain experiment, pump pulses generate phase-stable mid-infrared transients with frequency content from 10 to 100 THz via intrapulse difference-frequency generation [4]. This output is spatiotemporally superimposed with the probe beam and focused onto the electro-optic detection crystal (EOX). In this way, the electric field transient may be recorded in amplitude and phase via free-space electro-optic sampling [25]. We harness this setup to demonstrate the application of FIB-milled moth-eye structures as an ultrabroadband AR coating on the layered nonlinear material GaSe. Figure 3(b) outlines how the quantitative difference in amplitude between the main transient and its reflection-induced replicas may be exploited to examine the Fresnel reflection coefficients at the emitting side of the GX. When a mid-infrared pulse, depicted as a red solid line, is generated by optical rectification of the pump beam (green pulse in Fig. 3(b)), it propagates through the crystal and is partly reflected at the flat surface (upper half of Fig. 3(b)). An additional reflection on the opposite air-dielectric interface spatially overlaps the replica with the main beam. Subsequently, this pulse is transmitted into the EOX where it generates a delayed signal. The path of the echo is depicted as a red dashed line in Fig. 3(b). In contrast, the spurious delayed signal should be suppressed almost completely if the nanostructuring technique described in Sections 2 and 3 is applied (lower half of Fig. 3(b)). Laterally translating the GX switches the exiting beam on the GaSe surface from the nanostructured area to the unmodified flat region next to it. This procedure enables straightforward recording of a maximally comparable reference measurement without changes to any additional alignment parameters. In the following, we present and analyze data recorded using the setup and principles described above. Electro-optic signals taken with a 15-µm-thick GaSe GX are depicted in Fig. 4(a). The top panel displays a transient propagated through a flat GaSe surface as a blue solid line. The data features three separate waveforms. The first one is centered around a relative delay time of t D = 0. It is attributed to the fundamental multi-terahertz pulse generated in the GX. This signal will be denoted as the main transient below. It is followed by a second waveform which originates from reflections inside the GX and will be called the reflected transient. The additional replica located at t D = 325 fs is due to Fresnel reflections within the EOX. The time between the main and reflected transients amount to 275 fs and their relative field amplitude is 22%. These values are consistent with two additional reflections on GaSe-air interfaces with a refractive-index contrast of 2.72. Also, the delay corresponds to twice the geometrical thickness and a group refractive index of 2.75 [35]. In contrast, the red solid line in the lower panel of Fig. 4(a) features data recorded with the multi-terahertz beam propagating through the nanostructured surface. It exhibits a reflected transient with a maximum amplitude on the order of only a few percent of the main transient. The drastic decrease in peak amplitude of the echo already indicates an excellent performance of the structures. The temporal offset between both waveforms has decreased to 220 fs. This time delay corresponds to an optical path length of 12 µm, as expected due to the change in effective thickness after nanostructuring via FIB. This fact also shortens the interaction length during optical rectification. Thus, the electric field amplitude of the main transient reduces as well. However, this effect is canceled by the enhanced transmission of electromagnetic intensity at the moth-eye surface. Therefore, the electro-optic signals displayed in the top and bottom panel of Fig. 4(a) exhibit similar amplitudes. Note also that the second replica centered around a relative delay of t D = 325 fs is nearly identical to the measurement presented in the top panel since the EOX has not been modified.
To investigate the properties of our nanostructure AR coating more quantitatively, we first compute the spectrally integrated field reflection coefficient directly from the peak electric field amplitudes of main E main peak and reflected transients E refl peak . These values are related to the field reflectivity coefficients for the flat r flat and structured surface r struct as follows: E refl peak = E main peak r flat r struct . Using the literature values for the flat surface reflection [35] and the data displayed in Fig. 4(a), we find a value of r struct ≈ 0.078. Consequently, the intensity reflection coefficient becomes R struct = |r struct | 2 = |E refl peak /(E main peak r flat )| 2 ≈ 0.006. This result must be understood as an average reflectivity weighed by the spectral intensity of the MIR transients. We analyze this performance further by separating the main and reflected transients using supergaussian filter functions as marked by the dashed lines in Fig. 4(a). The resulting segments are then Fourier transformed. Afterwards, we determine the frequency-dependent reflection coefficients by dividing the resulting spectra of main and reflected transients emitted through the flat GaSe surface. This algorithm is applied separately to both measurements depicted in the upper and lower panels of Fig. 4(a). The result is displayed in Fig. 4(b). A blue solid line represents the case where the multi-terahertz transient propagates through the flat exit surface of the GX. This graph agrees well with the dash-dotted blue line depicting the result of Fresnels' equations for normal incidence with literature values for the refractive index of GaSe [35]. In analogy, the red solid line in Fig. 4(b) represents the amplitude reflection coefficient of the moth-eye structures, revealing a drastic reduction in reflectivity. Specifically, the field coefficients remain in the few-percent range over a large bandwidth. The dashed red line indicates the corresponding part of simulation results from Fig. 2(a). Interestingly, the measured data even outperforms the level predicted by our model described in Section 2 for frequencies between 10 and 20 THz. This observation may be explained by the fact that the focused ion beam penetrates the GaSe specimen deeper than intended, as it is clearly visible when comparing Figs. 2(a) and 1(c): an increase of the height of the structure redshifts the low-frequency onset of residual reflections (see Fig. 2(b)).
To enable direct comparison with typical characterizations of antireflective coatings, we also depict the intensity transmission spectra for both flat (blue dashed line) and nanostructured (red solid line) exit facets at the GX in Fig. 4(c). They are calculated from the field reflectivity in Fig. 4(b) assuming negligible absorption, i.e. T = 1 − |r| 2 . Values above 0.99 are observed over a bandwidth of multiple octaves spanning from 15 to 65 THz. This interval corresponds to a range from 4.5 to 25 µm in terms of wavelength.

Conclusion
In summary, we have demonstrated high-quality fabrication of moth-eye nanostructures on the layered material GaSe via focused-ion-beam milling. This achievement establishes a viable route to arbitrarily modify the surfaces of this highly nonlinear optical medium down to the nanoscale. The performance of our approach is remarkable considering the layered and therefore highly anisotropic character of this compound. Such a structure establishes an ultra-broadband AR coating. Reduction of the intensity reflectance by two orders of magnitude is achieved over a broad spectral range from 15 to 65 THz (corresponding to wavelengths between 4.5 and 25 µm). Consequently, we have provided an ultrabroadband solution for the problem of substantial reflection losses to the nascent topics of time-domain quantum optics and ultrasensitive field-resolved spectroscopy in the mid infrared.

Disclosures. The authors declare no conflicts of interest.
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.