Surfaces with adjustable optical properties are extensively studied and of interest for sensing , , , , controlled light absorption , color printing , , , among other applications. Plasmonics is one approach to enable special optical properties, like intense reflection, absorption or transmission in a targeted wavelength range. Surface plasmon polaritons, coherent oscillations of the electron density coupled to an electromagnetic wave, can be excited at interfaces between metals and dielectrics, or in metallic particles due to the confinement of the electrons within the particle boundaries. Notably, the choice of size and shape for tailored nanoparticles allows us to control the localized surface plasmon resonance (LSPR) wavelength within the limits imposed by intrinsic material properties. By means of modern nanofabrication methods, surfaces with tailored and arranged nanoparticles acting as optical antenna , ,  can be fabricated.
While numerous studies have been carried out on metallic nanoantennas, either as individual objects , , , , , , or organized in arrays , , , , , , semiconductor plasmonic nanoantenna surfaces have rarely been investigated , especially in ordered array arrangements , , . Highly doped semiconductors (HDSC) have been introduced as engineered metals or “designed metals” for plasmonics ,  as they offer the possibility of tuning the plasma frequency, an intrinsic parameter for traditional metals, via the doping level. Doping densities of several 1019 cm−3 have been reported for InAs , and densities up to 1020 cm−3 have been predicted . For the epitaxial growth of InAs on GaSb substrates, the incorporation of a few percent of Sb allows an improved crystalline quality due to the lattice-matched growth conditions  while the possibility of high carrier incorporation as in InAs is maintained. For high doping densities and due to the small effective electron mass, plasma wavelengths of 4 μm can be reached for InAs , making it and the lattice-matched alloy InAsSb for GaSb substrates ideal plasmonic materials for the mid-infrared (IR) spectral range.
The tunable plasma frequency of HDSC constitutes an additional degree of freedom besides the geometric arrangement of plasmonic resonators and might be beneficial to obtain designed optical properties. In contrast, gold or more generally noble metal nanoantennas for the near to mid-IR spectral range have to rely only on shape and geometric arrangement to obtain resonances in a targeted spectral range as their plasma frequency, in the UV spectral range , is constant. Typically, the noble metal nanoantennas for the mid-IR have high aspect ratios, making them the optical analogue to micro- and radiowave dipole antennas but with slightly modified scaling rules , , . They benefit furthermore from the lightning rod effect, the geometrical electric field enhancement at highly curved surfaces . Antenna dimers with nanometer size gaps have been employed to further increase the electric field enhancement and focus incident light into small hot spots , , , . The use of HDSC allows us to deviate from these design schemes, owing to the material properties, as the elongated shape or the interaction through a gap to decrease the resonance frequency is not necessarily needed to reach resonance frequencies in the mid-IR. This opens the way to simpler nanoantenna designs without gaps or high curvature.
In this article, we investigate ordered arrays of rectangular-shaped plasmonic nanoantennas fabricated from highly doped InAsSb epitaxial layers on a GaSb substrate. Due to its plasma frequency in the mid-IR spectral range, plasmonic resonances of highly doped InAsSb lie naturally in the mid-IR and are accompanied by high electric field enhancement compared to gold . The rectangular shape generates polarization selective plasmonic resonances. Arrays with different periodicities are studied experimentally and by finite-difference time-domain (FDTD) calculations in order to estimate the interaction range between resonators. The optical response of the sub-micrometric nanoantennas spaced of at least their size in the array varies only in intensity for different periodicities. Hence, the antennas are uncoupled, which is linked to the weak contribution from scattering to their extinction. An effect from the array can however be evidenced when the grating periodicity is large enough for diffractive modes to become radiative and when they are spectrally tuned to the LSPR sustained by the nanoantennas. The original approach in this article is to cover a large spectral range by the polarization switchable plasmonic resonances in simple, gap-free rectangular nanoantennas. This is particularly interesting for sensing applications, like resonant surface-enhanced infrared absorption (SEIRA) spectroscopy, which ideally requires a good spectral overlap between the plasmonic resonance and the narrow IR-active molecular vibrations , . The spectral overlap can easily be achieved by selecting the spectral band of interest by the polarization of the incident light, offering a new degree of freedom for the tuning of the resonances. As a case study, we demonstrate broadband SEIRA with vanillin as an exemplary analyte. The vanillin molecule displays several molecular vibration characteristics of the substituted aromatic ring at wavelengths in the mid-IR. An increase in the signal intensity of the vibrational features of factors up to 5.7 is obtained. Considering the active zones for surface enhancement in proximity of the nanoantenna corners, enhancement factors of 103 to 104 are achieved. Finally, an optimized readout for intensity-based surface plasmon resonance (SPR) sensing is proposed, exploiting the polarization selective resonances.
2 Experimental details
Plasmonic nanoantenna arrays are fabricated from 100-nm-thin epitaxial, Si-doped InAs0.91Sb0.09 films grown lattice matched on a 200-nm-thick GaSb buffer layer on the GaSb substrate. The doping level of the InAsSb film is 5.1×1019 cm−3 corresponding to a plasma wavelength λp=5.35 μm . The buffer layer is non-intentionally doped, and the GaSb substrate is n-type, Te-doped at a level of 8×1017 cm−3. Patterns are defined by standard UV lithography using dilute AZ MIR 701 photoresist. Rectangular patterns are obtained by superposition of two line patterns rotated by 90°. After development of the photoresist, the InAsSb film is chemically etched with C6H8O7:H2O2 . Photoresist is then removed with acetone, and the samples are cleaned with isopropanol and dried under N2 flow. The plasmonic nanoantennas are rectangular shaped with slightly rounded corners due to the proximity effect in the double lithographic exposure. A scanning electron microscope image of the surface is shown in Figure 1A. Figure 1B displays a scheme of the nanoantenna array with the axes reference used in the following to designate the polarization directions with respect to the nanoantenna axes.
IR spectroscopy of plasmonic nanoantenna samples is performed using an Hyperion 3000 IR microscope coupled to a Vertex 70 Fourier-transform IR spectrometer. A globar light source is used. The light is focused on the sample by a Cassegrain objective (15× magnification) with NA=0.4 and detected by a mercury cadmium telluride detector in the spectral range of 5500–450 cm−1. The acquired spectra are normalized to the spectrum of a gold mirror serving as reference.
3 Optical characterization
In consequence of the anisotropy of the side lengths of the rectangular nanoantennas, a strong polarization dependence of the optical response is expected , . Figure 2 displays the reflectance spectra of an array with periodicities Λx=1.4 μm, Λy=2.0 μm of resonators with side lengths wx=400±30 nm and wy=810±30 nm, obtained with unpolarized and polarized light. Under y polarization, one strong reflectance peak is revealed at λλl=16.8 μm, attributed to the longitudinal LSPR of the resonators, whereas two peaks are observed under x polarization, at λt=11.7 μm and λλt′=10.4 μm. The origin of this particular line shape under x polarization is linked to higher order excitations and the aspect ratio of the resonators. In y polarization, the peak at a short wavelength appears in simulations as a weak feature relatively far from the principal LSPR but is experimentally below the noise level. The transverse LSPR, associated with the short axis of the resonator, are at a smaller wavelength than the longitudinal LSPR . The reflectance intensity is weaker, due to the smaller dipole moment, or higher depolarization factor, of the transverse LSPR , , .
Next, we investigate the transition between the excitation of the longitudinal or transverse LSPR using intermediate polarizations not aligned with the main axes. The polarization angle Θ between the y axis (long axis of the rectangular nanoantennas) and the polarization vector is varied in steps of π/16 rad. From the measured reflectance spectra, the longitudinal and transverse LSPR wavelengths were extracted and the intensity value at these wavelengths was plotted against the polarization angle ΘΘ (Figure 3). Note that a baseline correction was performed to extract the variation of the LSPR intensity without considering the reflection from the substrate. Therefore, the reflectance of a bare GaSb substrate at the investigated longitudinal and transverse resonance wavelengths was subtracted. Figure 3 indicates that by changing the polarization, it is possible to switch between the longitudinal and transverse LSPR. The intensity of the longitudinal resonance decreases while the transverse resonances become more pronounced when increasing the polarization angle from 0° to 90°. The transition between the limiting cases can be fitted by cosine squared functions, with the maximum reflectance value extracted from the measurement. The dipole-like pattern in the polar plot confirms the polarization dependence . The polarization vector can be decomposed into components parallel and perpendicular to the long axis of the nanoantenna. When the component is large, the associated resonance is strong. Using an intermediate polarization direction or unpolarized light as it has been shown in Figure 2, it is possible to excite simultaneously both LSPR as a superposition of the orthogonal polarization directions. This can be applied when it is needed to cover a large spectral range.
Interestingly, both LSPR lie in the IR spectral range and can thus be exploited for resonant SEIRA for broadband identification, as will be shown below. In comparison, a typical gold nanorod antenna with resonances in the IR displays transverse resonances in another spectral range  due to its high aspect ratio, or the transverse resonance is below the noise level , so that only the longitudinal resonance can effectively be used for resonant SEIRA.
4 Interaction range in highly doped InAsSb nanoantenna arrays
Several nanoantenna arrays with different periods in the x and y directions were fabricated in order to investigate the influence of the array arrangement. Figure 4A displays the reflectance spectra of nanoantennas with dimensions wx=450±30 nm, wy=830±30 nm and varying periods in the x direction. The periodicity in the y direction is kept constant at 2 μm. A decrease of the reflectance maxima in either polarization direction is observed due to the lower density of nanoantennas on the surface. However, the spectral positions of the resonances are not influenced by the periodicity. The slight fluctuations are likely attributed to the uncertainty on the nanoantenna dimensions. Similar observations are obtained for variation of the period in the y direction (Figure 4C). In this case, the resonator dimensions are wx=430±30 nm, wy=760±30 nm and the constant periodicity in the x direction is 1.4 μm.
Our experimental measurements are supported by 3D FDTD calculations . One unit cell, including all symmetry planes, is modeled. The array arrangement is implemented by periodic boundary conditions. The spectral range from 1 to 25 μm is investigated under normal incidence of light. The average nanoantenna sizes indicated above from the fabricated samples were used (model for the variation of the transverse period: wx=450 nm, wy=830 nm; variation of the longitudinal period: wx=430 nm, wy=760 nm). We use slightly rounded corners for the resonator geometry with a curvature radius of 20 nm to exclude effects from sharp tips. Mesh size inside the nanoantenna and surrounding all its interfaces to the substrate and the air is 5 nm. The highly doped InAsSb is modeled by a Drude dielectric function:
with the high-frequency dielectric constant ε∞=10.4, the plasma frequency ωp=3.588×1014 rad s−1, and the damping parameter γ=1×1013 rad s−1. The plasma frequency is chosen according to the experimental measurements of the plasma wavelength of the samples, and the damping parameter has been extracted from reflectance measurements on uncorrugated InAsSb layers . As the GaSb substrate is slightly doped and becomes transparent at around 40 μm, it is also modeled by a Drude dielectric function with the following parameters: ε∞=14.2129, ωp=4.629×1014 rad s−1, and γ=5×1012 rad s−1.
In contrast to the simulations, in experimental measurements the intensity of the short wavelength transverse resonance is higher than the longer wavelength transverse resonance. The transverse LSPR at a longer wavelength seems to be strongly sensitive to the actual shape of the nanoantennas and is most visible if the resonator corners are accentuated. The investigation of the line shape depending on the exact nanoantenna shape goes beyond the scope of this article.
Figure 4B (D) confirms in simulation the decrease in the intensity of both longitudinal and transverse LSPR when the periodicity increases in the x (y) direction. We do not have evidence of spectral shifting of the LSPR depending on the period in the investigated range of array periodicities, in simulation under the condition of identical dimensions for the resonators. We deduce that the electromagnetic coupling between nanoantennas is negligible. The nanoantennas act as independent objects for the investigated range of periodicities. The reason for this will be discussed below.
Different interaction regimes in nanoparticle arrays have been identified in the literature, based mainly on examples of metallic, often Au and Ag nanoparticles , , , , , . Near-field interactions arise for gaps between antennas in the range of several tenths of nanometers. These spacings being small compared to optical and IR wavelengths, the interaction is often treated in an electrostatic framework of coupled dipoles , or alternatively by the plasmon hybridization model . Near-field interactions can be excluded for the presented HDSC nanoantenna arrays as the spacing between antennas is in the micrometric range.
Long-range far-field interactions occur due to the scattered field of each resonator in the array, leading eventually to constructive and destructive interference. To further investigate the origin of the insensitivity to long-range interaction in the antenna arrays, we calculated the scattering and absorption cross-sections for a single nanoantenna (see Supplementary Figure S1), exemplary with the lateral dimensions as in Figure 4A and B. The main contribution to the extinction comes from absorption, while scattering contributes clearly less. Consequently, the radiated power of the antennas is small, which reduces the antenna interaction . This allows us to densify the nanoantennas in arrays while maintaining the resonance quality. We now investigate under which conditions long-range, far-field interaction can become apparent.
Diffractive modes propagating at the substrate interface of the grating become radiative when the period Λ=λλeff=λλ/n, with the incident-free space wavelength λ and the refractive index n of the substrate. When λλeff>Λ, only the zeroth-order diffraction appears and the higher orders are non-radiative. But when Λ≥λeff, diffractive far-field interaction can arise , , . However, the effect might be weak in the HDSC nanoantenna arrays, as the scattering is reduced compared to the nonradiative decay channel as shown above. When tuning diffractive modes to be spectrally aligned with the LSPR, they become nevertheless apparent, as evidenced in simulations. In Figure 5, the arrays with diffractive modes spectrally tuned to the transverse (A) or longitudinal (B) resonance are compared to arrays where diffractive modes are not aligned with the LSPR and where, consequently, these weak features are not or scarcely visible. An estimation for the investigated resonances with nsubstrate=√ε∞=3.77 yields Λx=2.9 μm and 3.3 μm to have diffractive modes spectrally tuned to the transverse resonances or Λy=4.2 μm to have a diffractive mode tuned to the longitudinal resonance at 15.9 μm.
Combining individual LSPR with array resonances has been proven to be beneficial to enhance the sensitivity in gold nanoantenna arrays . Similarly, we demonstrate here the spectral superposition of LSPR and array resonances in HDSC arrays for rather large periodicities. However, the size relation between the nanoantenna dimensions and the necessary array periodicity is different, as the resonators can be much smaller yet sustaining resonances at long wavelengths due to the low plasma frequency compared to noble metals. As has been indicated in Figure 4, densifying the nanoantennas on arrays with smaller periodicities leads to stronger reflectance intensity. This densification is possibly beneficial compared to the large array periodicities necessary for the diffractive orders to become radiative, in this particular case of relatively small-sized nanoantennas with long wavelength resonances. Especially, a high densification with unaltered resonance quality should be possible due to the weak contribution of scattering to the extinction .
5 Resonant SEIRA and SPR sensing demonstration
Within the last decade, it has been explored that SEIRA can be improved when resonant, tailored nanoantennas are used , instead of rough metallic surfaces where the effect has initially been discovered . The polarization selective resonances of the investigated HDSC nanoantennas are particularly suitable for resonant SEIRA spectroscopy at mid-IR wavelengths. The condition of the resonant tuning between the large plasmonic resonance and the narrow IR absorption features of molecules is fulfilled at two center wavelengths and covers several absorption features close to the longitudinal and transverse resonance wavelengths, especially on the long wavelength side of the resonance maximum .
As a case study for SEIRA and SPR, we used vanillin (4-hydroxy-3-methoxybenzaldehyde) as an analyte molecule. Vanillin is the major compound of the vanilla bean  and can be chemically synthetized for mass production. It finds applications in food, pharmaceuticals and perfumery . The transmittance spectrum of vanillin, shown in Figure 6A, features several strong IR-active vibrational lines of the functional groups present in the molecule as well as the characteristic vibrations of the substituted benzene nucleus in the fingerprint region from 1500 to 500 cm−1  that are intended to be detected using the nanoantenna arrays. A transmittance spectrum of vanillin was obtained from a high concentrated solution (50 mg/mL) deposited on a transparent KBr platelet. The spectrum was normalized to the one of a clean KBr platelet.
For the resonant SEIRA demonstration, a nanoantenna array with dimensions wx=540±30 nm and wy=600±40 nm on a square array of 1.4 μm×1.4 μm was chosen. The transverse and longitudinal modes display a partial spectral overlap for this nanoantenna geometry. The spectral range of the fingerprint vibrations is covered by the plasmonic resonances, while the vibrations at shorter wavelength can be used as a reference for the strength of the vibrations. Vanillin was dissolved in ethanol with a concentration of 2 mg/mL. Then, a droplet of few μL was deposited on the sample surface and the solvent was evaporated. Around 10 nmol are thus deposited on the sample, the molecular mass of vanillin being 152.1 g/mol. Assuming a homogeneous distribution of the vanillin molecules on the sample surface of approximately 1 cm2, 0.5 ng of vanillin is located within the zone of 150×150 μm2 from which the reflectance signal is measured. This yields 12 femtogram per antenna, if we consider the antenna surface area, and thus 5×107 molecules per antenna. The number of molecules is three orders of magnitude higher than the best reported value for the detection of octadecanethiol self-assembled monolayers with a gold nanorod antenna . Reflectance measurements were performed on the same sample position on the bare sample and subsequently on the sample covered with vanillin. Figure 6B displays the reflectance curves for the orthogonal polarization directions allowing the excitation of either the longitudinal or the transverse LSPR. For both polarizations, several vibrational lines lie within the spectral band covered and thus interact with the large plasmonic resonance. This can be seen from the Fano line shape of the vibrational lines in this spectral range .
In order to evaluate the signal enhancement, the measured reflectance curves were fitted using the smoothing algorithm proposed by Eilers  (dashed lines in Figure 6B), excluding the vibrational signals. Then, the fit was used as a background signal to normalize the measured data to it. Thus, a mainly flat line but for the vibrational signals is obtained (Figure 6C and D), allowing us to compare the signal strengths in spectral ranges where plasmonic enhancement is expected to not impacted spectral ranges. The vibrational signal strength is obtained from this baseline corrected spectrum by a readout of the peak-to-peak value of the vibrational signals.
To assess the increase of the vibrational signal strength, we first obtained the relative intensities from the reference transmittance spectrum of vanillin for the vibrational features at 13.65, 15.81 and 16.95 μm. Intensities are given as percent of the strongest vibrational feature at 7.9 μm, attributed to the C–O stretching vibration of the vanillin molecule. Then, we proceeded analogously for the vibrational signals obtained on the nanoantenna array. The percentage values are indicated in Figure 6C and D for the lines where a significant enhancement of more than 10 percentage points compared to the reference spectrum is obtained. The comparison to the non-enhanced lines at a lower wavelength allows us to ensure that an identical number of molecules contribute to the signal in each of the measurements shown.
Not assessed were chemical effects and the molecular orientation on the different surfaces , namely the KBr platelet for the reference transmission measurements or the nanoantenna array, so that we considered only the significantly enhanced lines in the evaluation. Moreover, some line intensities might be reduced, due to the direct absorption of the vanillin, because direct absorption produces peaks in the reflectance spectra, whereas the Fano-type interaction with the plasmonic nanoantenna is here at the origin of an electromagnetic-induced transparency, seen as dip in the reflectance spectra. An enhancement can be observed when the electromagnetic effect outbalances the direct absorption.
For further comparison between the reference spectrum and the measurements on the nanoantenna arrays, the relative signal intensity increase was calculated by taking the ratio of the enhanced signals to the reference signal at the investigated wavelengths. Values range from 1.2 to 5.7 and are indicated in Table 1 associated with each vibrational line.
The enhanced signals originate mainly from the zone of maximum field enhancement close to the nanoantennas. Considering this, we may estimate the enhancement factor achieved through the use of the plasmonic structure, given by 
where ISEIRA is the enhanced vibrational signal strength, I0 is the strength of the unenhanced signal, A0 is the area covered with molecules and ASEIRA is the active surface where high field enhancement is achieved.
From the electric field profiles shown in Supplementary Figure S2, it can be found that the electric field is strongest near the nanoantenna corners. The sectional view (Supplementary Figure S2B) indicates that the field is especially enhanced on the substrate-antenna interface. For simplicity, we consider the field distribution particularly in the plane close to the interface shown in Supplementary Figure S2A, even if in some other planes there is less enhancement. We estimate the active surface ASEIRA per unit cell area A0 corresponding to a square of 20 nm side length at each corner. Only approximately half of the surface of the squares is accessible to the analyte, the other part being situated inside the nanoantenna. This active surface corresponds to 0.4‰ of the unit cell area. Enhancement factors from 2900 to 14,000 are obtained, as indicated in Table 1. This is one to two orders of magnitude higher than what has been reported for Ge nanoantennas, exploiting additionally a hotspot in a gap between nanoantennas  and is in the range of enhancement factors for noble metal nanoantennas found in other studies which range from 1000 to 100,000 depending on the antenna shape, material and arrangement . As already mentioned, the proposed semiconductor nanoantenna array in the investigated geometrical configuration does not exploit confinement in gaps or the lightning rod effect which is stronger at high aspect ratio nanoantennas, so that there is potential to reach even higher enhancement factors when these more sophisticated geometries are employed.
Furthermore, the resonator array with partially overlapping orthogonal resonances offers the possibility of optimizing the measured signal in SPR-sensing devices . SPR sensing exploits the modification of the refractive index due to the presence of molecules to detect the analyte. As plasmonic resonances are sensitive to the refractive index, they will convert the refractive index modification into an optically measurable signal. In a previous work, SPR sensing with highly doped InAsSb plasmonic nanostructures based on a readout of the wavelength shift upon refractive index modification was assessed . SPR sensing with simple instrumentation relies on the change in intensity, under illumination with a monochromatic light source and measured by a photodiode , typically at the wavelength of the initial resonance maximum or in the shoulder of the resonance peak. When the ideally narrow resonance shifts upon modification of the refractive index, the intensity decreases, especially when the resonance is moved largely out of the measured wavelength. Using an evaluation in this manner, we obtain a measured signal of ΔR=0.001 (ΔR=0.019) for the transverse (longitudinal) resonance with a readout at the resonance maximum at 13.9 μm (15.9 μm), as indicated in Figure 7. A stronger signal ΔR can be obtained when the readout is done at the wavelength of the intersection of the two resonances, for the exemplary structure at 14.6 μm. Upon an increase in the refractive index, the transverse resonance will shift toward the readout point whereas the longitudinal resonance will shift away from it. Evaluating the variation in signal intensity, ΔR=0.074 is obtained. Hence, the measured signal ΔR is more than three times stronger for an evaluation at the wavelength of the intersection point than for an evaluation at the longitudinal resonance’s wavelength. For an evaluation at the spectral position of the transverse resonance, the improvement is even higher.
We studied the polarization selective resonances of rectangular-shaped plasmonic nanoantennas made of highly doped InAsSb on GaSb substrates. The nanoantenna shape and material allow us to excite distinct longitudinal and transverse modes in the mid-IR. Switching between the spectral bands or excitation of all modes simultaneously is easily realized by the change of the polarization with respect to the resonator’s axes. For the investigated array periodicities in the micrometer range, the nanoantennas behave as isolated objects. Yet, for large periodicities, it is possible to tune diffractive grating resonances to the spectral position of the LSPR. Strongest reflectance intensity is achieved for small array periodicities, thus densifying the nanoantennas on the substrate. We demonstrated the detection of vanillin molecules by characteristic IR absorption lines using the transverse and longitudinal LSPR to cover different spectral bands. Furthermore, we proposed an improved readout method for SPR sensing exploiting the overlap of the transverse and longitudinal LSPR. Ultimately, the plasmonic nanoantennas can be designed to cover precisely the spectral bands needed for the enhancement of the absorption features of interest for SEIRA spectroscopy for a targeted analyte, or for maximum readout for SPR sensing, using the appropriate nanoantenna dimensions.
This work was partially funded by the French Investment for the Future program (EquipEx EXTRA, ANR 11-EQPX-0016), by the French ANR (SUPREME-B, ANR-14-CE26-0015), by European Union’s Horizon 2020 research and innovation programme (Marie Sklodowska-Curie grant agreement No. 641899) and by the Occitanie region. A. Mezy and M. Granier are acknowledged for helpful discussions about infrared spectroscopy. The authors thank Dr F. Neubrech for sharing his Eiler’s smoothing program for the evaluation of SEIRA signals.
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The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2017-0052).