Engineering the Infrared Optical Response of Plasmonic Structures with ϵ‐Near‐Zero III‐V Semiconductors

The pursuit for enhanced light‐matter interactions using ever more suitable plasmonic materials has led to the development of novel bulk materials, such as ϵ‐near‐zero (ENZ) media. The ability to control the free carrier density gives semiconductors a significant advantage over traditionally used noble metals and phonon‐based materials as ENZ media for infrared applications. A metal‐ENZ‐metal structure is designed of epitaxially‐grown III‐V semiconductors and patterned into nanoantennas by electron‐beam lithography (from 200 up to 1800 nm) and demonstrates plasmonic resonances tuned from the terahertz up to the near‐infrared, according to the ENZ doping level (1 × 1016, 1 × 1019, and 2 × 1019 cm‐3). Experimental results, corroborated by numerical simulations, show that the designed metal‐ENZ‐metal structure is a promising vehicle to provide additional insights regarding ENZ‐based phenomena including the resonance pinning, the near‐constant phase, and the dispersive nature of ENZ materials. It is believed that III‐V semiconductors within a metal‐ENZ‐metal structure address the problem of weak light‐matter interactions and shall greatly benefit infrared applications, e.g., sensing and communication, as they can be engineered to take advantage of both plasmon and ENZ effects and integrated onto modern photonics devices.


Introduction
The permittivity ϵ describes the response of a medium exposed to an electromagnetic field, and as such is of great interest when studying light-matter interactions and their associated applications. [1,2]Epsilon (ϵ)-near-zero (ENZ) materials refer to an emerging class of materials with a small real part of their permittivity (ℜ(ϵ) ≈ 0) at characteristic frequencies.This property gives rise to peculiar effects, such as high impedance (Z = √ (∕)), [3] unusually large wavelengths, [4] a strong electromagnetic field enhancement [5] and directionnality, [6,7] as well as a vanishingly small index of refraction ñ, provided the amagnetic material has low losses near ENZ regime.Consequently, numerous applications have already been developed in nonlinear optics, [8][9][10] telecommunications, [11,12] waveguiding, [4,13] as well as sensing, [14,15] amongst many others. [16]he underlying origin of a permittivity approaching zero can be different according to the material and its associated operating frequency.Several mechanisms lead to ENZ regime, such as lattice vibrations (i.e., phonons), electronic transitions, and free carriers oscillations.The free carriers oscillations cancel the permittivity at the plasma frequency, i.e., the metal/insulator transition frequency.ENZ materials include i) semiconductors (SCs) such as transparent conducting oxides (aluminum-doped zinc, [17] tin-doped indium, [18] gallium-doped zinc [19] oxides), and III-V SCs (GaAs, [20] AlGaAs/GaAs/AlGaAs quantum wells [5] ), ii) noble metals (Au and Ag [21] ), iii) polar dielectrics (SiC [7,22] ), iv) transition metal nitrides (TiN [23] ), v) correlated metals [24] (CaVO 3 , SrVO 3 ), as well as vi) artificially-designed ENZ, e.g., metamaterials [6] and hyperbolic materials. [25]he dielectric permittivity ϵ() is related to the plasma frequency through the following Equation (1): With ϵ ∞ the permittivity at high frequencies accounting for the deformation of the ion cores,  p the plasma frequency,  the frequency and  the plasma damping.Moreover, the plasma frequency is calculated by Equation 2: With n the free carrier density in cm -3 , e the elementary charge, ϵ 0 the vacuum permittivty and m* the considered carrier effective mass.This set of equations, known as the Drude-Lorentz model, describes the relationship between the ENZ regime and the free carrier density, and consequently how ENZ effects and plasmonics relate to one another through the plasma frequency  p .
Plasmonics studies the interactions between light and free carriers.Free electrons constitute a plasma that oscillates upon excitation by an electric field.Plasma oscillations carry a surface wave propagating along the metal/dielectric interface.This electromagnetic mode is known as surface plasmon-polaritons (SPP) and its nature depends on the optical properties, notably the dielectric permittivity ϵ() of both the metal and the dielectric involved in the system.The surface plasmon resonance (SPR) arises when the resonance conditions are fulfiled, i.e, when both energy and momentum, of light and plasma, coincide.Several wavevector matching techniques exist to permit light-plasma coupling with the two most common being the prism and surface patterning.In our study, we use the latter, and due to the subwavelength dimensions of the fabricated nanoantennas, the associated SPR acquires a localized feature, known as localized surface plasmon resonance (LSPR), and it is associated with a strongly enhanced electromagnetic field. [26]This highly enhanced electromagnetic field is the keystone of many plasmonbased applications, in particular sensing applications.
The infrared spectral region is at the heart of many medical, civil and military applications such as chemical and biological sensing, [27,28] pollution monitoring, [29] food and agricultural quality control, photodetection and imaging, lasers, et cetera.Modern nanoscience and photonics focus on phenomena, e.g., non-linear effects, plasmonics, or ENZ effects, that enhance the performance of devices with mentioned applications.To find a material with both plasmonic and ENZ features in the infrared, additionally being tunable, is challenging. [30]Noble metals remain the most commonly used plasmonic materials, still, these past few years, abundant research has been dedicated toward novel plasmonic materials as alternatives, [31][32][33][34][35] to compensate for the lack of tunability and efficiency of noble metals for specific applications.To list but a few, transformation-optics devices are limited by strong losses (i.e., intraband transitions and scattering within metals), integration within photonic integrated circuits is limited by nanofabrication challenges (e.g., percolation threshold, granularity, and roughness), chemical stability issues, incompatibility with silicon manufacturing (diffusion leading to deep traps) and invariable dieletric permittivity limiting their effective usage to discrete spectral ranges.
With plasma losses, one of the most limiting factor in infrared plasmonic systems, in terms of efficiency, revolves around the weak interactions between infrared light and matter.Metalinsulator-metal (MIM) structures are well-known for their ability to confine light at the subwavelength level through enhanced light-matter interactions.The theoretical understanding of MIM structures is well-known for a long time, [36] and it laid the foundations for numerous applications that have risen, with the modern improvement of growth and fabrication techniques, such as sensing, [37] waveguiding, [38] switches, [39] amongst others. [40]Various insulating layers have been studied throughout these research; yet, there is a lack of understanding about how MIM plasmonic structures behave when the insulator is doped such that its plasma frequency enters the ENZ regime.In this regard, we demonstrate that the optical response of the system is efficiently controlled with the ability to control both plasma frequencies of the metal and the insulator layers supporting a plasmonic mode at their interface in the ENZ regime.We address such questions and bring additional insights about such system, that can be viewed as a metal-ENZ-metal structure.
In this framework, we propose an all-III-V semiconductor MIM structure, degenerately-doped, featuring both ENZ and plasmonic behaviors, tunable from the THz up to the near infrared (NIR).III-V SCs grown by molecular-beam epitaxy (MBE) benefit from excellent single-crystal quality, atomic-level control of grown layers, high carrier mobility as well as CMOS technology compatibility through mature semiconductor industry techniques, with possible integration onto photonic integrated circuits and optoelectronic devices. [41]We study the influence of the insulator doping level on the plasmonic properties of the structure and demonstrate how the plasmonic resonance is influenced within the ENZ regime.Such system displays important versatility as III-V semiconductors can be heavily doped up to 10 20 per cm -3 , with great precision.Moreover, we provide additional insights for the understanding of ENZ-based effects, such as the LSPR pinning and its associated geometry-independent feature.Within ENZ regime, a system becomes very tolerant to fabrication defects, which is of particular interest as modern nanophotonics is often associated with sophisticated and expensive fabrication techniques.We demonstrate how III-V semiconductors are excellent candidates to engineer the optical response of a plasmonic system over the infrared and further investigate its optical properties.

The ϵ-Near-Zero Plasmonic Structure
The ENZ-based MIM structure is schematically represented on Figure 1.From bottom to top, the growth starts off with a heavily silicon-doped 1 μm-thick InAsSb:Si layer, marked as h m in Figure 1.This layer acts as a mirror (metallic behavior) up until around 5 μm in the infrared, which is required for reflectance measurements.Second, an ϵ-near-zero layer is grown, whose material, thickness, and doping level will be discussed later.Finally, a third heavily-doped thin layer of InAsSb:Si is grown, intended to be nanostructured into plasmonic nanoantennas.
Three different samples are compared in this study, namely sample A, B, and C. Three different spacer layer doping level have been evaluated: non-intentionally doped (nid) ≈1 × 10 16 , 1 × 10 19 , and 2 × 10 19 cm -3 , respectively.They are characterized by three different ENZ regimes, from the THz to the infrared, as shown in Figure 2, and calculated from the Drude-Lorentz model with Equations 1 and 2. Non-intentionally doped refers to a grown semiconductor whose free carrier density is slightly greater than The spacer layer is sandwhiched within two metallic layers and its doping level is adjusted so it acts as an ENZ layer.See Tables 1 and 2 for materials and geometries informations.
the intrinsic carrier concentration despite the fact that no intentional dopants were introduced.
After the growth of each sample, their thicknesses and surface quality are respectively assessed by high-resolution X-ray diffraction (cf. Figure S1, Supporting Information) and atomic force microscopy (cf. Figure S2, Supporting Information).Then the fabrication of the nanoantennas is performed in clean room environment.Optical microscopy images of the processed samples, after being processed in a clean room environment, are shown in Figure 3. Different areas, corresponding to various nanoantennas widths, have been fabricated.The fabrication quality was further evaluated with scanning electron microscopy (cf. Figure S3, Supporting Information) and atomic force microscopy (cf. Figure S4,   Figure 2. Real part of the permittivity ϵ expressed as a function of the wavelength (μm) and the wavenumber (cm -1 ), for three different doping levels: 1 × 10 16 (nid), 1 × 10 19 , and 2 × 10 19 cm -3 .The dashed red line highlights the wavelength at which the real part of the permittivity crosses zero; it is the ENZ line.ϵ is calculated with Equations ( 1) and ( 2).Be careful of the horizontal axis break.

Supporting Information). Table 2 includes all informations about geometrical parameters of the three samples.
Doping levels are verified by optically probing the free carriers concentration using Brewster (sometimes referred as Berreman) mode measurements (Figure 4). [42]We observe a peak corresponding to the highly-doped layers ( p1 ), and we also observe for samples B and C, a peak corresponding to the doped insulating spacer layer ( p2 ).Plus, from these measurements, the plasma damping rates  can be extracted using transfer-matrix formalizm.The informations regarding the materials, thicknesses, doping levels, and their associated plasma frequencies, for the three different structures are summarized in Table 1.It is important to keep in mind that  p1 >  p2 so that the structure behaves as a metal-insulator-metal structure as intended.
According to Tables 1 and 2, the antennas period, the spacer thickness, as well as the substrate are different for each samples.We hereby address these differences and their potential impact on the samples response.Regarding sample B's GaAs substrate, it theoretically introduces more crystalline defects (due to a lattice mismatch of ≈ 7% at InAs/GaAs interfaces [43] ), resulting into stronger plasma losses .However, in practice, by optically probing the Brewster mode, [42] we did not identify any significant loss increase (Figure 4), meaning that the substrate material does not significantly impacts the optical response of the structure.Second, the antennas period (800 nm for sample A, compared to 2 μm for samples B and C) slightly changes the antennas duty-cycle (i.e., the ratio between the antenna width and the antenna period) and, therefore, the structure effective refractive index, which itself impacts the LSPR frequency. [44,45]Third, the spacer thickness has direct consequences on the quarter-wavelength resonance, i.e., the first Fabry-Perot mode of the structure that occurs as destructive interferences within the spacer layer, [46,47] which has been found to influence the LSPR frequency through strong coupling phenomenon. [46]Although having an influence, these differences do not hinder the understanding of the article's message, which is about the ENZ-based insulator within a MIM structure, and its influence on the plasmonic response.

Experiment Results
Fourier-transform infrared (FTIR) spectroscopy is used to characterize the optical response of the samples.Figure 5 displays a standard FTIR reflectance measurement of the optical response, as a function of the wavenumber, from 500 up to 5000 cm −1 , respectively 20 down to 2 μm.The whole structure is metallic at frequencies lower than  p2 (dark grey region), the spacer layer then becomes dielectric while the top and bottom layers remain metallic at frequencies between  p2 and  p1 (light grey region), and finally, at frequencies larger than  p1 the whole structure becomes dielectric (white region).We observe that the LSPR, not to be confused with the quarter wavelength resonance (/4), occurs within the light grey region, between the two plasma frequencies [ p2 −  p1 ], which corresponds to the frequency range within, which the structure behaves as a MIM structure.Furthermore, the LSPR corresponds to a near perfect absorption, which is expected for such a structure. [48]irst, we study the influence of the nanoantenna width on the optical response of the structure.Figure 6 displays the FTIR mea-  surements of the optical responses of various antenna widths.We observe the characteristic red-shift of the LSPR (from blue to yellow curves) as the antenna width increases (represented as the black arrow).We also observe that as the antenna width increases, the associated LSPR slows down as we reach the plasma  frequency  p2 of samples B and C, meaning near ENZ regime, of the spacer layer below the nanoantennas.][51][52][53] This phenomenon is not observed for sample A because its spacer layer is non-intentionally doped, thus its free carrier concentration lies around 1 × 10 16 cm −3 , corresponding to a plasma frequency in the THz region according to Equation (2); therefore, the probed infrared spectral region is too far from its spacer ENZ regime to observe the LSPR pinning.One must keep in mind that fabricated antennas width, on samples B and C, range from few hundreds of nm up to nearly 2 μm, as opposed to sample A for which antennas of width greater than ≈600 nm have LSPR frequencies out of the MCT detector limit (≈500 cm −1 or 20 μm).We conclude that the optical response of the structures, not only depends on the nanoantenna width, but is also strongly dependent on the nature of the layer below the nanoantennas.Second, we study the influence of the spacer layer doping level n s on the optical response of the structure.Figure 7 shows the experimental (full lines) and simulated (dashed lines) optical responses of 500 nm-width nanoantennas for all three samples.We observe that the numerical electromagnetic simulations performed by rigorous-coupled wave analysis (RCWA) match experimental results.The LSPR frequencies are different for each samples; for sample A, B, and C, the LSPR is at 640, 1240, and 1400 cm −1 , corresponding to spacer layer doping levels of nid, 1 × 10 19 and 2 × 10 19 , respectively.Thus, the LSPR frequency increases as the doping level of the material, on which the antennas are fabricated, increases.Third, we evaluate the red-shift observed in Figure 6, as a function of the spacer layer doping level influence, observed in Figure 7. Figure 8 shows the relation between the LSPR frequency (and wavelength) as a function of the antenna width for all three samples.Experimental results are corroborated by numerical simulations performed by RCWA.We observe that as the antenna width increases, the LSPR frequency decreases (i.e., the wavelength increases: red-shift).The striking result is that for samples B and C, the red-shift is much slower than it is for sample A. Indeed, a width variation of 400 nm results in a redshift of around ≈250, ≈100, and ≈50 cm −1 for samples A, B, and C, respectively.This "slow-down" of the red-shift accentuates for samples B and C as the LSPR frequency reaches the plasma frequency of their respective spacer layer,  p2 (B) ≡ 1000 cm −1 and  p2 (C) ≡ 1300 cm −1 .As the spacer layer doping level increases and gets closer to the plasma frequency  p1 of the metal layers composing the MIM, the LSPR gets pinned within an increasingly narrower spectral range, defined as [ p2 −  p1 ].
In sum, within the plasma frequency range, i.e., in the ENZ regime, the LSPR frequency becomes nearly independent on the geometrical properties of the structures (Table 2), and conversely, the LSPR frequency becomes nearly dependent only on the material bulk properties of the structure (Table 1), themselves governed by the doping levels of the different layers.This results implies that within the ENZ regime, a structure will see its optical response dominated by the dispersive behavior (material dispersion), rather than by the geometry of the structure.This rather intriguing effect was reported in various papers addressing relatively different scientific investigations including waveguiding, [4,54] impedance matching, [55] antenna design, [7,56,57] perfect absorbers, [17] emission, [58,59] amongst others. [60,61]Employing III-V semiconductors allowed us to clearly highlight this LSPR pinning phenomenon, and it demonstrates how this class of materials is particularly interesting to study ENZ-based plasmonic phenomena in the IR.

Theoretical Results
To further understand physics fundamentals behind the LSPR pinning and its associated dispersive feature, we perform finitedifference time-domaine (FDTD) simulations.It allows to calculate the dispersion relation for the stacking considered in Figure 1. Figure 9 shows the dispersion relations, representing the light frequency  (rad.s−1 ), as a function of its wavevector k x , expressed in m −1 , along the x direction.Colored full lines correspond to solutions of the dispersion relation, associated with the propagation of electromagnetic modes, viz., plasmons.Since plasmons are surface waves propagating along an interface, they  are considered as guided modes and their wavevector is often referred to as the propagation constant  in the literature.
We observe that experimental results lay on the upper part of the solution, confined in the frequency range [ p2 −  p1 ].Note that calculations were performed without considering antennas periodicity in order to determine the permitted modes within the structure.The calculated solutions are characterized by a maximum: Asymptote 1 and a minimum: Asymptote 2. The Asymptote 1 is the well-established surface plasmons frequency  sp =  p1 ∕ √ 2. On the contrary, the Asymptote 2 is uncommon; [62,63] indeed plasmonics commonly involves a metal/dielectric interface with the dielectric being air, while in this case, the dielectric is a doped semiconductor that behaves as an insulator at frequencies greater than  p2 .We observe that the solution for a standard MIM structure (Figure 9 sample A) does not display the Asymptote 2; the latter arises as the doping level of the insulator of the MIM increases (Figure 9 samples B and C).
We can draw two important conclusions from this comparison between experimental and theoretical results.First, we observe that as the solution line approaches the plasma frequency of the insulator  p2 , its slope flattens down having for consequence a slow down in the relation linking light frequency to its wavevector.This bending results from the fact that the real part of the permittivity of the spacer vanishes until it theoretically reaches zero at  p2 .Hence, the ϵ-near-zero behavior of the spacer layer, as the working frequency approaches the plasma frequency  p2 , is responsible for the LSPR pinning observed experimentally, represented by the Asymptote 2.
Second, since the excited plasmonic mode is associated to the MIM structure, one can play on the optical properties of both the metal and the insulator, in particular, as mentioned in the introduction, the dielectric permittivities ϵ() through their plasma frequencies  p .Therefore, having the ability to tune this parameter end up being a powerful asset of III-V semiconductors over other plasmonic materials traditionally employed.Since III-V semiconductors can be doped up to 10 20 free carriers per cm 3 , their plasma frequency can be adjusted to the desired working range of any applications, from the THz up to the NIR, with great precision.
We confirmed that the experimental results correspond to the dispersion relation solution by calculating the mode effective refractive index, with Equation (3), [53,64] both theoretically from the solutions of Figure 9, and experimentally from the data gathered from Figure 8.
With c the light speed, k x the wavevector along the interface,  the angular frequency, m = 1, 2, … the resonance order,  LSPR the plasmonic resonance wavelength, L the antenna length, and ϕ r the phase of the modal reflection.We are interested in the fundamental resonance m = 1 and consider that the plasmonic antennas behave as classical half-wavelength antennas to fulfill the resonance condition, considering a modal reflection phase ϕ r taking into account SPP reflections within the antennas.
Figure 10 represents the effective refractive index calculated from Equation (3), expressed as a function of the wavelength and the angular frequency .We observe that the effective refractive index of the plasmon mode decreases drastically until plasma frequencies, as opposed to the surface plasmons frequency  sp at higher wavevector k x , for which it is known that the effective refractive index increases.The variation of the phase ϕ r associated to the antenna length becomes marginal as the antenna resonance enters the ENZ regime, as depicted by the increasing density of experimental points within the ENZ cone shown in the inset of Figure 10, meaning that the phase is nearly constant close to the plasma frequency. [53]The dispersion relation proved to be critical when it came to determine the effective refractive index of the plasmon mode; indeed, traditionally used effective refractive index models are inadequate for imperfect metal and insulator. [44,65]Therefore, solving the dispersion relation of a photonic structure is a more rigorous approach when dealing with non-perfect metal (working near its plasma frequency) and nonperfect insulator (varying refractive index), for which very few approximations can be defined. [66]e would like to draw reader's attention on the fact that, contrary to the claim that it is not possible to move the LSPR beyond the pinning frequency, as long as an insulator exists within the considered system, e.g, air, then the SPP propagation persists at the new metal/dielectric interface.This finding can be appreciated for sample C, as observed in Figure 8. Experimental results display LSPR frequencies beyond the plasma frequency of  p2 .Consequently, we observe that part of the experimental results lay below the plasma frequency of sample C on the dispersion relation solution of Figure 9.This implies that the nature of the plasmon has changed, i.e, the plasmon is not supported at the same interface as it was in the frequency range [ p2 −  p1 ].
Figure 11 displays the normalized electric field maps for sample C's nanoantennas of 400, 800 nm and 1.2 μm width, respectively Figure a-c, at their respective LSPR frequency: 1432, 1344, and 1290 cm −1 .We observe that the smallest antenna, resonating at higher frequency, displays a maximum electric field at the antenna/spacer interface.As the width of the nanoantenna increases, the electric field migrates from the lower interface to the antenna/air top interface, corroborating that the metal/dielectric interface supporting the plasmon changes when the LSPR frequency passes through a material transition, in this case, the plasma frequency.Figure 11d,e, respectively show the normalized magnetic field maps for the 400 nm and 1.2 μm wide antennas.We observe that the magnetic field is mainly confined within the spacer layer when it is dielectric, as one would expect for a MIM structure, as opposed to when the spacer becomes metallic at frequencies inferior to  p2 (C), then the magnetic field is pushed back in the air and the structure does not behave as a MIM anymore.These simulation results corroborate the experimental results and further evidence that III-V semiconductors and their associated fabrication techniques pave the way for a greater control of a plasmonic system optical response.

Conclusion
In conclusion, we have demonstrated that III-V semiconductor plasmonics is suitable to study the optical response of ENZ-based systems.They are associated with many practical advantages including: 1) cutting-edge growth and nano-fabrication techniques, e.g., respectively, molecular beam epitaxy and electron-beam lithography, 2) benefit from the mature semiconductor industry for their integration into photonic integrated circuits and their compatibility with CMOS technology, and 3) high and precise doping level in order to tune their ENZ spectral range.By means of these methods, we fabricated metal-insulator-metal structures, with a doped insulator in order to adjust its plasma frequency, i.e., ENZ regime, to various spectral range.We demonstrate that such a structure displays a tunable ENZ regime from the THz up to the NIR (≈ 5 μm), depending on the insulator doping level, with a plasmonic resonance tunable according to the nanoantennas dimensions.We studied the optical response of this system for three different insulator doping levels: 1 × 10 16 (nid), 1 × 10 19 , and 2 × 10 19 cm −3 , and for various nanoantennas widths, from ≈ 200 nm up to ≈ 1.8 μm.RCWA electromagnetic simulations confirmed experimental results and also attested, consequently, the high quality of growth and fabrication techniques.
We have determined the dispersion relation of our structures with FDTD simulations, which proved to be a more rigorous approach as compared to commonly used effective refractive index models, which are inadequate for non-perfect metal and insulator.We provide evidence that the resonance pinning originates from a material transition, in our case, the plasma frequency.Indeed, because we studied various insulator doping levels, associated with various plasma frequencies, we highlighted the resonance pinning under various circumstances and thus, we bring additional insights for the understanding of this pinning phenomenon.As long as an insulator exists within the system, a metal-insulator interface exists and it can support SPP modes, therefore, it explains why we experimentally observed the LSPR persisting at frequencies smaller than the plasma frequency, meaning that the pinning is spectrally localized and associated with the material transition.The underlying consequence of the LSPR pinning is the great tolerance to fabrication defects thanks to the geometry-independent behavior; a noteworthy asset as modern nanophotonics increasingly relies on expensive and sophisticated fabrication technologies.In the same vein, an optical response is essentially dominated by the dispersive behavior takes advantage of highly reliable and reproducible growth from molecular beam epitaxy.
To summarize, the metal-ENZ-metal structure proves to be an excellent vehicle to study and take advantage of ENZ phenomena such as the plasmonic resonance pinning, the near constant phase and the dispersive nature of ENZ materials.Great agreement between experimental results, RCWA simulations and theoretical results based on FDTD, demonstrates how III-V semiconductors, such as InAsSb and GaSb, can be employed to engineer the infrared optical response of plasmonic nanostructures.

Experimental Methods
Growth and Fabrication: The samples were grown by solid-source MBE.GaSb substrates were used for samples A and C, while GaAs was sample B substrate.All three MIM samples growth started off with a 200 nm thick GaSb buffer layer to bury lattice mismatch-induced and oxideinduced defects.Then a 1 μm thick InAsSb layer highly n-doped (≈5 × 10 19 cm −3 ) was grown.The next two layers were different for each sample in terms of doping levels and thicknesses.Silicon was used for n-type doping within InAs 0.91 Sb 0.09 .
Nanoantennas fabrication proceeds as follows: first, diluted AZ®nLOF 2020:AZ®EBR solvent (100:80) negative resist was deposited by spin coating (6000 rpm for 30 s, and baked at 110 °C for 1 min).Then, nanoribbons-shaped antennas were patterned using electron beam lithography (EBL from Raith GmbH nanofabrication coupled to a SEM from JEOL) and different electron beam dose tests were performed (from factor ×0.1 to ×0.8) with an initial electric current of 10 pA in order to electrically charge the resist to 14.67 μCcm −2 .Then the resist was baked a second time at 110 °C for 1 min and developed for 40 s using AZ®726 MIF developer.The InAsSb top layer was then etched using Ar-based plasma in inductively coupled plasma etching for 5 min (ICP-RIE from Oxford Instruments PLC); 25 sccm Ar, 5 Torr, RF generator power: 50 W, ICP generator power: 500 W, 60 °C, 10 sccm He.Multiple dose tests provided with many different widths of nano-ribbons written on different areas.
Spectroscopy: Spectra were obtained using Bruker Hyperion 3000 Fourier-transform infrared spectrometer (FTIR) with a × 15 magnification objective and a numerical aperture of 0.4.Each reflectance spectrum was the averaged result of 100 single spectra collected with a resolution of 2 cm −1 .The infrared detector was a mercury cadmium telluride (MCT) detector, cooled with liquid nitrogen, working from ≈ 2 μm up to ≈ 20 μm, respectively corresponding to 5000 down to 500 cm −1 .
Simulations: Numerical reflectance simulations were performed using open-access code RETICOLO supported on Matlab [67] using rigorous coupled-wave analysis (RCWA) method.Dispersion relation calculations were performed using finite-difference time domain method (FDTD) with Lumerical software FDTD solver.

Figure 1 .
Figure 1.Schematic diagram of the samples.The spacer layer is sandwhiched within two metallic layers and its doping level is adjusted so it acts as an ENZ layer.See Tables1 and 2for materials and geometries informations.

Figure 3 .
Figure 3. Optical microscopy images of samples A, B, and C. Each square correspond to a different combination of a defined size and dose applied to the electron beam voltage during the writing process of the lithography, resulting in various nano-ribbon antennas width.

Figure 4 .
Figure 4. Optical reflectance measurements of the Brewster mode for all three samples.Simulations are performed using transfer-matrix method on Matlab.

Figure 5 .
Figure 5.Typical reflectance measurements obtained by FTIR spectroscopy samples A, B,and C. The whole structure is metallic in the dark grey region, while it is dielectric in the white region.Within the light grey region, the top and bottom layers are metallic, while the spacer layer is dielectric.The white/light grey and light grey/dark grey interfaces correspond to the materials plasma frequencies, respectively,  p1 and  p2 , highlighted as red dotted lines.

Figure 6 .
Figure 6.Experimental reflectance spectra for various nanoantennas of increasing widths (from blue to yellow) of samples A, B, and C. The black arrows highlight the spectral red-shift of the LSPR as the nanoantennas width increases from 0.21 to 0.46 μm, from 0.22 to 1.43 μm, and from 0.29 to 1.75 μm, respectively for samples A, B, and C. SeeTable 2 for further information.

Figure 8 .
Figure 8. LSPR frequencies function of the nanoantennas width.Circles are experimental results, error bars are measured standard deviation of the nanoantennas width, dashed lines are RCWA numerical simulations and full lines are plasma frequencies (i.e., ENZ lines) of samples B and C, respectively at 1000 cm −1 and 1300 cm −1 .

Figure 9 .
Figure 9. Dispersion relations expressed as the light frequency  function of its wavevector along the x direction k x .The stacking considered for the calculus is displayed in Figure 1.Dashed lines are plasma frequencies of the heavily-doped InAsSb layers  p1 and doped InAsSb spacer  p2 of both samples B and C. The black line correspond to the light line in air.Circles correspond to experimental LSPR frequencies.

Figure 10 .
Figure 10.Effective refractive index n eff , as function of the wavelength and the angular frequency , for all three samples.Dashed lines correspond to plasma frequencies of samples B and C. Colored gradients highlight the shrink of the real part of the permittivity of samples B and C respective spacer layer, from ϵ = 1 until it reaches zero ϵ = 0 at their respective plasma frequencies.The inset represents the calculated modal reflection phase ϕ r , with ENZ regimes (1 > ℜ(ϵ) > 0) of samples B and C depicted as cones.Green, red, and blue data, respectively correspond to sample A, B, and C.