Terahertz spectroscopy has great potential for sensing a wide range of elementary excitations. However, terahertz studies are practically limited to macroscopic ensembles of compounds (e.g., thick pellets of crystallized molecules or highly concentrated solutions of nanomaterials) due to the long radiation wavelength (about 300 μm at 1 THz). In this chapter, we show how terahertz nanoantennas can overcome the current limitations of terahertz spectroscopy such as low sensitivity and low spatial resolution. We briefly discuss how to design the resonance characteristics of a dipole nanoantenna through a Fabry-Pérot model, and then we present the experimental characterization of the spectral response of ordered arrays of such devices. Furthermore, we demonstrate how nanoantenna arrays enable the possibility of retrieving the spectroscopic signature of a monolayer of quantum dots and, in principle, of many other organic or inorganic compounds. This technique, based on the idea of increasing the sensitivity through local field enhancement, is named nanoantenna-enhanced terahertz spectroscopy (NETS). A Fano-like interference between the fundamental mode of the nanoantennas and the phonon resonance of the quantum dots is observed, together with an enhancement of the absorption of the dots up to more than a million. Finally, we show how to extract the main spectroscopic information of the quantum dots through a simple coupled harmonic oscillator model. This novel technique can be widely applied in terahertz spectroscopic studies of nanocrystals and molecules, where extremely low concentrations are of concern.
- surface enhancement
- terahertz spectroscopy
Terahertz (THz) spectroscopy is a promising technique for sensing low-frequency modes (e.g., collective vibrations, phonons, magnons, intra-excitonic transitions) of a variety of materials and compounds . However, some of the main drawbacks of THz spectroscopy are its extremely low sensitivity and the difficulty to sense nano-objects as well as ultra-low amount of chemical compounds, due to the long radiation wavelength and the associated diffraction limitations. Recently, several research groups devoted their efforts to investigate metamaterials [2–4] and nanoslot-based [5–7] platforms tailored for the THz sensing of, for example, small molecules such as lactose, fructose, sucrose [6, 7] or microorganism such as fungi and bacteria . However, THz studies employing these techniques were not able to provide any spectral information regarding the investigated specimen. In the last decades,
2. Modeling, design and characterization of nanoantennas for terahertz light
2.1. Properties of metals and nanoantenna modeling at terahertz frequencies
In order to properly design and model THz nanoantennas, we first need to be able to describe the electromagnetic properties of a metal when it no longer behaves as a perfect conductor. In fact, already in the GHz domain, losses become an important constraint that microwave engineers have to deal with [18, 19]. In a first approximation, it is possible to retrieve the optical properties of a conductor by means of a simple model developed by Paul Drude in 1900, which considers the conducting material as an ideal gas of free electrons that move in a background of fixed positive ions. According to this picture, the valence electrons of the constituent atoms become conduction electrons and are able to freely move in the volume of the material. The complex dielectric function of the metal can therefore be obtained through a straightforward model describing the interaction of the electric field of the incoming radiation and this “sea” of electrons, which leads to the following expression :
where is the dielectric constant at high frequencies, is the plasma frequency (is the carrier concentration, the electron charge, the electron mass and the vacuum permittivity) and is the Drude scattering rate (is the carrier lifetime). As one can see, in this model, the complex dielectric function and consequently all the others optical parameters (i.e., the refractive index and the conductivity) are fully characterized by the material plasma frequency and scattering rate . Since the plasma frequency of noble metals lies in the visible UV region (e.g., for gold, ; for silver, ), at THz frequencies (), the real part of the permittivity results to be negative and significantly large in modulus. It is worth reminding that a finite and negative is a fundamental requirement for the existence of a surface wave (named
Taking advantage of the Drude description of the electromagnetic response of a metal and its extensions, we can develop a model able to predict the resonance characteristics of the basic element (i.e., a metallic nanoantenna) of the proposed NETS technique. This simplified model also allows a better understanding of the physical mechanism that gives rise to the optical response of such nanodevices. Let us consider the simplest nanoantenna geometry, a cylindrical wire of fixed radius
For simplicity, we discuss only the propagation of the fundamental surface mode
where is the effective index of the propagating surface mode and is introduced to take into account the apparent increase of the antenna length, due to the reactance of the antenna ends. The complex effective refractive index for a cylindrical wire can be derived from the Maxwell’s equations by applying the proper boundary conditions at the dielectric—metallic cylinder interface , which leads to the following equation :
whereand () are the modified Bessel functions, , ,
where is the field that couples at the tips of the nanoantenna and is the phase accumulated along the wire by the propagating surface mode in half round-trip. Figure 1b shows the resonance characteristics of a 100-μm-long gold wire nanoantenna (80 nm diameter) in vacuum, as obtained using Eq. (4). In this example, one can clearly see the first two (odd) modes of the nanoantenna, corresponding to the conditions and , respectively.
2.2. Design, fabrication and characterization of nanoantenna arrays
The Fabry-Pérot model presented above allows an initial and insightful investigation of the resonance properties of a single nanoantenna. However, the proposed NETS technique makes use of far-field measurements to retrieve the spectral properties of the specimen under investigation. In order to guarantee an easily detectable signal in the far field, arrays of nanoantennas are commonly used. Short- and long-range interactions between neighboring nanoantennas lead to changes in the resonance characteristics of an array when compared to a single isolated element . In such scenario, a fine-tuning of the array resonances can be conducted by means of electromagnetic simulations, which allow taking into account the overall electromagnetic response of the system.
Once the proper architecture has been designed, it can be fabricated by employing electron-beam lithographic techniques. More specifically, for the arrays investigated in Refs. [21, 22], we used the following procedure: a 120-nm thick poly(methylmethacrylate) (PMMA) layer was spin-coated on a 500-μm thick, high-resistivity (>10 kΩcm) (100)-oriented silicon substrate. High-resistivity silicon was selected as a substrate since it is transparent and has a constant refractive index in the THz range. Charging effects that may occur during electron exposure over an insulating substrate have been prevented by means of a 10-nm-thick Al layer that was thermally evaporated on the PMMA surface. A high-resolution Raith150-Two e-beam writer at 15 keV beam energy and 520 μC/cm2 exposure dose was used to prepare the nanoantenna patterns. After the Al removal in a KOH solution, the exposed resist was developed in MIBK/isopropanol (IPA) (1:3) for 30 s. Then, a 5-nm-thick adhesion layer of titanium was prepared using electron beam evaporation, with a 0.3-Å/s deposition rate in a high vacuum chamber (base pressure 10−7 mbar). In situ thermal evaporation (0.3-Å/s deposition rate) of a 60 nm gold film was obtained using a high temperature source mounted inside the vacuum chamber. After the film deposition, the unexposed resist was removed with acetone and rinsed out in IPA. The residual PMMA resist and organic contaminants were removed by means of O2 plasma ashing for an improved lift-off. The two-dimensional arrays, composed of aligned nanoantennas with a fixed spacing
To characterize the spectral response of these samples, we employed a standard
Because of the strong absorption of water molecules in the THz region, the measurements were performed in a nitrogen-purged environment. For the investigated arrays, the nanoantenna covering factor (defined as the ratio of the area covered by the nanoantennas to the total area of the array) is <1%, so that the transmitted spectrum when the THz radiation is polarized perpendicular to the nanoantenna main axis (nonresonant excitation) is found to be substantially equal to the one of a bare silicon substrate. For this reason, the array transmittance, named
where is the nanoantenna extinction cross section, and are the absorption and scattering cross sections respectively, is the geometric cross section,
Furthermore, to simplify the simulated geometry while taking into account the influence of the silicon substrate, we considered nanoantennas entirely embedded in a homogenous medium of effective dielectric constant: , where
It is possible to observe that, as expected, the peak resonance wavelength increases linearly with the antenna length. This behavior can be further investigated using Eq. (2), and the simple Fabry-Pérot description discussed in the previous section (Section 2.1). Since is known to be of the order of the lateral dimension of the antenna [20, 26], it can be neglected in our case (), and we can simply write: . The numerical results of the individual nanoantenna (magenta squares) can be therefore fitted with this equation to retrieve the effective refractive index. Notably, the obtained value, = 2.83, is higher than the background index employed in the simulations: . This means that a gold nanowire with lateral section as in the studied case (200 × 60 nm2) cannot be considered as an ideal conductor at THz frequencies (i.e., the electric field of the propagating surface mode penetrates inside the metal). Comparing the numerical values obtained for the resonance of an individual nanoantenna (magenta squares) with the experimental data (black crosses in Figure 4), we notice that the experimental values slightly shift toward shorter wavelengths. This shift is attributed to the long-range dipolar interaction between neighboring nanoantennas in the array, which is known to affect the resonance properties of the system [16, 18]. Indeed, when the nanoantennas are organized in an array configuration, each element of the array is excited by a superposition of the incident electromagnetic field and the field scattered by the other elements. In order to corroborate this observation, we performed numerical simulations with periodic boundary conditions, to accurately evaluate the response of an array with a 20 μm spacing in both directions on the plane. These results are reported in Figure 4 (red squares) and show a blue-shift of the array resonance frequency, confirming the origin of the shift observed in the experimental data. The residual difference between simulated and experimental values may be due to the uncertainty in the effective dielectric constants of the materials involved . For applications exploiting the
Figure 5a (magenta curve) shows the field enhancement factor at the nanoantenna tip as a function of frequency, which is defined as the ratio of the local to the free-space field. A broad resonance centered at around 1.3 THz can be observed, with a peak field enhancement of a few hundreds. Figure 5a also displays the values of and , as well as their sum (right axis). It is worth noticing that both absorption and scattering significantly contribute to the far-field resonance properties of the nanoantennas, featuring a peak at the same frequency of 1.5 THz. The near-field resonance peak thus results to be red-shifted (of about 200 GHz) with respect to the far-field peak. This behavior was previously observed in the optical frequency region and was attributed to plasmon damping [34–36]. In fact, by modeling the nanoantenna as a damped harmonic oscillator driven by the external electric field, the oscillator energy dissipation can be associated to the far-field extinction cross section of the nanoantenna, while the oscillator amplitude corresponds to the nanostructure near-field response. When damping is present, the peak of the oscillator amplitude is known to appear at a frequency that is lower than the natural frequency of the oscillator, while the maximum of the energy dissipation remains un-shifted . Therefore, the magnitude of the resonance shift between the near-field and far-field response is directly related to the total damping of the system, in terms of intrinsic ohmic loss in the metal and radiative damping . In order to demonstrate the nature of this phenomenon at THz frequencies, we substituted gold and its realistic dielectric constant in the simulations with a perfect electric conductor (PEC, i.e., a material with infinite conductivity). Figure 5b shows the results of this procedure. As expected, in the case of a PEC, the contribution of absorption vanishes, and the far-field properties are ruled by scattering. In addition to a narrower resonance, the near-field peak was found to be almost coincident with the far-field peak. Thus, the red-shift of the near-field resonance observed in THz gold nanoantennas is mainly a consequence of ohmic damping. For an effective implementation of NETS, this effect has to be taken into account during the design of the nanostructures, in order to achieve the desired near-field response.
3. Enhanced terahertz sensing and spectroscopy
As discussed in Section 2, metallic nanostructures can strongly increase the local THz electric field and can thus enhance the interaction of the incident radiation with a specimen placed in their proximity, this being the basic concept of NETS. Similar strategies, exploiting an augmented radiation-matter interaction, have been already successfully employed. For example, waveguide-assisted THz sensing  makes use of a guided geometry (e.g., in a parallel plate configuration), so that the effective interaction length can be increased up to several centimeters, enabling spectroscopic investigations of thin layers of biomolecules , explosives  and drugs . The drawback of this approach is that the specimen has to be deposited throughout the whole length of the waveguide to effectively exploit the enhanced interaction. In a similar way, THz sensing using spoof plasmons (i.e., bound electromagnetic waves on corrugated metallic surfaces) also needs that the specimen under investigation is deposited along the entire propagation length of the THz surface wave . On the other hand, THz sensors based on metamaterials [2–4] have shown to be effective in sensing thin films of various compounds, down to the sub-micrometer level. Metamaterials indeed possess a narrowband resonance, whose position in frequency is strongly sensitive to the surrounding environment. For instance, Park et al.  recently proposed a metamaterial-based THz sensor capable of detecting live microorganism such as molds, yeast cells and bacteria. In particular, they prepared metallic arrays of square rings with a micro-gap at the center and functionalized the sensor with an antibody specific to bacteria (
In recently years, a new approach based on nanoslots [5–7] resonating at THz frequencies has been proposed by Park et al. , which has shown the possibility of strongly enhancing the THz absorption coefficient of molecules. In particular, they fabricated and tested a set of single nanoslot antennas (see illustration and SEM images in Figure 6) of fixed length
More recently, Lee et al.  demonstrated a nanoslot-array-based (see Figure 7a) THz sensing method which enables the selective detection of carbohydrate molecules (such as D-glucose, fructose, sucrose and cellulose). Here, two different nanoslot arrays with slot lengths
In the next section, we will discuss the use of engineered arrays of dipolar nanoantennas, reported in Section 2, to implement surface-enhanced spectroscopy in the THz spectral region. This technique basically translates the concept introduced by SEIRA for the infrared region into the THz domain and provides a valuable tool for THz spectroscopic investigations of ultra-low amounts of chemical compounds. In particular, we will summarize some of our recent results regarding the use of resonant dipole nanoantenna arrays to retrieve the spectroscopic response of a test sample: a monolayer of cadmium selenide quantum dots (CdSe QDs).
3.1. Resonant dipole nanoantenna arrays for enhanced THz spectroscopy
In Section 2, we discussed the properties of dipole nanoantenna arrays in the THz region. As mentioned, the simplest design for a resonant nanoantenna is represented by a metallic nanorod of length equal to about half of the effective wavelength of the exciting radiation (half-wavelength dipole nanoantenna) [20, 26]. In this configuration, the electric field concentrates into two sub-wavelength “hot-spots” at the antenna extremities. By moving from an isolated nanoantenna to nanostructures coupled end-to-end through a narrow gap, it is possible to increase and localize the electric field even further within such gap . Figure 8a shows the nanoantenna arrangement employed in our investigation . Several arrays of gold dipole nanoantennas (5 × 5 mm2) were again fabricated on high-resistivity silicon substrates using e-beam lithography. We fixed the nanoantenna height and width at
Additionally, the array spacing is also a critical parameter for engineering the frequency response of the nanostructures [22, 43]. Indeed, this spacing modifies the interaction between neighboring nanoantennas and has the ability to promote, by means of in-phase coupling, their collective excitation. This can result in resonance shift and narrowing, as well as lead to higher local fields. Figure 8c reports two examples of array geometries engineered to match the phonon resonance of the dots. In particular, it shows the field (amplitude) enhancement factor in the center of the gap, being defined here as the ratio of the local electric field at position in the presence of the nanoantennas to the field in the same position considering a bare substrate with no structures. The effective localization of the THz electric field into sub-wavelength nano-volumes is illustrated in Figure 8b (lower part), which shows a 2D simulation of around the gap region under resonant conditions. In the center of the nanogap, extremely high values of (more than a thousand) are reached, which is fundamental for the successful realization of enhanced THz spectroscopy of nanomaterials. In fact, inside these gaps, the usually small effective absorption cross section of a nano-object at THz frequencies can be greatly amplified (up to more than a million times in the presented case), since it scales with .
3.1.1. Terahertz-enhanced spectroscopy of a monolayer of CdSe QDs
CdSe QDs were selected as a model system for our investigation since they can be prepared with high precision in shape and size, and they are known to form a compact and uniform layer, whose thickness can be accurately controlled. QDs with an average diameter of 5.2 nm were chemically synthesized using a previously developed protocol . Figure 9a shows a transmission electron microscope (TEM) image of the dots, highlighting good size uniformity. The spectral response of the QDs was then retrieved through Fourier transform spectroscopy  (Bruker 70/v Fourier transform spectrometer) in a transmission configuration. Figure 9b presents the THz transmittance of a 100-nm-thick layer of QDs drop-casted on a bare silicon substrate. Their phonon resonance (Fröhlich mode)  is clearly visible as a transmission dip centered at ~5.65 THz. For the demonstration of NETS, a uniform monolayer of CdSe QDs was then spin-coated over the fabricated arrays (see detail of the gap region in Figure 9c).
Afterward, the THz transmittance of the four fabricated samples (with slightly shifted resonance frequencies) was again measured, and the results are shown in Figure 10a. For nonresonant excitation (not shown, polarization of the THz light set perpendicular to the long axis of the nanoantennas), the transmission of the samples was equivalent to the one of a bare silicon substrate, thus the presence of the QDs could not be detected. This result is in agreement with the QD response reported in Figure 9b for a 100-nm-thick layer. Indeed, for such thin layers, the transmittance change (i.e., the difference in transmittance between the reference silicon substrate and a substrate covered with the CdSe layer) results to be proportional to the layer thickness (, where is the layer attenuation coefficient). Considering that a transmission change of ~3.5% was measured for a 100-nm-thick layer (Figure 9b), a change of <0.2% should be expected for a monolayer, which is below the sensitivity of our experimental apparatus.
Conversely, when the nanoantennas were resonantly excited (polarization along their long axis), a clear anti-resonant peak, located in proximity of the QD phonon frequency
3.1.2. Absorption enhancement
The results presented in Figure 10 show that NETS allows sensing ultra-low quantity of compounds (in our proof-of-concept experiment, a monolayer of CdSe QDs) through the formation of a Fano-like resonance. This is clearly visible and corresponds to a spectral feature of the specimen under investigation, which couples with the nanoantenna mode of the array. As already discussed in the beginning of this section, NETS relies on the fact that a specimen absorption is strongly sensitive to the local electric field, which can be greatly increased (see field enhancement values in Figure 8c) in proximity of nanoantennas. In this regard, we made use of numerical simulations to quantitatively estimate this effect in the case of our NETS arrays. The overall array absorption enhancement at the QD phonon resonance frequency can be evaluated by calculating the surface integral of at resonance, and dividing it by the total sensing area
In particular, for the case of the array with
Considering again the array with
3.1.3. Analytical description through a two coupled harmonic oscillator model
A direct and simple analytical model can be used to describe the NETS measurements, in order to shed more light on the underlying physical mechanism and extract the main spectroscopic information of the investigated specimen. Indeed, the observed Fano-like interference can be modeled by considering a system composed of two coupled harmonic oscillators [52, 53]: one representing the nanoantenna resonance mode and the other the phonon mode of the QDs. The first oscillator is characterized by a resonance frequency and damping (being the full width at half maximum of the resonance), while the second one has a resonance frequency and a damping factor . The two systems can be connected together through the coupling constant . Since the phonon mode of the QD monolayer is weakly excited by the far-field radiation, we consider the first (nanoantenna) oscillator to be the one excited by the external driving force: . Under this approximation, the equations of motion can be written as:
Assuming a harmonic displacement, , the amplitude of the nanoantenna oscillator can be written as:
Figure 11 shows how the absolute value squared of the nanoantenna oscillator amplitude (blue solid line) can properly reproduce the main characteristics of our experimental results (red circles, representing the normalized extinction efficiency, extracted from the experimental transmittance, for the array with
In this chapter, we have shown how to design arrays of THz nanoantennas to perform enhanced THz spectroscopy. In the beginning, we have discussed the properties of metals at THz frequencies, retrieving the complex dielectric function through the Drude model. In order to describe the resonance response of an individual dipole nanoantenna, the basic element of our investigation, we have introduced a Fabry-Pérot resonator model for a surface wave over a metallic wire. Through this simple quasi-analytical model, the resonance characteristics of a nanoantenna can be quickly evaluated, avoiding time-consuming numerical simulations. Afterward, we have presented both numerical and experimental results regarding the electromagnetic response of THz nanoantenna arrays. In particular, we have shown that, by varying the length of the nanoantennas, the resonance peak of the array can be tuned to cover the THz band offered by standard THz sources. In addition, we have discussed the resonance shift that arises between the near- and far-field responses of nanoantennas. We have shown that, in these devices, the near-field resonance peak can substantially red-shift in comparison to the far-field peak, due to the ohmic damping within the metal. This is an important information for the practical implementation of NETS, since the targeted absorption enhancement relies on the local field in proximity of the nanostructures. Subsequently, we have summarized some recent results reported in the literature on THz sensing via metamaterials and metallic nanostructures. Finally, we have presented the demonstration of NETS, reporting results obtained on a monolayer of CdSe QDs by means of engineered nanoantenna arrays coupled through nanogaps. As a result of the direct coupling between the nanoantenna mode and the phonon resonance of the QDs, the formation of an evident Fano-like interference (centered at the phonon resonance frequency) over the array response was observed. The high field enhancement (more than one thousand) obtained in the center of the nanogaps enabled an increase of the absorption cross section of the QDs up to more than a million times, which in turn allowed the ultrasensitive characterization of the QD spectroscopic signature. Moreover, we have shown that a simple model based on coupled harmonic oscillators can be employed to reproduce the Fano-like interference and extract the main spectroscopic characteristics (absorption peak frequency and bandwidth) of the investigated specimen. NETS has thus been proven to be a useful tool for the spectroscopic characterization of ultra-low quantities of nanomaterials. Very recently, using a similar strategy, Ueno et al.  performed surface-enhanced THz spectroscopy of amino acid molecules by means of arrays of gold dipole nanoantennas. This promising result shows that NETS can also be effectively extended to ensembles of molecules, and specifically to organic compounds of biological relevance.