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Abstract
Hybridization induced transparency (HIT) resulting from the coupling between the material absorption resonance and the artificial structure (metamaterial) resonance provides an effective means of enhancing the sensitivity in the terahertz spectroscopic technique-based sensing applications. However, the application of this method is limited by the versatility to the samples with different volumes, because the samples usually have a refractive index larger than unity and their presence with different thicknesses will lead to a shift of the structure resonance, mismatching the material absorption. In this work, we demonstrate that by using InSb coupled rod structures, whose electromagnetic response in the terahertz band can be easily controlled by using ambient parameters like the temperature or magnetic field, the HIT effect can be easily tuned so that without the needs to change the rod geometry, one can realize efficient terahertz sensing with different sample thickness.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz (THz) band (0.1-10THz), although the least explored in the electromagnetic spectrum, is believed to be the most technologically important spectral range, driven by the possibilities of “seeing” through many optically opaque materials like packing plastics and identifying the composition of materials, especially for those with similar colors to human eyes, e.g. wheat powder and drugs [1,2]. Such elemental identification arises from the fact that many chemical molecules have intra-/inter-molecule rotational or vibrational resonances located within this spectral regime. These resonances can be macroscopically characterized by the imaginary parts of the relative dielectric constant of the bulk material. Traditionally, direct transmission through a geometry containing the sample is a commonly used approach to measure the absorption of materials over a spectral range of interest [3]. The molecule-dependent absorption frequency provides compositional information, while the absorbance quantifies the amount. Due to the relatively large wavelengths (few tens of microns to one millimeter) of THz radiations and the small imaginary part of the permittivity (most samples should still be categorized as lossy dielectrics), the required sample thickness is quite large to achieve a well pronounced absorption dip in the transmission spectrum. This scenario, which can be shown using the Beer-Lambert law, limits the applications of THz spectroscopy in many circumstances. Higher sensitivity of THz sensing with low volume or concentration of sample is required to further push the applications of THz techniques, as with trace gas sensing [4] or biomedical diagnosis.
To date, many approaches have been explored and investigated to achieve enhanced THz sensing for low-volume detection. For example, using a waveguide to increase the radiation interaction with the sample [5], or using a cavity structure so that the THz radiations will interact for a multiple of times with the samples embedded in the cavity [6]. The concept of hybridization induced transparency (HIT) [7], also known as absorption induced transparency [8], arising from the coupling between artificial structures, typically metamaterial unit cells, and the material resonances [9], is an interesting and promising technique. HIT has been investigated for the interactions between electromagnetic waves and matters ranging from visible to the THz regimes. One main drawback of this technique for sensing is that the metamaterial resonance should match spectrally the material absorption; thus, it is accompanied with the lack of versatility when using varied sample volume. Practically, most samples have a refractive index larger than unity. As a result, a change in the sample amount also changes the electromagnetic environment of the artificial structure and results in a spectral shift of the structure resonance. Since it is hardly possible to modify the physical resonator geometries after fabrication, other strategies must be used to manipulate the electromagnetic property of the resonator material itself to realize spectral tuning. To this end, electrically-gated graphene resonators in the mid-infrared spectrum were demonstrated in spectral tuning of resonances with the application of DC voltage [10]. In the THz band, however, such spectral tuning may not be so significant due to a larger contrast between the sub-nanometer thickness of the monolayer graphene structure and the larger wavelengths. Furthermore, electric gating may present more challenges and complexity in the device fabrication. Conventional plasmonic materials for THz and RF bands, namely noble metals like copper, require extreme experimental conditions such as a static magnetic field as high as a few tesla [11] to achieve spectral tuning, due to the high concentration of electrons in these materials.
In this paper, we numerically demonstrate that the HIT effect can be dynamically tuned with ease by using the III-V semiconductor, InSb, as the THz plasmonic material. Due to the proper concentration level of electrons in thermally excited InSb at room temperatures, the plasma frequency of InSb is located in the THz band [12], leading to a negative yet moderate (the absolute value is on the order of 10) part of the permittivity required for the excitation of confined surface plasmon polariton (SPP) mode which still maintains a relative small imaginary part thanks to the high mobility of carriers [13]. InSb based THz resonators are analogous to plasmonic nanoantennas in the visible and near-infrared [14] and will be used as the resonators constituent for the HIT effect in this paper. The thermal responsivity of this III-V semiconductor can simply be tuned by changing the ambient temperature or applying a static magnetic field of modest strength. In both cases, the permittvity of InSb is changed, resulting in a mode effective index change of the supported SPP mode and a subsequent resonance shift of the InSb rods. Then the InSb rod resonance can be adjusted matching the material absorption of the target sample for a variety of thicknesses. Such properties can be exploited to simplify the practical implementation of dynamic tuning, eliminating the complexities associated with gated graphene structures, since no electrodes or laborious fabrication processes are required. As a result, a tunable HIT effect can be more efficiently achieved, and favorable for the THz sensing for a variety of sample thicknesses.
2. Structure
The HIT effect is shown in Fig. 1(a). The absorption of a material is usually accompanied by an energy transition from the ground state to the excited state, followed by a subsequent relaxation like thermal decaying. This process can be modeled using a Lorentz oscillator, manifesting the dielectric constant of the bulk material in the Lorentz form. As a result, the sample can be treated as a homogenous material. The resonances can be simplified using a series of Lorentz models in the numerical analysis. For the HIT effect, a resonator with the same resonance as the target material, is used. The coupling between the two resonators [9] give rise to two hybrid states (shown as two yellow bars on the rightmost panel of Fig. 1(a)) between which a transparency in the absorption spectrum, instead of a superimposed absorption, is observed. Normally, the material absorption and the structural resonance have different bandwidths (characterized by different colors of the excited state expansion in Fig. 1(a)). The HIT scheme draws parallels to electromagnetically-induced-transparency (EIT), where metamaterials with a radiative element (bright) are coupled with a subradiant (dark) element [15–17]. We note, however, the coupling strength between the two resonances, along with its resonance bandwidth, must be carefully engineered to achieve HIT, as opposed to the weak coupling or strong coupling phenomenon [18]. The transmittance contrast between the transparency peak and its adjacent dip is affected by both the material thickness and the spectral matching between the material resonance and the structure resonance. For the same thickness, a higher contrast suggests that a smaller thickness can be used and a higher sensitivity can then be expected. As a result, the latter should be adjusted to get the highest contrast to characterize the material volume with the highest sensitivity.α-lactose, which has a typical material absorption at 0.53THz [19], is chosen as the model sample. Note that the enhanced sensitivity achieved using the HIT technique is compared with THz sensing using the bare sample, so other materials can also be used. The permittivity of α-lactose can be modeled using a Lorentz term to characterize this material resonance:
where is used to indicate the background permittivity of α-lactose off this resonance, is the strength factor of this resonance at, γ1 is the resonance bandwidth. These four parameters are found to be 3.145, 0.052, 2π × 0.53 × 1012 rad/s and 2π × 25.3 × 109 rad/s, by fitting the transmission of THz radiations through a α-lactose slab using experimental data from a continuous-wave THz spectroscopy [19]. and γ1 can be obtained from the resonance position and bandwidth, is related with the absorptivity through the sample whose thickness is already known, and can be determined by the fringes in the transmission spectrum due to Fabry-Perot resonances through the slab. α-lactose is then assumed to uniformly coat the area of the THz resonators, composed of an array of coupled InSb rods, whose top view is schematically illustrated in Fig. 1(b). The rounded-edge rods have diameter equal to the rod width W, and gap is g. In this paper, all InSb structures are assumed to have a thickness of 500 nm, positioned on a quartz crystal substrate (refractive index: 2) and coated with an α-lactose layer. The thickness of the α-lactose layer is greater than 500 nm, so that the InSb rods can be considered embedded in a uniform cladding.The free carriers in the InSb material can be thermal-excited and the concentration characterized using the following empirical formula [21]:
where N is in cm−3, the product of Boltzmann constant and absolute temperature, kT, is in eV. It can be found that at room temperature of 300K, the free carrier density is as high as 1.96 × 1016 cm−3. Similar to noble metals like Au and Ag, the plasma frequency is determined by the free carrier density and the effective carrier mass m* as follows:Combining Eqs. (1) and (2), it can be easily found that the plasma frequency of InSb is located in the THz band. As the temperature increases, the concentration of free carriers grows, increasing the possibility of carrier collisions. This in turn is reflected by the decrease of carrier mobility as a function of temperature. The relationships between carrier collision frequency γ2, mobility μ and temperature are governed by the following equations:
With Eqs. (1)-(5), the permittivity of InSb can be characterized similarly to noble metals using the Drude model as:
For InSb, the off-resonance permittivity is 15.68 and the effective electron mass m* equals to 0.014 me, where me is the mass of an electron. Using Eqs. (1)-(6), the electromagnetic response of both α-lactose and InSb can be modeled. The transmission spectrum of the THz radiation through the α-lactose coated InSb coupled-rod array is then calculated using the finite-element method (FEM) in this work.
We now demonstrate the use of HIT for the detection of α-lactose using a THz transmission spectrum and the drawback with it for different sample thicknesses. The resonance of the InSb rods should be designed to match the absorption of α-lactose at 0.53 THz. For this purpose, only the length L of the rods shown are tuned, while the other geometrical parameters are fixed as W = 2R = 5μm, g = 0.5μm, Px = 70 μm and Py = 12 μm. In the FEM calculations, a plane wave with the polarization along the long axis of the InSb rods is normally incident to excite the SPP mode in the InSb rods. Periodic boundary conditions are used to account for the array effect. When α-lactose is absent, it is found that L = 24.3 μm leads to a transmission spectrum with a resonance at 0.53THz, which is shown in Fig. 2(a). The resonant electric field distribution at the bottom plane of the InSb rods is shown as the inset of Fig. 2(a), exhibiting an enhancement factor around 70. The field enhancement level, close to that achieved with optical nanoantennas [20], can provide the required coupling strength between the InSb resonance and the α-lactose absorption to achieve the HIT effect. With an α-lactose layer covering the InSb rods, the spectrum is red-shifted to 0.47 THz (Fig. 2(b)) as a result of the α-lactose refractive index which is close to 3.145. A thicker α-lactose layer (> 1μm) will lead to further red-shift. Although the phenomenon of HIT can be seen around 0.53 THz, the highest contrast will be obtained when two transmission dips are symmetric around the peak. In this case, L should then be shortened so as to blue shift the structure resonance back to 0.53 THz when 1 μm thick of α-lactose is present. Unfortunately, the adjusted InSb rod geometry will experience another red-shift again if a second layer of α-lactose e.g. 2 μm covers the structure, and is a limitation of HIT sensing. It can only be designed to match the target sample of a certain thickness, which practically, would be unknown.
Fig. 2 (a) Calculated transmission spectrum when the length of the InSb rods are tuned so that the structure resonance matches the absorption of α-lactose at 0.53THz. Inset shows the magnitude of electric field at resonance along the substrate surface. (b) The transmission spectrum when 1μm-thick of α-lactose covers the same rod structure.
Thanks to the electromagnetic property of InSb material, which can be easily affected by the ambient conditions like the temperature, we will show in the next two sections that the resonance of the InSb rods can be manipulated without changing the geometry of the rods, and improving its applicability in sensing.
3. Tunable HIT using temperature
From Eq. (2), it can be seen that the carrier concentration of InSb is largely dependent on the temperature. Then, the plasma frequency of InSb shifts according to Eq. (3), leading to a change of its permittivity at a certain frequency below the plasma frequency, and culminate in the collective resonance of InSb resonator. We will use a 1 μm thick α-lactose to demonstrate the spectral tunability. As the coated InSb rods always lead to a significant red-shift of the resonance, to use the same geometry for the THz sensing of a thicker α-lactose, we first reduce the length L of the rods so that the introduction of α-lactose will result in a red-shift of InSb rod resonance towards to 0.53 THz. The value of L is chosen to be 20 μm, and the calculated transmission spectrum at the temperature of 300K is shown with a purple line in Fig. 3(a) when 1 μm of α-lactose coats the array. It is clear that transmission dip on the right of the transparency peak is more pronounced than the left. Nevertheless, when the temperature decreases from 300K to 296K in decrements of 1K, the results show that the transmission dip left of the transparency peak becomes stronger while the right dip weakens. This indicates that the original resonance of the InSb dips experiences a red-shift, steered by the temperature. The most optimal HIT is observed at temperature around 298K, exhibiting a transmission contrast of 0.516/0.493 between the transmission peak and the more proximal transmission dip, which is much higher than the transmission contrast around 0.888/0.882 for the THz through the same thickness of bare α-lactose.
Fig. 3 Transmission spectrum exhibiting the HIT effect when the temperature changes for two different α-lactose thickness, 1μm in (a) and 2 μm in (b).
The same geometry can be used for other thickness values of the α-lactose layer. For example, we increased the α-lactose thickness to 2 μm and due to the large refractive index of it, the transmission spectrum slightly red-shifted (cf. the results for 300K in Figs. 3(a) and (b)), and now the resonance from the InSb rods is on the left of 0.53 THz. Then one can increase the temperature to tune it towards 0.53 THz, and the result for the calculated transmission spectra are shown in Fig. 3(b). Apparently, the original transmission curve at the temperature of 300K gradually moves to the right, leading to the perfect HIT effect around 302K.
Our results demonstrate the strong dependence of InSb property on temperature, with the resonance tunable with temperature changes of a few degrees. A higher change in the temperature can help to realize HIT-based THz sensing for sample volumes beyond a single pre-defined number. For all its merits with regards to its thermal sensitivity, this means that the performance of InSb based THz components is vulnerable to temperature variations. Fortunately, a temperature control with the stability less than 0.1 degrees can be realized without much difficulty.
4. Tunable HIT using static magnetic fields
Besides temperature, the free carrier distribution inside the InSb material can be easily influenced by an applied magnetic field B, resulting in a cyclotron frequency ωc = eB/m* comparable to ωp2 even when B is a moderate value. This magneto-optical effect is more pronounced in the THz regime than in the optical frequencies because ωp2 is smaller in the THz band, requiring a weaker B to achieve a comparable ωc. This effect has been exploited to realize a THz isolator [21] when the magnetic field results in a non-symmetric permittivity tensor for the InSb material. For a magnetic field applied along the same direction as the incident THz radiations (see Fig. 1(b), along z + direction), the permittivity of InSb changes to the tensorial form:
while ε3 remains the same form as described in Eq. (6) because the carrier redistribution is not affected in the direction the same as the magnetic field. The α-lactose layer is set to 1 μm to demonstrate the tunability using the magnetic field, and the temperature is fixed at 300 K. Again, the InSb rod length is assumed to be 20 μm, resulting in a structure resonance larger than 0.53 THz when the α-lactose layer is present (see the blue line in Fig. 4 and note the more pronounced dip on the right). However, when a magnetic field to the sample, the two transmission dips can be rebalanced, indicating a structure resonance that is shifted to lower frequencies with increasing magnetic field. An optimized HIT effect is observed when the magnetic field is 0.15 T, which is a level easy to implement experimentally. Using a static magnetic field to tune the HIT effect provides a new alternative for THz sensing, as a result of the introduction of cyclotron frequency when using semiconductors.Fig. 4 Transmission spectrum exhibiting the HIT effect when a static magnetic field is applied along z + direction across the structure.
5. Conclusion
In conclusion, we have demonstrated the tuning of the HIT for THz sensing using the III-V material InSb-based coupled-rod array. By changing the ambient temperature or magnetic field, the material response can be modified. We have shown that, using resonators of a fixed geometry, it is possible to selectively match the structure resonance with the material absorption. The use of ambient conditions such as temperature or magnetic field, is experimentally favorable compared to electrically-gated methods. We note that the sensitivity of HIT is limited by the resonance quality factor of the artificial structures. For the InSb rods investigated in this paper or regular metal-based metamaterials, the quality factor is at the order of 10 and the HIT is effective for sample thickness only down to micron level. Other resonances with higher quality factors, like dielectric based photonic crystal cavities, can help to realize solid state sample sensing with the thickness at sub-100nm level [22] or gas sensing at ppm level [6]. However, we believe that this work can still boost the use of the HIT in THz sensing with improved sample thickness versatility, and push forward the applications of THz sensing techniques in various fields, especially in those where a variety of sample thicknesses at micron level are required.
Funding
National Natural Science Foundation of China (Project number: 51511140421), Jiangsu Science and Technology Project (BE2017003-2), Suzhou Technological Innovation of Key Industries (SYG201844)
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