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Abstract
In this paper, a metamaterial absorber that achieved absorption tuning by electricity and light control has been proposed in the terahertz (THz) regime. The THz absorber exhibits an absorbance of 97.5% at a resonant frequency of 0.245 THz. First, we simulated the absorption spectra under different structural parameters. Then the absorption characteristics are analyzed under different Fermi energies and pump fluences. When the Fermi energy changes from 0 to 1 eV, the peak absorbance decreases from 97.5% to 56.2%. As the fluence of the pump beam increases from 0 to 100 µJ/cm2, the peak absorbance decreases from 97.5% to 42.8%. The amplitude modulation depth T of our designed absorber is approximately 0.55. Electric and magnetic resonances are proposed in this article, which allows for nearly perfect absorption. Finally, the absorption for both transverse electric and transverse magnetic modes were investigated under different incident angles, from 0° to 75° with a step-width of 15°. The absorber can be potentially applied to THz detection, imaging, and sensing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials, an artificially composite material, are widely used in various fields owing to their unique properties of negative index, near zero index, perfect absorption and perfect transmission [1–3]. With the development of metamaterials, they have attracted intense attention for its promising applications in broadband absorption [4], color printing [5], analog computing using graphene [6], and beam manipulation [7]. THz waves refer to electromagnetic waves with frequency ranges between 0.1 and 10 THz [8]. THz technology has recently experienced rapid development, showing significant practical value in biological imaging, communication, sensing, and spectroscopy [9–12]. In 2008, Landy et al. designed the first metamaterials absorber, which achieved nearly perfect absorption in microwave bands [3]. Subsequently, perfect absorbers in visible [13,14], infrared [15], THz [16,17], and microwave bands [18,19] were proposed. In terms of frequency band, the absorber can achieve single-band, dual-band [20], and multi-band [21] absorption, as well as narrowband and broadband [21,22] absorption.
At present, the research hot spots tend to be on the tunable absorber [23]. Traditional absorbers typically consist of metal, dielectric, and metal planes [24]; once the structure is fabricated, the absorption spectrum is determined, limiting the practical application [25]. One popular way nowadays is to adopt novel tunable materials that can be controlled by pump beam, electricity, heat, carriers doping, et al. For example, the absorber can be tuned by graphene [26], the conductivity of which is controlled by an applied voltage. A tunable absorber with periodically cross-shaped graphene layer can achieve peak absorbance tuning by controlling the Fermi energy [26]. Recently, temperature sensitive materials-based absorbers have also been developed, which have attracted researchers’ attention, such as strontium titanate (STO) [27] and vanadium dioxide (VO2) [28]. Xin Huang et al. [27] demonstrated a metamaterial absorber with a metal cylinder-STO-metal plane structure that enables the resonant peak tuning in the THz regime by controlling the temperature of STO. Huan Liu et al. [28] investigated a symmetrical L-shaped VO2 array absorber that achieved a broadband tunable absorption at different temperatures of VO2. Also, other new materials have also been found to realize high energy losses in the THz band. Wei Zheng et al. [29] proposed an absorber based InSb, which achieved center frequency movement with the temperature changing of InSb. A tunable absorber consist of layers of black phosphorus separated by dielectrics was reported, which realizes the tuning of peak absorbance at different electron doping concentrations of black phosphorus [30]. Bulk Dirac semimetal metasurface based tunable absorber have been employed for realizing tuning by controlling the Fermi energy of Dirac semimetal [31].
In this paper, a tunable absorber is introduced with the used of graphene and doped silicon combination as one structure in the THz regime to achieve absorption tuning. In our proposed absorber, the tunable characteristic is achieved by adjusting the Fermi energy of graphene from 0 eV to 1 eV and pump fluence of doped Si layer from 0 to 200 μJ/cm2. The amplitude modulation depth T of 0.55 can be achieved. The tunable absorption mechanism is further explored by examining electric and magnetic field energy density distributions. Simultaneously, our designed structure can remain at 80% peak absorbance with an incident angle of up to 60° for TM and TE mode.
2. Structure and design
The designed tunable THz metamaterial absorber based on graphene and doped silicon is presented in Fig. 1(a); the unit cell consists of a regular octagonal graphene layer, strontium titanate material layer, doped silicon layer; and a gold background layer. The corresponding geometry dimensions of the unit cell are illustrated in Fig. 1(b), where the period p = 80 µm and the side length of the regular octagonal graphene monolayer a = 40 µm. The thicknesses of doped Si layer and strontium titanate material layer are h = 50 µm and t = 2 µm, respectively. The conductivity of gold with a thickness b = 0.2 µm is given by σgold = 4.07×107 S/m, the thickness of which is much bigger than the skin depth in the THz range. To obtain the specific performance of the proposed metamaterial absorber, numerical calculations are carried out using the frequency domain solver of CST Microwave Studio (www.cst.com). In the simulation, the open boundary condition is arranged in the z direction of the structure when the unit cell boundary condition is used in the x/y direction. The reflectance (R) and transmittance (T) are obtained by reflection coefficient S11 and transmission coefficient S21. Notice that no electromagnetic wave penetrates the structure, therefore, S21 is closed to 0. Subsequently, the absorption (A) was calculated using the equation A = 1 − |S11|2 = 1 − R.
Fig. 1. (a) Schematic view of the proposed tunable THz absorber. (b) Unit cell of the structure with geometrical parameters, the parameters of the absorber are set as p = 80 μm, t = 2 μm, h = 50 μm, b = 0.2 μm, a = 40 μm. The permittivity dispersion (real part: dotted line and imaginary part: solid line) of doped Si in the different layer under the pump fluence of 200 μJ/cm2 is shown on the middle.
We define the electric field transverse along the x-axis as the TE mode and the magnetic field transverse along the x-axis as the TM mode. In our paper, simulation results are obtained under TM mode as shown in Fig. 1(b). Graphene’s conductivity consists of intraband and interband contributions, which can be expressed by the Kubo formula as follows [12]:
The relative permittivity of doped silicon in the THz range is modeled by the Drude response model [33,34]:
in which ${{\varepsilon }_\infty }$ is the intrinsic permittivity of Si with a value of value of 11.68, γ is the collision frequency with a value of 1.9573×1012 s-1. The plasma frequency ωp is expressed by: where N is the free carrier concentration with a value of 0.03×1018 cm-3, m* is the effective mass of the free carriers, with a value of 0.37 m0, m0 is the mass of the electron,${{\varepsilon }_0}$ is the permittivity of free space, and e is the electron charge. After calculation, the value of ωp is 1.6042×1013 rad/s in the case of no pump fluence.When pump beam is incident perpendicular to the absorber, it can change the carrier concentration of the doped silicon layer, causing the plasma frequency ωp to change. But it is unable to excite carriers homogeneously in the Si layer. The carrier density N distribution in the doped silicon along the z direction can be expressed by [35]:
where $\beta$ is the absorption coefficient for the pump beam with the value of 1020 cm-1, p is the pump fluence at the top surface of the structure with the unit of μJ/cm2, z is the depth along the doped silicon, e is the charge on an electron, h is Plank’s constant, and v is the frequency (375 THz) of the pump beam [35]. According to Eq. (5), the carrier density distribution along the z direction is calculated as shown in Fig. 2. It can be seen that the carrier concentration decreases exponentially as the depth of z increases under different pump fluences.Fig. 2. The theoretically calculated carrier density distribution along the z-axis in the doped Si layer for different pump fluences. The dotted bars represent the carrier density for each slice used in the simulation for the 200 μJ/cm2 pump fluence.
We can use the experimentally validated hierarchical model to simulate the gradient-distributed carrier density in doped silicon under a pump beam [35]. The height of the Si layer is 50 µm. In our simulation, we divide the layer into ten slices, where each slice has a thickness of 5 µm. Under different pump fluences, each layer has a different carrier concentration N as shown in Table 1.
Table 1. In simulation, the carrier density N and the plasma frequency ωp for different layers with different pump fluences
For the 200 μJ/cm2 pump fluence as shown in Fig. 2, the distributions of the carrier density N in each slice are consistent with the theoretically calculated carrier density distribution along the z-axis. The corresponding plasma frequency ωp is also calculated by Eq. (4) which determines the dielectric constant of doped silicon. In order to have the pump beam of normal incidence incident on the absorber, a terahertz wave with a 15-degree angle of oblique incidence is needed, as shown in Fig. 2. However, a terahertz wave of normal incidence is used in our simulation due to its angularly insensitive structure. The subsequent incident angle analysis will verify this characteristic.
Strontium titanate is a kind of thermal active material whose complex relative permittivity is temperature dependent. When the temperature of STO increases from 70 to 300 K, the material-loss in the THz band decreases, and the lower the temperature, the higher the thermal-sensitivity [36]. The relative permittivity of STO can be expressed as follows [36,37]:
Metasurface tuning can be achieved by doping two-dimensional materials, including graphene, highly doped semiconductors (such as silicon, germanium), phase change materials (such as VO2, germany-antimony-tellurium), etc [38]. In our structure, graphene and doped silicon are both commercially available and inexpensive compared with other materials [26,39]. In addition, complementary metal-oxide semiconductor (CMOS)-compatible silicon has experienced rapid development over the past decade [38], which provides more possibility for the chip integration of our structure. We have designed a set of feasible absorber production process. First, we purchase commercially doped silicon film. Second, a layer of 200 nm gold is deposited on the silicon side and a STO film is deposited on the other side. Third, uniform atomic monolayer of graphene was grown by an optimized chemical vapor deposition method. The as-grown graphene was then transferred onto STO film via atomic layer deposition (ALD), then patterned into closely packed regular octagonal arrays using e-beam lithography with poly (methyl methacrylate) as an electron beam resist [39]. Oxygen plasma (40W, 500 mT, 15 s) was used to etch away the exposed area, leaving the periodic regular octagonal graphene pattern protected by a poly layer, which was then removed with acetone [39].
3. Simulated results and discussion
First, the reflection, transmission, and absorption spectral outcomes are analyzed under graphene Fermi energy Ef = 0 eV in the case of no pump fluence. The working frequency band of this absorber is 0.1 to 1 THz. As observed from Fig. 3, the reflectance rate of 2.5% is realized at frequency 0.245 THz, so the peak absorbance of 97.5% can be achieved in the case of zero transmission.
Fig. 3. Reflection, transmission, and absorption spectral outcomes in the TM mode. The frequency represents as ω/2π.
Second, the influence of geometrical dimensions of the structure on the spectral response is investigated. Figure 4(a) presents simulated absorption spectrum for different thickness values t of the STO material at Fermi energy Ef = 0 eV in the case of no pump fluence. When we increase t from 1 μm to 4 μm, absorption peak shifts to the left and yields an absorption efficiency > 97%. We also discuss the effect of the regular octagonal graphene layer with length values a of 20 μm, 30 μm, 40 μm, 50 μm, respectively. It can be clearly seen from Fig. 4(b) that when the length of graphene is reduced from 50 μm to 20 μm, there is no effect on the absorption. This is due to the fact that the graphene area is large enough not to change the absorption. The structural parameters of the absorber in our paper are: p = 80 μm, t = 2 μm, h = 50 μm, b = 0.2 μm, a = 40 μm.
Fig. 4. (a) Absorption spectra for four different thickness values t of the STO material. (b) Absorption spectra for four different lengths values a of the regular octagonal graphene layer. The frequency represents as ω/2π.
We further investigated the absorption amplitude tunable property of the absorber by changing the Fermi energy of graphene and the pump fluence of doped Si layer. When the pump beam is incident, the beam power is the order of milliwatts magnitude, which has little effect on the conductivity of graphene [40,41]. Figure 5(a) shows the absorption spectra under different Fermi energies in the case of no pump fluence. As illustrated in Fig. 5(a), when the Fermi energy Ef changes from 0 to 1 eV, the peak absorbance decreases from 97.5% to 56.2% at the center frequency 0.245 THz. When the absorption intensity changes, the center frequency remains the same. Here, a surface plasmon resonance effect is demonstrated: a finite nanostructure supports dipolar plasmon resonances that couple directly to incident light [39]. Graphene sheet is equivalent to a surface plasmon, which has a large effect on electric dipole absorbing than dipole resonant frequency [42]. Figure 5(b) shows the absorption spectra under different pump fluences at Fermi energy Ef = 0 eV. As shown in Fig. 5(b), as the fluence of the pump beam increases from 0 to 100 µJ/cm2, the peak absorbance decreases from 97.5% to 42.8% with a blueshift of center frequency due to the photo-excitation of the carriers in the Si layer. The peak frequency is 0.245, 0.254, 0.282, and 0.534 and 0.768 THz, respectively. It is worth noting that when the pump fluence reaches 200 µJ/cm2, the peak absorbance increases slightly.
Fig. 5. (a) Absorption spectra under different Fermi energies in the case of no pump fluence. (b) Absorption spectra under different pump fluences at Fermi energy Ef = 0 eV. The frequency represents as ω/2π.
To better demonstrate the modulation effect of the absorption amplitude, the distribution of the peak absorbance under different modulation modes are further analyzed below. Figure 6(a) shows the peak absorbance and the full width at half maximum (FWHM) values at Fermi energies Ef = 0, 0.2, 0.4, 0.6, 0.8, 1 eV, in the case of no pump fluence. Figure 6(b) shows the peak absorbance and the FWHM values with pump fluences of 0, 25, 50, 100, 200 µJ/cm2 at Fermi energy Ef = 0 eV. We use the modulation depth T to analyze the amplitude modulation range. We define T as the maximum value of peak absorbance (Amax) minus the minimum value of peak absorbance (Amin). As shown in Fig. 6(a), when the Fermi energy increased from 0 to 1 eV, the peak absorbance was 97.5%, 88.9%, 78.2%, 69.2%, 61.9% and 56.2%, respectively; and the modulation depth T of 0.413 was achieved in the form of electrical modulation. The FWHM values increased from 155 to 405 GHz. It can be observed from Fig. 6(b) that the peak absorbance decreased to 42.8% when the pump fluence increased from 0 to 100 µJ/cm2; the modulation depth T almost reached 0.55 in the form of light modulation. It is worth mentioning that when the pump fluence increases to 100 µJ/cm2, the FHWM increases significantly, close to 900 GHz.
Fig. 6. (a) The peak absorbance (blue curve with the left ordinate) and the FWHM (orange curve with the right ordinate) values under different Fermi energies in the case of no pump fluence. (b) The peak absorbance (blue curve with the left ordinate) and the FWHM (orange curve with the right ordinate) values under different pump fluences at Fermi energy Ef = 0 eV.
We summarized the previous work of the tunable THz absorber [26,28,30,42,43] in Table 2. Its performance, including the working waveband, peak absorbance, the modulation depth T, and the tuning method is presented. Compared with some tunable absorbers in Table 2, our design can achieve a larger modulation depth. But there are also absorbers with higher modulation depth. Our absorber has the advantage of flexible modulation, which can realize both electricity and light modulation modes.
Table 2. Performance comparison of the tunable THz absorber
To better understand the tunable absorption mechanism, the electric field energy density and magnetic field energy density distribution are investigated under different Fermi energies. Figure 7 (a-c) present the electric field energy density distribution and Fig. 7 (d-f) present the magnetic field energy density distribution at the center frequency 0.245 THz, for Fermi energies Ef = 0, 0.4, 1 eV in the case of no pump fluence. When the Fermi energy of graphene increases from 0 to 1 eV, the electric field and magnetic field energy density clearly decrease in the STO material and Si layer as shown in Fig. 7 (a-c) and (d-f). The augment of Fermi energy leads to the increase of electromagnetic absorption of graphene layer, which reduces the energy to reach the STO and the Si layer. As shown in Fig. 7(a) and 7(d), we can observe that strong electric and magnetic fields are primarily focused on the STO material layer and Si layer, which indicates large electric and magnetic energy losses. This phenomenon corresponds to the high absorption rate in Fig. 5(a). It is noteworthy that the electrical losses in Fig. 7(a-c) are significantly reduced, which indicates a weakening of the electrical resonance. As shown in Fig. 7(d-f), the magnetic field energy density also significantly decreases, indicating that the magnetic resonance weakens. In Fig. 7 the electric and magnetic field energies at the edge of the regular octagonal graphene layer show a trend of enhancement, owing to the increased conductivity of graphene. There are also electric and magnetic resonances in the graphene layer; however, these primarily exist in the STO material layer and the Si layer. To summarize, electric and magnetic resonances achieve nearly perfect absorption.
Fig. 7. Electric field energy density distribution under different Fermi energies at the center frequency 0.245 THz, in the case of no pump fluence. (a) Ef = 0 eV. (b) Ef = 0.4 eV. (c) Ef = 1 eV; magnetic field energy density distribution under different Fermi energies at the center frequency 0.245 THz, in the case of no pump fluence. (d) Ef = 0 eV. (e) Ef = 0.4 eV. (f) Ef = 1 eV.
The tunable mechanism is further explored by investigating the electric field energy density and magnetic field energy density distribution under different pump fluences. Figure 8(a-c) show the electric field energy density distribution at different peak frequency points (0.245 THz, 0.282 THz, 0.534 THz) corresponding to the pump fluence 0, 50, 100 µJ/cm2, respectively. Figure 8(d-f) show the corresponding magnetic field energy density distributions. As shown in Fig. 8(a-c), (d-f), when the pump fluence increases from 0 to 100 µJ/cm2, the electric field and magnetic field energy density significantly reduce, indicating that electric and magnetic resonances weaken. A decrease in resonance means a decrease in absorption, which precisely explains the decrease of peak absorbance in Fig. 5(b).
Fig. 8. Electric field energy density distribution under different pump fluences, at Fermi energy Ef = 0 eV. (a) No pump fluence. (b) 50 µJ/cm2. (c) 100 µJ/cm2; magnetic field energy density distribution under different pump fluences, at Fermi energy Ef = 0 eV. (d) No pump fluence. (e) 50 µJ/cm2. (f) 100 µJ/cm2.
In a practical application, the light source is incident on the device at an oblique angle, thus, it is of significant value to design a large angle insensitive absorber. The absorption spectra of oblique incidence in the TM and TE modes are investigated with angles of 0°, 15°, 30°, 45°, 60°, and 75°, respectively, shown in Fig. 9. The simulated results are obtained in the case of no pump fluence and Fermi energy Ef = 0 eV. It can be observed from Fig. 9(a) and (b) that the absorption curves are coincident with the angles of 0° in TM and TE modes, which indicates the characteristic of polarization independence. As shown in Fig. 9(a) and (b), the absorber sustains over 90% peak absorbance when the incident angle is below 45°, for both TM and TE modes. In the TM mode, when the incident angle is greater than 60°, the absorption is below 80%. This is because the direction of the magnetic field varies with the angle of incidence, which results in a decrease of magnetic resonant strength. However, the direction of the magnetic field is maintained in TE mode, which can remain above 80% of the peak absorbance, in the case of an incident angle below 75°, as shown in Fig. 9(b). This tunable absorber can maintain a high absorption rate under large angle incidence, thus, it may have great application value with the characteristic of larger angle insensitivity.
Fig. 9. Absorption spectra of the absorber, as a function of the incident angle and frequency, under oblique incident angles of 0°, 15°, 30°, 45°, 60°, 75°, respectively. (a) TM mode. (b) TE mode. The frequency represents as ω/2π.
Conclusion
In our work, we present a tunable absorber, which can be tuned by electricity and light. This absorber can remain a nearly 98% absorption rate at the resonant frequency 0.245 THz. Our designed absorber can achieve the modulation depth T of approximately 0.55. The tunable absorption mechanism is explored by examining the electric and magnetic field energy density distributions of the structure at different Fermi energies and pump fluences. Our designed absorber can remain at 80% peak absorbance with an incident angle of up to 60° for TM and TE mode. It has the advantages of polarization independence, angle insensitivity, and a thin dimension. By changing the structural parameters or combining with other adjustable materials, this absorber is expected to achieve narrow-band absorption. This characteristic makes it possible to realize sensing [44]. At the same time, the absorption frequency band of the absorber can also be changed in this way, which can be applied to solar harvesting [45]. In addition, incident THz waves are absorbed by the metamaterial absorber, converted to heat, and subsequently detected by detectors [46]. Therefore, this proposed absorber also has great application potential in THz imaging.
Funding
National Natural Science Foundation of China (61875251, 61875179).
Disclosures
The authors declare no conflicts of interest.
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