We show that perfect absorption of terahertz wave can be achieved in a compact system where an ultrathin film of lossless dielectric is coated on a doped semiconductor substrate. Due to the nontrivial reflection phase shift at the interface between the two media, strong resonant behavior and the concomitant antireflection occur at wavelengths that are much larger than the thickness of the dielectric film, resulting in strong absorption of the incident wave in a wide frequency range. Using this mechanism, we design a broadband terahertz absorber by coating a Ge film on a highly doped GaAs substrate. We show that such a system not only has a perfect absorption peak, but also exhibits high absorptance (over 0.9) within a fractional bandwidth of over 20%. By varying the free carrier density in the GaAs substrate, the central frequency of the absorption band can be tuned from 1.79 to 2.69 THz. In addition, the absorption performance of the proposed system is shown to be insensitive to both incident angle and polarization. Our results offer a low-cost way for the design of absorption-based THz devices.
© 2016 Optical Society of America
There has been recent interest in composite optical materials capable of absorbing incident electromagnetic energy at desired frequencies. Two main types of microstructure-based systems have been employed in the design of artificial absorbing media. One is the thin film coating system, in which a lossy semitransparent dielectric film backed by metal or Bragg reflector forms an asymmetric Fabry-Perot (FP) cavity and absorption is gradually accumulated within the dielectric layer [1–6]. To achieve constructive or destructive interference to enhance the absorption, the dielectric film is typically at least a quarter-wave in thickness. Another is the metamaterial-based system, where strong absorption occurs at the resonant frequencies of the subwavelength unit cells [7–11]. In contrast to the traditional thin film absorber, the metamaterial-based absorber can be much thinner than the operating wavelength.
While electromagnetic absorber could be of potential use in diverse field throughout the spectrum, it has attracted special attention in terahertz (THz) frequency range where the electromagnetic response of natural materials is comparatively devoid. Although the engineered electromagnetic materials, i.e. metamaterials, can realize perfect absorption at THz frequencies, the absorption is narrowband due to the resonant nature of the metamaterial . The absorption bandwidth has become one of the key factors to measure the performance of the metamaterial-based absorbers. A method was recently used to broaden the absorption bandwidth by blending resonant frequencies of individual resonating elements [13–16]. However, integrating many microresonators with different sizes on the same substrate is a great challenge for current fabrication technology. In addition, the absorption band is generally fixed, which limits the practical applications of the metamaterial-based absorbers [17–20].
Recently, it was demonstrated that perfect absorption can be achieved in a special coating system where the thickness of the coating layer is much smaller than the incident wavelength . In such a system, a highly absorbing dielectric layer was coated on an opaque and lossy substrate. By utilizing the nontrivial phase shift at the interface between the lossy media, absorption resonance can form inside the ultrathin absorbing film. Based on this mechanism, a practical design of ultrathin film absorber which works at mid-infrared region was proposed by coating a vanadium dioxide film on sapphire substrate . However, such a mechanism cannot be extended to terahertz frequencies because there are no natural materials that can meet the requirement for the absorbing dielectric layer and the opaque substrate of the coating system at this frequency range.
In this paper, we propose a novel method to realize perfect absorption by using a system comprising an ultrathin lossless dielectric film on a doped semiconductor substrate, where the impedance of the system is designed to match with that of the incident medium to eliminate the reflection. For the practical design of THz absorber, we choose Ge and highly doped GaAs as the materials for the dielectric layer and the substrate, respectively. We show that such a system cannot only achieve perfect absorption at the resonance frequency, but also exhibit strong absorption within a wide frequency range. We also show that the absorption band of the proposed design can be tuned and the absorption performance is insensitive to both incident angle and polarization.
2. Design principle
When a layer of lossless dielectric is coated on a perfect electric conductor (PEC) [Fig. 1(a)], there is no absorption because the incident light cannot enter into the PEC substrate and the reflectance equals unity. If the coating material is replaced by an absorbing dielectric [Fig. 1(b)] with thickness d and refractive index = nd’ + ind”, absorption resonance can be observed when d ~mλ/4nd’, where m is an integer and λ is the incident wavelength. In this case, there will be no absorption resonance when d is smaller than λ/4nd’. On the other hand, if a lossless dielectric film is deposited on metal with finite optical conductivity [Fig. 1(c)], absorption resonance may happen even though d « λ/4nd’ owing to the nontrivial phase shift (not limited to 0 or π) at the interface between the two media. However, in this case, the total absorption is small because only a small part of the incident energy is absorbed by the metal. Recently, it was demonstrated that perfect absorption can be achieved in a coating system where a sapphire substrate is covered by an ultrathin film of vanadium dioxide which is much thinner than the incident wavelength . However, such a method cannot be applied for the design of THz absorber because both strongly absorbing dielectric and opaque substrate with suitable absorption are required, and natural materials cannot meet this requirement at THz frequencies. We here propose a different way to design the thin film absorber by coating an ultrathin lossless dielectric layer on a doped semiconductor substrate, as shown in Fig. 1(d), to achieve antireflection. A nontrivial reflection phase shift can be generated at the interface between the coating and the lossy substrate, resulting in destructive interference of the waves reflected back to the incident medium from the ultrathin coating and hence a minimum reflection of the coating system.
We here consider an ideal design for the proposed system of Fig. 1(d), the refractive indices of the lossless dielectric layer and the substrate are set as 4 and 1 + i, respectively. In this coating system, a zero-reflection dip and a corresponding perfect absorption peak appear at wavelength λ » d, as show in Fig. 1(e). Figure 1(f) shows the retrieved effective parameters extracted via inversion of the S parameters . It can be seen that the coating system exhibits a nearly perfect impedance-match to free space, i.e., at wavelength where the reflection dip exists.
To demonstrate how to achieve antireflection through a lossless dielectric coating that is much thinner than the wavelength of light, we first assume that a lossless dielectric layer is coated on a hypothetical substrate with a complex refractive index . Using the multiple beam interference method , the reflection coefficient of such an optical coating system can be written asFigure 2 shows the value of as a function of both the real and imaginary parts of when nd is fixed as 2. It can be seen that gets close to -π when Re() > nd and Im() → 0. On the other hand, gets close to 0 when Re() < nd and Im() → 0. When Im() is fixed as a non-zero value, decreases with increasing Re(). By solving Eq. (2a), we can obtain the solutions of which is presented by the pink line in Fig. 2. It can be seen that the solutions of satisfy 1 < Re() < nd2. It is worth to be noted that, as moving from the right to the left end of the pink line, the value of varies from -π to 0. Therefore, antireflection can be achieved by a lossless dielectric coating, which is much thinner than λ/4nd, around the left end of the pink line. These results are crucial to the design of ultrathin film THz absorber, which will be discussed in the following section.
3. Results and discussion
Based on the above discussions, we choose Ge, a lossless dielectric with a relatively large refractive index nd = 4 at THz region, as the coating material so that the antireflection coating layer can be designed to be very thin. To achieve perfect absorption, a suitable material should be chosen for the substrate which can completely absorb the incident wave penetrating through the antireflection coating. Dielectric exhibits small absorption at THz frequencies, thus it is not a good candidate of the substrate material since it makes the substrate bulky. Metal generally has a too large refractive index at THz region to meet the requirement for antireflection (1 < Re() < nd2), thus it is not suitable to be the substrate as well.
Recently there has been interest in a new class of engineered metals based on heavily doped semiconductors for long-wavelength applications. Si, InAs, or heavily doped zinc oxides were demonstrated that their plasmon frequencies are at near- or mid-infrared region [24–28] and they can mimic the shorter wavelength optical properties of traditional noble metals . Benefited from the electron effective mass which is an order of magnitude smaller than that of Si, the plasma frequency of highly doped n-type GaAs can be shifted down to THz range. The frequency-dependent complex conductivity of the doped GaAs can be described via the Drude model , where ω is the angular frequency, γ is the collision frequency (γ = e/(μ(N) × m*)), ωp is the plasmon frequency (), m* = 0.067m0 (m0 is the mass of the free electron) is the effective carrier mass in n-doped GaAs, N is the carrier density, μ is the carrier mobility, e is the free electron charge. The values of N and μ can be obtained by fitting the Drude model to the experimental data measured at different doped carrier concentration . Then, the dielectric constant of the doped GaAs can be written as30].
Figure 3(b) shows the refractive index of the doped GaAs with N = 1.35 × 1017 cm−3 as a function of frequency . As discussed in last section, is closer to zero for smaller Re() when Re() < nd, which corresponds to a thinner thickness of the coating layer required for achieving antireflection. As shown in Fig. 3(b), the minimum of Re() is 1.46 within the considered frequency range, which is much smaller than the refractive index of Ge. Therefore, an ultrathin layer of Ge can realize the antireflection effect. Figure 3(c) shows as functions of the real and imaginary parts of the refractive index of a hypothetical substrate. The pink line represents the required values of which can satisfy Eq. (2a). The black line represents the values of the refractive index extracted from Fig. 3(b). It can be seen from Fig. 3(c) that there is a cross point of the black and pink lines, which corresponds to the value of at the frequency f0 = 2.55 THz, as shown in Fig. 3(b). According to Eq. (2b), the value of is calculated to be about −1.2 rad and the thickness of the Ge layer is 3 μm at the frequency f0. Figure 3(d) plots the reflection and absorption spectra for the GaAs substrate with and without the Ge coating layer. Here, the thickness of the GaAs substrate is set as 500 um so that the THz waves penetrating into the substrate are all absorbed. It can be seen that a perfect absorption peak is achieved at frequency 2.55 THz through the ultrathin antireflection coating layer of Ge. Here, the thickness of the Ge coating layer is only about 1/40 of the incident wavelength. In comparison, the maximum absorptance can only reach 0.83 for the GaAs substrate without the Ge coating layer.
By varying the free carrier concentration from N = 5.0 × 1016 to 1.7 × 1017 cm−3 , the refractive index of the highly doped GaAs layer can be tuned, as shown in Figs. 4(a) and 4(b). Figure 4(c) shows the absorption spectra at normal incidence for the coating system comprising a 3-μm-thick Ge film on a doped GaAs substrate. The simulation results from finite difference time domain (FDTD) method and those from transfer matrix method (TMM) agree well with each other. It can be seen from Fig. 4(c) that a perfect absorption peak appears at 2.55 THz when N = 1.35 × 1017 cm−3, in accordance the theoretical prediction in Fig. 3. In this case, the absorptance over 0.90 can be achieved within a fractional bandwidth of over 20%. As the carrier concentration varies from 5.0 × 1016 to 1.7 × 1017 cm−3, the absorption peak shifts from 1.79 to 2.69 THz. It can also be seen from Fig. 4(c) that as the absorption resonance deviates from 2.55 THz, the absorptance at the resonance frequency decreases only a little (the minimum value is 0.978 within the considered frequency range from 1.79 to 2.69 THz) although the amplitude condition for achieving antireflection (i.e. Equation (2a)) is destroyed to some extent. Therefore, we can realize almost perfect absorption from 1.79 THz to 2.69 THz by tuning the free carrier concentration of the doped GaAs.
For conventional thin film absorbers where a lossy dielectric medium is coated on the metal or Bragg reflector [Fig. (1b)], the interference effects rely on the phase accumulation of light for a round-trip propagation within the optical cavities formed by the coating layer, and are typically sensitive to the angle of incidence. Therefore, the absorption performance is different at different incident angles, which limits the applications of these absorbers. This shortcoming can be improved by our proposed design. As the Ge coating layer is much thinner than the illuminated wavelength, the phase accumulation during the propagation through the coating is small. Therefore, the total phase accumulation, which includes both the interface and propagation phase shifts, is mainly attributed to the phase change at the interface. As a result, the absorption performance of the proposed absorber should be insensitive to the incident angle. Figure 5 shows the simulated absorption spectra for incident angles from 0° to 60° for a doped GaAs substrate, the carrier density of which is N = 1.03 × 1017 cm−3, coated with 3 µm of Ge. It can be seen from Fig. 5 that the position and the bandwidth of the absorption band for both polarizations remain almost invariant as the incident angle varies from 0° to 45°, which means that the proposed thin film absorber is efficient for applications under multidirectional illumination.
Compared to the previous design of ultrathin film absorber, our coating system is more practical in THz region since natural materials can meet the requirements for achieving the broadband and angle-insensitive absorption. Another advantage of the proposed structure is that the central frequency of the near-perfect absorption band can be effectively tuned within a wide frequency range without changing the geometric parameters. Such a property is quite useful for THz techniques where tunable devices are desired.
In summary, we have proposed an effective method to achieve broadband absorption through an ultrathin coating layer of lossless dielectric on a lossy substrate. As a nontrivial reflection phase change exists at the interface between the coating and substrate, strong wave interference and thus the antireflection effect can form even if the dielectric film is much thinner than the illuminated wavelength. This mechanism is implemented with an ultra-thin (~λ/40) Ge layer on heavily-doped GaAs substrate. We shown that such a coating system can realize perfect absorption peak at THz region. Moreover, this system can maintain strong absorption (absorptance over 0.9) in a wide frequency range (the fractional bandwidth of over 20%). By varying the doping level of the GaAs, the central frequency of the broad absorption band can be tuned from 1.79 to 2.69 THz. In addition, the absorption performance of the proposed system was shown to be angle- and polarization-insensitive. Our results have the potential for a variety of applications where absorption-based THz devices are required.
This work was supported by National Natural Science Foundation of China (Grant No. 11274126) and Key Program of Guangdong Natural Science Foundation (Grant No. 2015A030311018). Yihang Chen acknowledges financial support from Program for Guangdong Excellent Young Teacher.
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