Broadband terahertz absorption enabled by coating an ultrathin antireflection film on doped semiconductor

Hongxing Wu; Fenghua Shi; Yihang Chen

doi:10.1364/OE.24.020663

1. Introduction

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 [12]. 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 [21]. 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 [21]. 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 ${\tilde{n}}_{d}$ = n_d^’ + in_d^”, absorption resonance can be observed when d ~mλ/4n_d^’, 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/4n_d^’. 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/4n_d^’ 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 [21]. 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.

Fig. 1 Schematic of the coating systems comprising a dielectric layer with thickness d and substrate. (a) A lossless dielectric layer on a perfect electric conductor (PEC). There is no absorption at all wavelengths. (b) A lossy dielectric layer deposited on a PEC substrate. Absorption resonance occurs when d ~mλ/4n_d^’. (c) A lossless dielectric layer on a metal substrate, which can excite a resonance even when d « λ/4n_d^’ owing to the non-trivial phase shifts at the interface between the two media, but the absorption is not strong since only a fraction of incident wave can be absorbed by the metal. (d) An ultrathin lossless dielectric layer (d « λ/4n_d) on a doped semiconductor can support a strong absorption resonance because almost all of incident energy penetrates into the semiconductor and dissipates. (e) Reflection and absorption spectra and (f) the extracted effective parameters for a design of Fig. 1(d) where the refractive indices of the lossless dielectric and the substrate are set as 4 and 1+i, respectively.

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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 [22]. It can be seen that the coating system exhibits a nearly perfect impedance-match to free space, i.e. $\tilde{Z} (ω) = \sqrt{{\tilde{μ}}_{e f f} (ω) / {\tilde{ε}}_{e f f} (ω)} = 1$ , 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 ${\tilde{n}}_{2}$ . Using the multiple beam interference method [23], the reflection coefficient of such an optical coating system can be written as

\tilde{r} = \frac{r_{01} + {\tilde{r}}_{12} e^{j 2 δ}}{1 + r_{01} {\tilde{r}}_{12} e^{j 2 δ}}

where

r_{01}

is the reflection coefficient for wave incident from air to the lossless dielectric coating layer, and

{\tilde{r}}_{12}

is the complex reflection coefficient for wave incident from the dielectric coating to the substrate. Both

r_{01}

and

{\tilde{r}}_{12}

can be obtained by Fresnel equations. δ = 2πdn_d/λcosθ is the phase change when wave propagates through the dielectric layer. Here d and n_d are the thickness and refractive index of the lossless dielectric layer, θ is the incident angle. To realize antireflection, i.e.

| \tilde{r} | = 0

, two conditions should be satisfied simultaneously:

| r_{01} | = | {\tilde{r}}_{12} |

2 m π = 2 δ + φ ({\tilde{r}}_{12})

where m is an integer. When m = 0, the required thickness of the lossless dielectric layer for achieving antireflection is

d = \frac{- φ ({\tilde{r}}_{12})}{π} \frac{λ}{4 n_{d}^{}}

. It can be obtained that d ~λ/4n_d for

φ ({\tilde{r}}_{12})

~-π and d ~0 for

φ ({\tilde{r}}_{12})

~0. It means that the value of

φ ({\tilde{r}}_{12})

greatly influences the thickness of the antireflection coating layer. Figure 2 shows the value of

φ ({\tilde{r}}_{12})

as a function of both the real and imaginary parts of

{\tilde{n}}_{2}

when n_d is fixed as 2. It can be seen that

φ ({\tilde{r}}_{12})

gets close to -π when Re(

{\tilde{n}}_{2}

) > n_d and Im(

{\tilde{n}}_{2}

) → 0. On the other hand,

φ ({\tilde{r}}_{12})

gets close to 0 when Re(

{\tilde{n}}_{2}

) < n_d and Im(

{\tilde{n}}_{2}

) → 0. When Im(

{\tilde{n}}_{2}

) is fixed as a non-zero value,

φ ({\tilde{r}}_{12})

decreases with increasing Re(

{\tilde{n}}_{2}

). By solving Eq. (2a), we can obtain the solutions of

{\tilde{n}}_{2}

which is presented by the pink line in Fig. 2. It can be seen that the solutions of

{\tilde{n}}_{2}

satisfy 1 < Re(

{\tilde{n}}_{2}

) < n_d². It is worth to be noted that, as moving from the right to the left end of the pink line, the value of

φ ({\tilde{r}}_{12})

varies from -π to 0. Therefore, antireflection can be achieved by a lossless dielectric coating, which is much thinner than λ/4n_d, 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.

Fig. 2 $φ ({\tilde{r}}_{12})$ as a function of the real and imaginary parts of ${\tilde{n}}_{2}$ when n_d is fixed as 2_. The pink line represents the solutions of ${\tilde{n}}_{2}$ to Eq. (2a).

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3. Results and discussion

Based on the above discussions, we choose Ge, a lossless dielectric with a relatively large refractive index n_d = 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( ${\tilde{n}}_{2}$ ) < n_d²), 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 [29]. 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 ${\tilde{σ}}_{s} = ε_{0} ω_{p}^{2} / (γ - i ω)$ , where ω is the angular frequency, γ is the collision frequency (γ = e/(μ(N) × m*)), ω_p is the plasmon frequency ( $ω_{p} = \sqrt{N e^{2} / (ε_{0} m^{*})}$ ), 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 [30]. Then, the dielectric constant of the doped GaAs can be written as

{\tilde{ε}}_{s} = {(n_{s}^{'} + i n_{s}^{''})}^{2} = ε_{s} + i {\tilde{σ}}_{s} / (ε_{0} ω),

where ε_s is the high frequency dielectric constant of undoped GaAs and it is taken as 12.9 [30].

Figure 3(b) shows the refractive index ${\tilde{n}}_{s}$ of the doped GaAs with N = 1.35 × 10¹⁷ cm⁻³ as a function of frequency [30]. As discussed in last section, $φ ({\tilde{r}}_{12})$ is closer to zero for smaller Re( ${\tilde{n}}_{2}$ ) when Re( ${\tilde{n}}_{2}$ ) < n_d, which corresponds to a thinner thickness of the coating layer required for achieving antireflection. As shown in Fig. 3(b), the minimum of Re( ${\tilde{n}}_{s}$ ) 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 $φ ({\tilde{r}}_{12})$ as functions of the real and imaginary parts of the refractive index ${\tilde{n}}_{2}$ of a hypothetical substrate. The pink line represents the required values of ${\tilde{n}}_{2}$ which can satisfy Eq. (2a). The black line represents the values of the refractive index ${\tilde{n}}_{s}$ 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 ${\tilde{n}}_{s}$ at the frequency f₀ = 2.55 THz, as shown in Fig. 3(b). According to Eq. (2b), the value of $φ ({\tilde{r}}_{12})$ 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.

Fig. 3 (a) Side view of the thin film THz absorber structure. A doped GaAs substrate is coated with an ultrathin layer of Ge. (b) Real and imaginary parts of the refractive index of GaAs as a function of frequency when the carrier density N = 1.35 × 10¹⁷ cm⁻³. (c) $φ ({\tilde{r}}_{12})$ as functions of the real and imaginary parts of the refractive index ${\tilde{n}}_{2}$ of a hypothetical substrate coated with a Ge (n_d = 4) layer. The pink line represents the solutions of ${\tilde{n}}_{2}$ to Eq. (2a). The black line represents the values of ${\tilde{n}}_{s}$ extracted from (b). (d) Reflectance and absorptance vs frequency for the doped GaAs substrate with and without a 3 μm Ge coating layer.

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By varying the free carrier concentration from N = 5.0 × 10¹⁶ to 1.7 × 10¹⁷ cm⁻³ [30], 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.

Fig. 4 Under different free carrier concentration N, the (a) real and (b) imaginary parts of the refractive index of the doped GaAs and the (c) absorption spectra at normal incidence for the doped GaAs substrate coated with a 3-μm-thick layer of Ge. The solid lines and circles correspond to the results from TMM and FDTD method, respectively.

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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.

Fig. 5 Simulated absorption spectra for (a) TE and (b) TM wave, respectively, as a function of incident angle for doped GaAs coated with 3 μm of Ge. Here, the carrier density of the doped GaAs is N = 1.03 × 10¹⁷ cm⁻³.

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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.

3. Conclusion

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.

Acknowledgments

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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Broadband terahertz absorption enabled by coating an ultrathin antireflection film on doped semiconductor

Abstract

1. Introduction

2. Design principle

3. Results and discussion

3. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (4)

Optics Express