Bilayer metallic nanofilms as broadband antireflection coatings in terahertz optical systems

Wei En Lai; Huai Wu Zhang; Yao Hua Zhu; Qi Ye Wen; Wei Wei Du; Xiao Li Tang

doi:10.1364/OE.22.002174

1. Introduction

Terahertz radiation in the electromagnetic spectrum lies between microwave and infrared radiation, which is well within the range of both macromolecular vibration and rotational frequencies. During recent years, terahertz technology has become increasingly attractive because of its potential applications [1, 2]. One important application of terahertz technology is terahertz spectroscopy and imaging, which are becoming potential tools for characterizing or imaging various materials including semiconductors, high-temperature superconductors, and biomaterial specimens.

For the application of terahertz technology, a terahertz system requires many passive components, such as terahertz beam splitting prisms, modulators, and filters. Many THz components and devices are fabricated on substrates with a high refractive index. Therefore, these components and devices cause unwanted multiple reflections because of the refractive index mismatch at the interface between two different materials. The unwanted multiple reflections should be eliminated in terahertz systems. For instance, in THz spectroscopy measurement, such reflections significantly influence the accuracy of extracted sample information [3, 4]. Hence, to eliminate the unwanted reflections, antireflection coatings in the terahertz region have been studied. Antireflection coatings consisting of quarter-wave dielectric layers were studied by Kawase and Hiromoto [5]. Quarter-wave dielectric antireflection layers have generally been applied in the visible range. However, in the broadband terahertz frequency range, this approach is quite challenging because it might be difficult to satisfy the requirement of realizing quarter-wave dielectric antireflection layers. On the other hand, antireflection coatings consisting of metamaterials have been demonstrated by Chen et al. [6]. Another type of antireflection coating based on nanostructure has been studied [7–10]. However, these antireflection coatings comprising metamaterial or nanostructure have complex fabrication requirements, so their practical applications may be limited. Ultrathin metallic films were studied as efficient wave-impedance matching layers in the terahertz frequency region by Kroll et al. [11] and Thoman et al. [12]. However, their wave-impedance matching layers were based mainly on a single-layer homogeneous metal film with high conductivity. Their experiments were performed only in the transmission geometry of terahertz spectroscopy.

In this paper, antireflection coatings consisting of bilayer metallic Fe₁₉Ni₈₁/Cu nanofilms are studied both theoretically and experimentally in the broadband terahertz and far-infrared ranges. The performance of the antireflection coatings is verified in the transmission and reflection geometries of terahertz spectroscopy. Further, the application of our antireflection coatings to terahertz measurement of liquid and biological samples is studied. Terahertz measurements of liquid and biological samples are generally performed in the reflection geometry [3]. In this geometry, samples are typically placed on a substrate, which is made of a material with minimal absorption and without limitations on the incidence angle and polarization state of the incident terahertz field at terahertz frequencies, such as quartz or silicon. However, in terahertz reflection measurements of liquid and biological samples, the unwanted reflections significantly interfere with the important reflection from the samples [3, 4], so the accuracy of the extracted sample information is reduced. In this paper, we propose a novel method using our broadband antireflection coatings to eliminate the unwanted reflections and to improve the calculation of the optical properties of liquid and biological samples.

2. Theory

We apply Maxwell’s electromagnetic boundary conditions to the interface between two media with refractive indices $n_{s u b}$ and $n_{a i r}$ , as shown in Fig. 1(a) and 1(b). Electromagnetic waves transmitted through the interface between two media are generally described by the characteristic impedance [13, 14]. The change in the impedance at the interface between the two media causes changes in reflection and transmission during wave propagation. The characteristic impedance of electromagnetic waves in a medium is expressed as $Z = \frac{| {\vec{k}}_{t} \times {\vec{E}}_{t} |}{| {\vec{H}}_{t} |} = \frac{Z_{0}}{\tilde{n}}$ , where ${\vec{k}}_{t}$ , ${\vec{E}}_{t}$ , and ${\vec{H}}_{t}$ are the unit vectors of wave propagation and the tangential components of the electric and magnetic fields, respectively. $Z_{0} = \sqrt{u_{0} / ε_{0}}$ is the impedance of free space. $\tilde{n} = \sqrt{{\tilde{ε}}_{r}}$ is the complex refractive index.

Fig. 1 Reflection and refraction of the electromagnetic wave transmitted through the optical system, where the electric field $\vec{E}$ is perpendicular to the plane of incidence and the magnetic field $\vec{H}$ is parallel to the plane of incidence (a). Reflection and refraction of the electromagnetic wave transmitted through the optical system, where the electric field $\vec{E}$ is parallel to the plane of incidence and the magnetic field $\vec{H}$ is perpendicular to the plane of incidence (b).

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For thin conducting films with thickness $d$ , which is smaller than the skin depth $δ_{0}$ $(d < < δ_{0})$ , the electromagnetic fields have no spatial dispersion over the film [13, 14]. The tangential component of the electric field $\vec{E}$ is continuous across the film. The discontinuity of the magnetic field $\vec{H}$ is caused by the surface currents $J$ in the conducting film. The ultrathin bilayer metallic nanofilms described here meet the above requirements. $\tilde{σ}$ and $d$ are the conductivity and thickness of metal films, respectively. Further, in reflection and refraction during electromagnetic wave propagation, the component of the electric field $\vec{E}$ perpendicular to the incidence plane is called S polarization, as shown in Fig. 1(a). The component of the electric field $\vec{E}$ parallel to the incidence plane is called P polarization, as shown in Fig. 1(b). Hence, there are two cases to be distinguished. First, the electric field $\vec{E}$ is perpendicular to the plane of incidence (S polarization) in Fig. 1(a). The electromagnetic boundary conditions at the interface between the two media with refractive indices $n_{s u b}$ and $n_{a i r}$ separated by the bilayer metallic films, as indicated in Fig. 1(a), can be written as

{\vec{E}}_{i s} + {\vec{E}}_{r s} = {\vec{E}}_{t s}

and

({\vec{H}}_{i p} \cdot \cos θ_{s u b} - {\vec{H}}_{r p} \cdot \cos θ_{s u b}) - {\vec{H}}_{t p} \cdot \cos {θ^{'}}_{a i r} = J_{s},

where

J_{s} = {\vec{E}}_{t s} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i} .

According to Snell’s law, the incident angle $θ_{a i r}$ is equal to the refraction angle ${θ^{'}}_{a i r}$ . The reflection and transmission coefficients in the S polarization mode are obtained by solving Eqs. (1)–(3), as follows:

r_{s} = \frac{{\tilde{n}}_{s u b} \cos θ_{s u b} - {\tilde{n}}_{a i r} \cos θ_{a i r} - Z_{0} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}}{{\tilde{n}}_{s u b} \cos θ_{s u b} + {\tilde{n}}_{a i r} \cos θ_{a i r} + Z_{0} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}}

and

t_{s} = \frac{2 {\tilde{n}}_{s u b} \cos θ_{s u b}}{{\tilde{n}}_{s u b} \cos θ_{s u b} + {\tilde{n}}_{a i r} \cos θ_{a i r} + Z_{0} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}} .

Then, the electric field $\vec{E}$ is parallel to the plane of incidence (P polarization) in Fig. 1(b). The electromagnetic boundary conditions at the interface between two media of refractive indices $n_{s u b}$ and $n_{a i r}$ separated by the bilayer metallic films, as indicated in Fig. 1(b), can be written as

{\vec{E}}_{i p} \cdot \cos θ_{s u b} - {\vec{E}}_{r p} \cdot \cos θ_{s u b} = {\vec{E}}_{t p} \cdot \cos {θ^{'}}_{a i r}

and

({\vec{H}}_{i s} + {\vec{H}}_{r s}) - {\vec{H}}_{t s} = J_{p},

where

J_{p} = {\vec{E}}_{t p} \cdot \cos {θ^{'}}_{a i r} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i} .

According to Snell’s law, the incident angle $θ_{a i r}$ is equal to the refraction angle ${θ^{'}}_{a i r}$ . The reflection and transmission coefficients in the P polarization mode are obtained by solving Eqs. (6)–(8), as follows:

r_{p} = \frac{{\tilde{n}}_{a i r} \cos θ_{s u b} - {\tilde{n}}_{s u b} \cos θ_{a i r} + Z_{0} \cos θ_{s u b} \cos θ_{a i r} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}}{{\tilde{n}}_{a i r} \cos θ_{s u b} + {\tilde{n}}_{s u b} \cos θ_{a i r} + Z_{0} \cos θ_{s u b} \cos θ_{a i r} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}}

and

t_{p} = \frac{2 {\tilde{n}}_{s u b} \cos θ_{s u b}}{{\tilde{n}}_{a i r} \cos θ_{s u b} + {\tilde{n}}_{s u b} \cos θ_{a i r} + Z_{0} \cos θ_{s u b} \cos θ_{a i r} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}} .

According to Eqs. (4) and (9), the reflection at the interface is suppressed when the interface is impedance matching, i.e., when the reflection coefficients $r_{s}$ and $r_{p}$ are equal to zero. To achieve the zero reflection at the silicon-Fe₁₉Ni₈₁/Cu-air interface, the numerators in Eqs. (4) and (9) have to vanish. For the S polarization mode, this can be written as

{\tilde{n}}_{s u b} \cos θ_{s u b} - {\tilde{n}}_{a i r} \cos θ_{a i r} = Z_{0} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i} .

For the P polarization mode, it can be written as

{\tilde{n}}_{s u b} \cos θ_{a i r} - {\tilde{n}}_{a i r} \cos θ_{s u b} = Z_{0} \cos θ_{s u b} \cos θ_{a i r} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i} .

When the incident angle $θ_{a i r}$ is equal to zero, the equations for the impedance matching condition in the S and P polarization modes are given by ${\tilde{n}}_{s u b} - {\tilde{n}}_{a i r} = Z_{0} \cdot \sum_{i = 1}^{2} {\tilde{σ}}_{i} d_{i}$ .

In the terahertz frequency range, most metals satisfy the Hagen–Rubens regime, so the real part ${\tilde{σ}}_{r}$ of the metal conductivity is only weakly frequency dependent with a negligible imaginary component ${\tilde{σ}}_{i}$ [11, 14, 15]. In our experiment, Fe₁₉Ni₈₁ has a lower conductivity than Cu. To obtain zero reflection at the silicon–Fe₁₉Ni₈₁/Cu–air interface, we changed the thickness of the Fe₁₉Ni₈₁ films to achieve optimal impedance matching. The chosen substrate should generally be made of a material with minimal absorption at terahertz frequencies, such as quartz or silicon. In this paper, we used high-resistivity silicon as the substrate. The refractive indices of silicon and air at the terahertz frequencies are almost real constants ( ${\tilde{n}}_{S i} = 3.42$ and ${\tilde{n}}_{a i r} = 1.0$ ). We investigated the antireflection behavior of our film samples by monitoring the second pulse in the terahertz transmission and reflection modes.

3. Experimental setup

The thin bilayer Fe₁₉Ni₈₁/Cu films in this paper were prepared by RF magnetron sputtering. High-resistivity silicon was used as the substrate. The thickness of the thin films was determined using a surface profiler (Tenco P-10). To study the antireflection behavior of our metal film samples, the samples were measured at room temperature ( $300 K$ ) using terahertz time-domain spectroscopy (THz-TDS) and mid-infrared/far-infrared spectroscopy (PerkinElmer Spectrum 400 FT Mid-IR/Far-IR spectrometer). The THz-TDS was performed in transmission and reflection modes. The frequency bandwidth in the terahertz system was limited to 2.5 THz. Outside this frequency range, the signal was too weak to obtain an acceptable signal-to-noise ratio in the terahertz system. The THz beam path was purged with dry nitrogen to avoid absorption by water vapor. In the THz transmission geometry, the terahertz beam through the focusing lens was directed to the sample, as shown in Fig. 2(a). In the THz reflection geometry, parabolic off-axis focusing mirrors were used to direct the terahertz beam to the sample (incidence angle $θ_{a i r} = 3 0^{\circ}$ ), as shown in Fig. 2(b). The basic concept for the implementation of optimal impedance matching is similar to that of rough microfocusing in optical systems. First, the theoretical thickness of the Cu films in the impedance matching condition was calculated using the DC conductivity of the Cu films. Owing to the high conductivity of the Cu films and the error between the theoretical calculation and the experiment, a film thickness of about 6.1 nm was selected to approach 80% of the theoretical thickness. Then, by controlling the thickness of the Fe₁₉Ni₈₁ films to maintain the same thickness as the Cu films, optimal impedance matching can be achieved. The experimental silicon substrates (resistivity $> 2000 Ω \cdot cm$ ) were cut from a 0.5-mm-thick wafer. The use of these thin silicon substrates in terahertz measurement of liquid and biological samples can reduce the effect of dispersion on the experimental results [3].

Fig. 2 Schematic of terahertz pulse transmitted through the uncoated and the coated substrates in the transmission (a) and the reflection geometries (b).

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In the experimental application of the antireflection coatings to terahertz measurement, the silicon substrate coated with the antireflection coatings was used to measure the reflection $R_{r e f}$ as a reference, as shown in Fig. 3(a). Further, a de-ionized water sample on the uncoated silicon substrate was measured; the time-domain waveforms of the measured superposed reflections $R_{r e f} + R_{s a m}$ from both the air/substrate interface and the substrate/sample interface are shown in Fig. 3(b). Because the phase of the signal in THz-TDS depends on the position of the reflected surface, even small errors in the phase lead to appreciable errors in extracting the sample information in the reflection geometry. In the experiment, the coated substrate and the bare substrate holding sample were held in the same position on the stage by a clamp, so the misplacement error between them was reduced. In addition, when the experimental data were processed, a simple correlation method was used to correct the phase error between the reflection $R_{r e f}$ from the coated substrate and the reflection $R_{r e f} + R_{s a m}$ from the bare substrate holding the sample. The correlation method is described in detail elsewhere [4]. These measurements were performed three times, to ensure the accuracy of the experimental results.

Fig. 3 Schematic diagrams to illustrate the measurement configurations for the reference reflection (a) and the sample reflection (b).

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In the measurement of the sample on the silicon substrate, the measured electric field $E_{r e f + s a m} (t)$ in THz-TDS arose from the superposed reflections $R_{r e f} + R_{s a m}$ , as shown in Fig. 7. $E_{r e f + s a m} (t)$ is given by $E_{r e f + s a m} (t) = E_{r e f} (t) + E_{s a m} (t)$ , where $E_{r e f} (t)$ and $E_{s a m} (t)$ were the electric fields resulting from the pulses $R_{r e f}$ and $R_{s a m}$ , respectively. $E_{r e f} (t)$ was measured from the coated silicon substrate. Thus, $E_{s a m} (t)$ was obtained from $E_{s a m} (t) = E_{r e f + s a m} (t) - E_{r e f} (t)$ . Further, the Fourier transformations of $E_{r e f} (t)$ and $E_{s a m} (t)$ were $E_{r e f} (ω)$ and $E_{s a m} (ω)$ , respectively. Therefore, the sample information was extracted from $E_{r e f} (ω)$ and $E_{s a m} (ω)$ according to Fresnel theory. The calculation process is described in detail elsewhere [16, 17].

4. Results and discussion

In terahertz transmission measurements, the measured THz signals consisted of several THz pulses, as shown in Fig. 2(a). The main pulse $T_{0}$ was transmitted through the substrate, and the secondary pulse $T_{1}$ was first reflected from the back side of the substrate. The amplitudes of both pulses were normalized with respect to the amplitude of a THz pulse transmitted through air. The normalized amplitude of the main and secondary THz pulses transmitted through Fe₁₉Ni₈₁ coatings of different thicknesses on silicon substrates are shown in Fig. 4(a). The thickness of the Fe₁₉Ni₈₁ coating influenced the electric field amplitude of the main and secondary pulses. The amplitude of the main pulse decreased as the thickness of the Fe₁₉Ni₈₁ increased because of absorption losses in the metal film. In addition, the amplitude of the secondary pulse also decreased. For a suitable thickness of the Fe₁₉Ni₈₁ layer, the secondary pulse completely vanished.

Fig. 4 Amplitude of the main and the second terahertz pulses transmitted through the silicon substrate with ultrathin bilayer Fe₁₉Ni₈₁ /Cu film in transmission geometry (a); Amplitude of the main and the second terahertz pulses reflected from the silicon substrate with ultrathin bilayer Fe₁₉Ni₈₁ /Cu film in reflection geometry (b).

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In terahertz reflection measurements, the measured THz signals reflected from both sides of the silicon substrate also consist of several THz pulses, as shown in Fig. 2(b). The main pulse $R_{0}$ was reflected from the front side of the substrate, and the secondary pulse $R_{1}$ was reflected from the back side of the substrate, as shown in Fig. 2(b). The amplitudes of the main and secondary pulses were normalized with respect to the amplitude of a THz pulse reflected from a standard Au mirror. Similarly, the thickness of the Fe₁₉Ni₈₁ layer affected the electric field amplitude of the secondary pulse reflected from the substrate/film interface, as shown in Fig. 4(b). The amplitude of the main pulse was constant because the main pulse was reflected only from the air/substrate interface. The amplitude of the secondary pulse increased as the thickness of Fe₁₉Ni₈₁ layer increased. For a suitable thickness, the secondary pulse completely vanished.

The experimental results from transmission and reflection measurements were in good agreement with those predicted by the theoretical model. The discrepancy between the experimental and theoretical results was attributed to the limited validity of the Drude model [11, 12]. Furthermore, deviation of the optical parameters of the ultrathin metal film from those of the Drude model was usually observed. The parameters of the theoretical model were obtained by measuring the DC conductivity of the Fe₁₉Ni₈₁ and Cu layers. Therefore, the optimal thickness of the metallic antireflection coatings was determined mainly by experimental measurement.

For the transmission and reflection measurements, the secondary pulse after the main pulse in the uncoated silicon substrate was used as a reference. In the terahertz transmission measurement, the secondary pulse $T_{1}$ transmitted through the Fe₁₉Ni₈₁ film of the optimal thickness was completely suppressed compared with the reference transmitted through an uncoated substrate, as shown in Fig. 5(a). In the terahertz reflection measurement, the second ( $R_{1}$ ) and third ( $R_{2}$ ) pulses from the Fe₁₉Ni₈₁ film of the optimized thickness were completely suppressed compared to the reference from an uncoated substrate, as shown in Fig. 5(b). The experimental results of the transmission and reflection measurements demonstrated the effectiveness of our bilayer metallic antireflection coatings in the terahertz frequency range.

Fig. 5 Time domain waveforms of the measured main and second terahertz pulses transmitted through the uncoated and coated substrates in transmission geometry (a); Time domain waveforms of the measured main and second terahertz pulses reflected from the uncoated and coated substrates in reflection geometry (b).

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The transmission of the optimally coated silicon substrate was compared with that of an uncoated silicon substrate by using Fourier transform infrared (FTIR) measurement in the far-infrared frequency range, as shown in Fig. 6. For the uncoated substrate, the measured spectrum oscillated severely because of interference within the substrate. However, the measured spectrum of the coated substrate showed no detectable interference fringes. Compared with that of the uncoated substrate, the average transmission of the coated substrate was reduced from $55 %$ to about $22 %$ . However, the severe oscillations of the spectrum due to interference within the substrate were completely removed, and a high-quality spectrum was obtained. The experimental results of the FTIR measurement demonstrated the effectiveness of the bilayer metallic antireflection coatings in the far-infrared region.

Fig. 6 Transmittance of uncoated and coated silicon substrates obtained by the Fourier transform infrared spectroscopy (FTIR).

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The de-ionized water sample on the silicon substrate was measured using the proposed method; the time-domain waveforms are shown in Fig. 7. The THz pulse $R_{s a m}$ reflected from the substrate/water interface was accurately recovered using our method, as shown in Fig. 7. The refractive index and absorption coefficient of the de-ionized water obtained using our method match the data from a database [3, 18] closely, as shown in Fig. 8. The small discrepancy in the absorption spectra between the experimental results and the data from the database was caused by residual atmospheric moisture in the THz beam path. Absorption lines caused by the moisture were superimposed on the absorption spectra of the testing liquid. As a result, by using the proposed method, the unwanted reflection interfering with the reflection $R_{s a m}$ was eliminated well, and the sample reflection $R_{s a m}$ from the substrate/sample interface was accurately recovered, as shown in Fig. 7. The proposed method significantly improves the calculation of the optical properties of liquid and biological samples.

Fig. 7 Time domain waveforms of the measured reference $R_{r e f}$ , the measured superposed reflection $R_{r e f} + R_{s a m}$ and recovered reflection $R_{s a m}$ by using our proposed method.

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Fig. 8 The refractive index and the absorption coefficient of the de-ionized water using our method.

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5. Conclusions

In conclusion, we demonstrated that ultrathin bilayer metallic nanofilms can be used as efficient broadband antireflection coatings in the terahertz frequency range. The ultrathin bilayer metallic antireflection coatings are applicable in the terahertz field. Moreover, we demonstrated a novel method of reflection terahertz spectroscopy using these coatings to eliminate unwanted reflections and to improve the calculation of the optical properties of the sample. The proposed method enables reliable and easy terahertz measurements of liquid and biological samples in the reflection geometry.

Acknowledgments

Wei-en Lai is supported by NSFC under Grant No. 61131005 and 6102106.This work is partly supported by “the Fundamental Research Funds for the Central Universities” under Grant No. ZYGX2010J034. Specialized Research Fund for the Doctoral Program of Higher Education(No.20110185130002). The “Fundamental Research Funds for the Central Universities” (No.ZYGX2010J034), and the CAEP THz Science and Technology Foundation(No.CAEPTHZ201207).The authors thank Emma Pickwell-MacPherson for helpful discussion.

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Bilayer metallic nanofilms as broadband antireflection coatings in terahertz optical systems

Abstract

1. Introduction

2. Theory

3. Experimental setup

4. Results and discussion

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (8)

Equations (12)

Optics Express