Abstract

We present the potential of ultrathin bilayer metallic nanofilms for use as broadband antireflection coatings in the terahertz frequency range. The metallic layers are modeled using a wave-impedance matching approach. The experimental and theoretical results are in good agreement. Further, a novel method using our broadband antireflection coatings is proposed to eliminate unwanted reflections that interfere with the important reflection from the sample in terahertz reflection measurement. The proposed method significantly improves the calculation of the optical properties of liquid and biological samples.

© 2014 Optical Society of America

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 [710]. 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 nsub and nair, 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=|kt×Et||Ht|=Z0n˜, where kt, Et, and Ht are the unit vectors of wave propagation and the tangential components of the electric and magnetic fields, respectively. Z0=u0/ε0 is the impedance of free space. n˜=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 Eis perpendicular to the plane of incidence and the magnetic field 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 E is parallel to the plane of incidence and the magnetic field His 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 δ0(d<<δ0), the electromagnetic fields have no spatial dispersion over the film [13, 14]. The tangential component of the electric field E is continuous across the film. The discontinuity of the magnetic field H is caused by the surface currents J in the conducting film. The ultrathin bilayer metallic nanofilms described here meet the above requirements. 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 E perpendicular to the incidence plane is called S polarization, as shown in Fig. 1(a). The component of the electric field 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 Eis 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 nsub and nair separated by the bilayer metallic films, as indicated in Fig. 1(a), can be written as

Eis+Ers=Ets
and
(HipcosθsubHrpcosθsub)Htpcosθair=Js,
where

Js=Etsi=12σ˜idi.

According to Snell’s law, the incident angle θair is equal to the refraction angle θair. The reflection and transmission coefficients in the S polarization mode are obtained by solving Eqs. (1)(3), as follows:

rs=n˜subcosθsubn˜aircosθairZ0i=12σ˜idin˜subcosθsub+n˜aircosθair+Z0i=12σ˜idi
and

ts=2n˜subcosθsubn˜subcosθsub+n˜aircosθair+Z0i=12σ˜idi.

Then, the electric field 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 nsub and nair separated by the bilayer metallic films, as indicated in Fig. 1(b), can be written as

EipcosθsubErpcosθsub=Etpcosθair
and
(His+Hrs)Hts=Jp,
where

Jp=Etpcosθairi=12σ˜idi.

According to Snell’s law, the incident angle θair is equal to the refraction angle θair. The reflection and transmission coefficients in the P polarization mode are obtained by solving Eqs. (6)(8), as follows:

rp=n˜aircosθsubn˜subcosθair+Z0cosθsubcosθairi=12σ˜idin˜aircosθsub+n˜subcosθair+Z0cosθsubcosθairi=12σ˜idi
and

tp=2n˜subcosθsubn˜aircosθsub+n˜subcosθair+Z0cosθsubcosθairi=12σ˜idi.

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 rs and rp 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

n˜subcosθsubn˜aircosθair=Z0i=12σ˜idi.
For the P polarization mode, it can be written as

n˜subcosθairn˜aircosθsub=Z0cosθsubcosθairi=12σ˜idi.

When the incident angle θair is equal to zero, the equations for the impedance matching condition in the S and P polarization modes are given by n˜subn˜air=Z0i=12σ˜idi.

In the terahertz frequency range, most metals satisfy the Hagen–Rubens regime, so the real part σ˜r of the metal conductivity is only weakly frequency dependent with a negligible imaginary component 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 (n˜Si=3.42 and n˜air=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 (300K) 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 θair=30), 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 >2000Ωcm) 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 Rref 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 Rref+Rsam 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 Rref from the coated substrate and the reflection Rref+Rsam 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 Eref+sam(t) in THz-TDS arose from the superposed reflections Rref+Rsam, as shown in Fig. 7. Eref+sam(t) is given by Eref+sam(t)=Eref(t)+Esam(t), where Eref(t) and Esam(t) were the electric fields resulting from the pulses Rref and Rsam, respectively. Eref(t) was measured from the coated silicon substrate. Thus, Esam(t) was obtained from Esam(t)=Eref+sam(t)Eref(t). Further, the Fourier transformations of Eref(t) and Esam(t) were Eref(ω) and Esam(ω), respectively. Therefore, the sample information was extracted from Eref(ω) and Esam(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 T0 was transmitted through the substrate, and the secondary pulse T1 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 R0 was reflected from the front side of the substrate, and the secondary pulse R1 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 T1 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 (R1) and third (R2) 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 Rsam 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 Rsam was eliminated well, and the sample reflection Rsam 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 Rref, the measured superposed reflection Rref+Rsam and recovered reflection Rsam 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.

References and links

1. B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002). [CrossRef]   [PubMed]  

2. M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002). [CrossRef]  

3. S. Huang, P. C. Ashworth, K. W. Kan, Y. Chen, V. P. Wallace, Y. T. Zhang, and E. Pickwell-MacPherson, “Improved sample characterization in terahertz reflection imaging and spectroscopy,” Opt. Express 17(5), 3848–3854 (2009). [CrossRef]   [PubMed]  

4. W. E. Lai, H. W. Zhang, Y. H. Zhu, and Q. Y. Wen, “A Novel Method of Terahertz Spectroscopy and Imaging in Reflection Geometry,” Appl. Spectrosc. 67(1), 36–39 (2013). [CrossRef]   [PubMed]  

5. K. Kawase and N. Hiromoto, “Terahertz-wave antireflection coating on Ge and GaAs with fused quartz,” Appl. Opt. 37(10), 1862–1866 (1998). [CrossRef]   [PubMed]  

6. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010). [CrossRef]   [PubMed]  

7. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). [CrossRef]   [PubMed]  

8. Y. W. Chen, P. Y. Han, and X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009). [CrossRef]  

9. C. Brückner, T. Käsebier, B. Pradarutti, S. Riehemann, G. Notni, E. B. Kley, and A. Tünnermann, “Broadband antireflective structures applied to high resistive float zone silicon in the THz spectral range,” Opt. Express 17(5), 3063–3077 (2009). [CrossRef]   [PubMed]  

10. C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, and A. Tünnermann, “Broadband antireflective surface-relief structure for THz optics,” Opt. Express 15(3), 779–789 (2007). [CrossRef]   [PubMed]  

11. J. Kröll, J. Darmo, and K. Unterrainer, “Metallic wave-impedance matching layers for broadband terahertz optical systems,” Opt. Express 15(11), 6552–6560 (2007). [CrossRef]   [PubMed]  

12. A. Thoman, A. Kern, H. Helm, and M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008). [CrossRef]  

13. S. W. McKnight, K. P. Stewart, H. D. Drew, and K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

14. M. Dressel and G. Gruener, Electrodynamics of Solids (Cambridge Press, 2002).

15. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).

16. P. U. Jepsen, U. Møller, and H. Merbold, “Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy,” Opt. Express 15(22), 14717–14737 (2007). [CrossRef]   [PubMed]  

17. P. U. Jepsen, J. K. Jensen, and U. Møller, “Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy,” Opt. Express 16(13), 9318–9331 (2008). [CrossRef]   [PubMed]  

18. Terahertz Database, http://thzdb.org.

References

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  • |
  • |

  1. B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
    [CrossRef] [PubMed]
  2. M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
    [CrossRef]
  3. S. Huang, P. C. Ashworth, K. W. Kan, Y. Chen, V. P. Wallace, Y. T. Zhang, E. Pickwell-MacPherson, “Improved sample characterization in terahertz reflection imaging and spectroscopy,” Opt. Express 17(5), 3848–3854 (2009).
    [CrossRef] [PubMed]
  4. W. E. Lai, H. W. Zhang, Y. H. Zhu, Q. Y. Wen, “A Novel Method of Terahertz Spectroscopy and Imaging in Reflection Geometry,” Appl. Spectrosc. 67(1), 36–39 (2013).
    [CrossRef] [PubMed]
  5. K. Kawase, N. Hiromoto, “Terahertz-wave antireflection coating on Ge and GaAs with fused quartz,” Appl. Opt. 37(10), 1862–1866 (1998).
    [CrossRef] [PubMed]
  6. H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
    [CrossRef] [PubMed]
  7. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
    [CrossRef] [PubMed]
  8. Y. W. Chen, P. Y. Han, X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009).
    [CrossRef]
  9. C. Brückner, T. Käsebier, B. Pradarutti, S. Riehemann, G. Notni, E. B. Kley, A. Tünnermann, “Broadband antireflective structures applied to high resistive float zone silicon in the THz spectral range,” Opt. Express 17(5), 3063–3077 (2009).
    [CrossRef] [PubMed]
  10. C. Brückner, B. Pradarutti, O. Stenzel, R. Steinkopf, S. Riehemann, G. Notni, A. Tünnermann, “Broadband antireflective surface-relief structure for THz optics,” Opt. Express 15(3), 779–789 (2007).
    [CrossRef] [PubMed]
  11. J. Kröll, J. Darmo, K. Unterrainer, “Metallic wave-impedance matching layers for broadband terahertz optical systems,” Opt. Express 15(11), 6552–6560 (2007).
    [CrossRef] [PubMed]
  12. A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
    [CrossRef]
  13. S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).
  14. M. Dressel and G. Gruener, Electrodynamics of Solids (Cambridge Press, 2002).
  15. M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).
  16. P. U. Jepsen, U. Møller, H. Merbold, “Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy,” Opt. Express 15(22), 14717–14737 (2007).
    [CrossRef] [PubMed]
  17. P. U. Jepsen, J. K. Jensen, U. Møller, “Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy,” Opt. Express 16(13), 9318–9331 (2008).
    [CrossRef] [PubMed]
  18. Terahertz Database, http://thzdb.org .

2013 (1)

2010 (1)

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (2)

P. U. Jepsen, J. K. Jensen, U. Møller, “Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy,” Opt. Express 16(13), 9318–9331 (2008).
[CrossRef] [PubMed]

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

2007 (4)

2002 (2)

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[CrossRef]

1998 (1)

1987 (1)

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

Ashworth, P. C.

Azad, A. K.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Beard, M. C.

M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[CrossRef]

Brückner, C.

Chang, Y. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Chattopadhyay, S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Chen, F.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Chen, H. T.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Chen, K. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Chen, L. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Chen, Y.

Chen, Y. W.

Y. W. Chen, P. Y. Han, X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009).
[CrossRef]

Darmo, J.

Drew, H. D.

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

Ferguson, B.

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Han, P. Y.

Y. W. Chen, P. Y. Han, X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009).
[CrossRef]

Helm, H.

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

Hiromoto, N.

Hsu, C. H.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Hsu, Y. K.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Huang, S.

Huang, Y. F.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Jen, Y. J.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Jensen, J. K.

Jepsen, P. U.

Kan, K. W.

Käsebier, T.

Kawase, K.

Kern, A.

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

Kley, E. B.

Kröll, J.

Lai, W. E.

Lee, C. S.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Liu, T. A.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Lo, H. C.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

McKnight, S. W.

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

Merbold, H.

Møller, U.

Moorjani, K.

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

Notni, G.

O’Hara, J. F.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Pan, C. L.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Peng, C. Y.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Pickwell-MacPherson, E.

Pradarutti, B.

Riehemann, S.

Schmuttenmaer, C. A.

M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[CrossRef]

Steinkopf, R.

Stenzel, O.

Stewart, K. P.

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

Taylor, A. J.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Thoman, A.

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

Tünnermann, A.

Turner, G. M.

M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[CrossRef]

Unterrainer, K.

Wallace, V. P.

Walther, M.

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

Wen, Q. Y.

Zhang, H. W.

Zhang, X. C.

Y. W. Chen, P. Y. Han, X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009).
[CrossRef]

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Zhang, Y. T.

Zhou, J.

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Zhu, Y. H.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. W. Chen, P. Y. Han, X. C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94(4), 041106 (2009).
[CrossRef]

Appl. Spectrosc. (1)

Infrared Phys. Technol. (1)

S. W. McKnight, K. P. Stewart, H. D. Drew, K. Moorjani, “Wavelength-independent anti-interference coating for the far-infrared,” Infrared Phys. Technol. 27, 327–333 (1987).

J. Phys. Chem. B (1)

M. C. Beard, G. M. Turner, C. A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106(29), 7146–7159 (2002).
[CrossRef]

Nat. Mater. (1)

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007).
[CrossRef] [PubMed]

Opt. Express (6)

Phys. Rev. B (1)

A. Thoman, A. Kern, H. Helm, M. Walther, “Nanostructured gold films as broadband terahertz antireflection coatings,” Phys. Rev. B 77(19), 195405 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105(7), 073901 (2010).
[CrossRef] [PubMed]

Other (3)

M. Dressel and G. Gruener, Electrodynamics of Solids (Cambridge Press, 2002).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1980).

Terahertz Database, http://thzdb.org .

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Figures (8)

Fig. 1
Fig. 1

Reflection and refraction of the electromagnetic wave transmitted through the optical system, where the electric field E is perpendicular to the plane of incidence and the magnetic field 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 E is parallel to the plane of incidence and the magnetic field H is perpendicular to the plane of incidence (b).

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

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

Fig. 4
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).

Fig. 5
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).

Fig. 6
Fig. 6

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

Fig. 7
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.

Fig. 8
Fig. 8

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

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

E is + E rs = E ts
( H ip cos θ sub H rp cos θ sub ) H tp cos θ air = J s ,
J s = E ts i=1 2 σ ˜ i d i .
r s = n ˜ sub cos θ sub n ˜ air cos θ air Z 0 i=1 2 σ ˜ i d i n ˜ sub cos θ sub + n ˜ air cos θ air + Z 0 i=1 2 σ ˜ i d i
t s = 2 n ˜ sub cos θ sub n ˜ sub cos θ sub + n ˜ air cos θ air + Z 0 i=1 2 σ ˜ i d i .
E ip cos θ sub E rp cos θ sub = E tp cos θ air
( H is + H rs ) H ts = J p ,
J p = E tp cos θ air i=1 2 σ ˜ i d i .
r p = n ˜ air cos θ sub n ˜ sub cos θ air + Z 0 cos θ sub cos θ air i=1 2 σ ˜ i d i n ˜ air cos θ sub + n ˜ sub cos θ air + Z 0 cos θ sub cos θ air i=1 2 σ ˜ i d i
t p = 2 n ˜ sub cos θ sub n ˜ air cos θ sub + n ˜ sub cos θ air + Z 0 cos θ sub cos θ air i=1 2 σ ˜ i d i .
n ˜ sub cos θ sub n ˜ air cos θ air = Z 0 i=1 2 σ ˜ i d i .
n ˜ sub cos θ air n ˜ air cos θ sub = Z 0 cos θ sub cos θ air i=1 2 σ ˜ i d i .

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