We investigate the potential of anti-ferromagnetic nanofilms as broadband antireflection coatings in the terahertz frequency range. The anti-ferromagnetic layer is modeled by an analytic wave-impedance matching approach. The experimental results of the transmission and reflection measurements demonstrate the effectiveness of our antireflection coatings. Furthermore, we use anti-ferromagnetic nanofilms as antireflection coating for a terahertz beam splitter. Compared with conventional terahertz beam splitters consisting of an uncoated thick silicon wafer, the coated silicon beam splitter has two advantages: elimination of multiple reflections and improvement of the signal-to-noise ratio for terahertz time-domain spectroscopy in reflection geometry.
© 2015 Optical Society of America
Recently, terahertz (THz) technology has become increasingly attractive because of its potential applications [1–3 ]. Important applications of THz technology are spectroscopy and imaging, which are becoming tools for characterizing a variety of materials including semiconductors, high-temperature superconductors, and biomaterial specimens [4, 5 ].
A mature THz technology does not only require emitters and receivers but also passive components to guide THz waves. This includes lenses [6, 7 ], waveguides [8, 9 ], mirrors , wave plates , and beam splitters [12–16 ]. Many THz components and devices are fabricated on substrates with a high refractive index [17, 18 ]. As a consequence, these components and devices cause unwanted multiple reflections arising from the refractive index mismatch at the dielectric interface. These multiple reflections lead to an undesired modulation in the frequency domain due to Fabry-Pérot oscillations. This modulation can significantly influence the performance of THz systems . In order to eliminate the unwanted reflections, various antireflection layers in the THz range have been studied. One approach which is well known from optical frequencies uses quarter-wave dielectric layers as antireflection coating . This approach is quite challenging in the broadband terahertz frequency range since it is difficult to satisfy the requirements for a broad frequency region with only one layer. Furthermore, antireflection layers using non-magnetic films have been demonstrated [21, 22 ]. However, these antireflection layers are mainly based on a homogeneous single-layer metallic film with a high conductivity and were only characterized in transmission geometry. Further concepts for antireflection coatings, such as those employing metamaterials , graphene , dimethylsulfoxide compounds  and nanostructures [26–28 ], have been recently demonstrated. Yet, metamaterials only work within a narrow frequency band. Furthermore, each of the aforementioned concepts relies on complex fabrication techniques. There is still a large demand for new materials with better performances.
In this paper, we study a broadband antireflection coating consisting of anti-ferromagnetic Ir25Mn75 thin films for the THz range. Antiferromagnetic materials are versatile materials that are stable, low-cost and easy to fabricate. The performance of the antireflection layer is verified in transmission and reflection geometries.
In addition, we propose to use our antireflection coating for a THz beam splitter made of silicon. THz beam splitters are important components in terahertz time-domain spectrometer (THz-TDS) systems working in reflection geometry at normal incidence. Furthermore, they can be found in Michelson interferometers for THz waves .
In the past several approaches for beam splitters have been presented. Some of them lead to polarizing beam splitters. Some use very thin layers which could be sensitive to vibrations. Hence, in most cases beam splitters in terahertz systems are made of a thick silicon wafer . Yet, unwanted multiple reflections may cause a problem in this case.
However, the method we propose here can eliminate such unwanted reflections and improve the signal-to-noise ratio compared with a bare silicon beam splitter. Additionally, it offers a cost-effective alternative to thick silicon beam splitters as the silicon wafers can be considerably thinner.
2. Theoretical model of antireflection coatings
Figure 1 schematically shows a substrate with refractive index which is covered by the antireflection coating. It also shows the transmitted THz beam and its multiple reflections. Let us briefly recall the theoretical description for electromagnetic waves encountering such interfaces. One important parameter is the characteristic impedance [30, 31 ] which is expressed as. Here is the complex refractive index and is the impedance of free space.
If the thickness of the thin conducting film is smaller than the skin depth , the electromagnetic fields have no spatial dispersion over the film [30, 31 ]. In the terahertz frequency range, most metals satisfy the Hagen–Rubens regime , so the real part of the metal conductivity has only a weak frequency dependence with a negligible imaginary component [31, 32 ].
The reflection coefficients for s-polarization and p-polarization are :
and:Eqs. (1) and (2) , the reflection at the interface is suppressed if the interface is impedance matched, i.e. when the reflection coefficients and are equal to zero. This is achieved if the numerators in Eqs. (1) and (2) are zero, i.e. if the following equations hold.
For the s-polarization:
When the incident angle is equal to zero, the equations for the impedance matching conditions for s- and p-polarization reduce to . To obtain zero reflection at the substrate-Ir25Mn75-air interface, we changed the thickness of the Ir25Mn75 films to achieve optimal impedance matching.
In this paper, we demonstrate impedance matching for a high-resistivity silicon substrate. Silicon shows a negligible absorption at THz frequencies and, hence, the refractive indices of silicon and air are almost real constants . Furthermore the dispersion of silicon in the lower THz frequency range is negligible . The thin films we prepared satisfy the Hagen–Rubens regime, so that the real part of the film conductivity is almost constant with a negligible imaginary component in terahertz frequency range [21, 22, 31, 32 ]. According to the Eqs. (1) and (2) , the reflection coefficients are mainly determined by the real part of the film conductivity. Therefore, the reflection coefficients derived from the Eqs. (1) and (2) are almost constant in terahertz frequency range. This enables broadband antireflection coatings in the THz range.
In the following we first simulate the reflection coefficients () for the second reflection () of the Ir25Mn75-silicon system for different incidence angles and different sheet resistances in p- and s- polarization. The results are shown in Fig. 2(a) and 2(b) . The simulations show that the sheet resistance of the coating has great influence on the reflection coefficients of the secondary reflection.
3. Characterization of the antireflection coating
We now come to the experimental verification of the above described concept. We investigate the performance of the thin film at normal incidence (0°). According to the theoretical calculation from the previous section, we know that impedance matching for this angle can be achieved for a sheet resistance of 156.4 Ω. Since there is a direct connection between the thickness of the thin film and the sheet resistance (higher thickness leads to a lower resistance), thin films with different thicknesses were prepared by RF magnetron sputtering. The high-resistivity silicon with a thickness of 0.5 mm was used as the substrate. The thicknesses of the thin films were determined by a surface profiler (Tenco P-10). The sheet resistances of the thin films were determined by a four-probe measurement. For one sample, which is investigated in the following, we found a sheet resistance of 156.26 Ω. This value is quite near to the ideal value for normal incidence.
To investigate the antireflection behavior of the Ir25Mn75-silicon system we use a fiber coupled THz-TDS system with a bandwidth of 2 THz. We monitor the second pulse for normal incidence in transmission geometry as well as in reflection geometry at room temperature.
For the reflection geometry, the measured signal reflected from the bare substrate consists of several THz pulses (red curve), as shown in Fig. 4(a) . The main pulse is reflected from the front side of the substrate, and the secondary pulse and third pulse is reflected from the back side of the substrate. For the coated substrate, the second pulse and third pulse (blue curve) are completely suppressed compared with that of the bare substrate, as shown in Fig. 4(a).
Also for transmission geometry the measured signal for the bare substrate consists of several pulses (red curve), as shown in Fig. 4(b). The main pulse is transmitted through the substrate. The secondary pulse is reflected from the back side of the substrate. For the coated substrate, only the transmitted main pulse can be seen (blue). However, due to some absorption in the metal film the amplitude of the main pulse transmitted through the coated substrate is about 32% lower than the main pulse transmitted through the bare substrate. The experimental results of the reflection and transmission measurements demonstrate clearly the effectiveness of our antireflection coating in the terahertz frequency range.
4. THz beam splitter optimized by antireflection coating
In this section, we show that our antireflection coating can improve the performance of a THz-TDS system working in reflection geometry. The setup is schematically shown in Fig. 5 . A beam splitter is used to separate the incoming beam from the beam that is reflected from the sample. Usually a bare thick silicon wafer is used as beam splitter. As discussed above this approach has the drawback that unwanted reflections lead to multiple pulses. This is in particular problematic if the THz waveform is transformed to the frequency domain to extract spectral information on a sample. One approach to solve this problem is to reduce the size of the measuring window. Yet, this leads to reduced spectral resolution, which is a major drawback. As a second option, a very thick silicon wafer can be used. But high quality thick silicon wafers are expensive. Here we show that our antireflection coating can lead to a cost-efficient component with good performance.
In the following, we compare a coated beam splitter to an uncoated beam splitter. The thickness of silicon substrate is 1 mm. Typically, a beam splitter is used at an incidence angle of (). According to Fig. 2(b) the ideal sheet resistance for this case is 181.8 Ω in p-polarization mode. Yet, among the samples available the one which most closely matches this value has a sheet resistance of 217.8 Ω. As the angle of incidence for this value and p-polarization is the measurements are carried out using this angle.
In the experiment, the coated substrate and the bare substrate were placed in the same position on the sample holder in order to reduce the misplacement error between the measurements, as shown in Fig. 5. These measurements were performed three times, to ensure the reproducibility of the experimental results.
Figure 6(a) shows the time domain waveforms for the uncoated beam splitter (red) and the coated beam splitter (blue). It can be seen that an unwanted second pulse is measured in the case of the uncoated beam splitter. This second pulse leads to fast oscillations in the spectrum. This can be seen in Fig. 6(b) which compares the spectra corresponding to the two time domain waveforms. Besides, one can see that the presented coating is truly broadband as the bandwidth of the signal is not reduced.
Furthermore, one notices that the signal amplitude of the main pulse is slightly higher for the case of the coated beam splitter. In order to compare the performance of both beam splitters quantitatively, we calculate the energy of the main pulse within the time window indicated by the dashed lines in Fig. 6(a). The terahertz signals acquired are a discrete series of data points. The energy of the pulse is given be the temporal integral. Since we have discrete points here we use a sum and . Here is the amplitude of the electric field, is dielectric constant,is permeability, is sampling point and is the total number of sampling points. From this calculation it follows that the coating of the beam splitter increases the detected energy of the main pulse by 51.3%. In this sense the coated beam splitter improves signal-to-noise ratio in terahertz spectroscopy compared with that of uncoated beam splitter.
In conclusion, we demonstrated the application of anti-ferromagnetic nanofilms as efficient broadband antireflection coatings in the terahertz frequency range. Moreover, we presented a novel method using our antireflection coating for a silicon beam splitter in a THz-TDS setup. We have shown that the coated beam splitter has two advantages: elimination of multiple reflections and improvement of the signal-to-noise ratio. Furthermore, thin silicon substrate can be used. This leads to a cost-efficient component for THz-TDS systems operating in reflection geometry. Hence, the coated beam splitters hold the potential to increase the overall performance of THz-TDS systems.
This work is partly supported by the CAEP THz Science and Technology Foundation.
References and links
1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
2. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011). [CrossRef]
3. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50(3), 910–928 (2002). [CrossRef]
4. R. Ulbricht, E. Hendry, J. Shan, T. F. Heinz, and M. Bonn, “Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy,” Rev. Mod. Phys. 83(2), 543–586 (2011). [CrossRef]
7. S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, M. Koch, and T. Probst, “Optical properties of 3D printable plastics in the THz regime and their application for 3D printed THz optics,” J. Infrared Millim. Terahertz Waves 35(12), 993–997 (2014). [CrossRef]
8. K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009). [CrossRef] [PubMed]
9. M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90(11), 113514 (2007). [CrossRef]
10. C. Jansen, S. Wietzke, V. Astley, D. M. Mittleman, and M. Koch, “Mechanically flexible polymeric compound one-dimensional photonic crystals for terahertz frequencies,” Appl. Phys. Lett. 96(11), 111108 (2010). [CrossRef]
12. C. C. Homes, G. L. Carr, R. P. S. M. Lobo, J. D. Laveigne, and D. B. Tanner, “Silicon beam splitter for far-infrared and terahertz spectroscopy,” Appl. Opt. 46(32), 7884–7888 (2007). [CrossRef] [PubMed]
13. C. W. Berry and M. Jarrahi, “Broadband terahertz polarizing beam splitter on a polymer substrate,” J. Infrared Millim. Terahertz Waves 33(2), 127–130 (2012). [CrossRef]
16. T. Niu, W. Withayachumnankul, A. Upadhyay, P. Gutruf, D. Abbott, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Terahertz reflectarray as a polarizing beam splitter,” Opt. Express 22(13), 16148–16160 (2014). [CrossRef] [PubMed]
17. H. T. Chen, J. Zhou, J. F. O’Hara, and A. J. Taylor, “A numerical investigation of metamaterial antireflection coatings,” Tstnetwork. Org. 3(2), 66–73 (2010).
18. W. E. Lai, H. W. Zhang, Y. H. Zhu, Q. Y. Wen, W. W. Du, and X. L. Tang, “Bilayer metallic nanofilms as broadband antireflection coatings in terahertz optical systems,” Opt. Express 22(3), 2174–2184 (2014). [CrossRef] [PubMed]
21. 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]
23. 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]
24. Y. Zhou, X. Xu, F. Hu, X. Zheng, W. Li, P. Zhao, J. Bai, and Z. Ren, “Graphene as broadband terahertz antireflection coating Graphene as broadband terahertz antireflection coating,” Appl. Phys. Lett. 104(5), 051106 (2014). [CrossRef]
25. F. Yan, E. P. J. Parrott, X. D. Liu, and E. Pickwell-MacPherson, “Low-cost and broadband terahertz antireflection coatings based on DMSO-doped PEDOT/PSS,” Opt. Lett. 40(12), 2886–2889 (2015). [CrossRef] [PubMed]
26. 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]
27. X. Wang, Y. Li, B. Cai, Y. Zhu, X. Wang, Y. Li, B. Cai, and Y. Zhu, “High refractive index composite for broadband antireflection in terahertz frequency range High refractive index composite for broadband antireflection in terahertz frequency range,” Appl. Phys. Lett. 106(23), 231107 (2015). [CrossRef]
28. L. Ding, Q. Yang, S. Wu, and J. H. Teng, “Polarization independent broadband terahertz antireflection by deep-subwavelength thin metallic mesh,” Laser Photonics Rev. 8(6), 941–945 (2014). [CrossRef]
29. M. Wichmann, M. Stein, A. Rahimi-Iman, S. W. Koch, and M. Koch, “Interferometric characterization of a semiconductor disk laser driven terahertz source,” J. Infrared Millim. Terahertz Waves 35(6–7), 503–508 (2014). [CrossRef]
30. K. M. 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(5), 327–333 (1987). [CrossRef]
31. M. Dressel and G. Gruener, “Electrodynamics of Solids,” Electrodynamics of Solids (Cambridge Press, 2002).
32. M. Born and E. Wolf, “Principles of optics,” Principles of Optics (Pergamon Press, 1980).
33. D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time domain-spectroscopy with terahertz beams of dielectrics an semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]