The requirements for a broadband antireflective structure in the THz spectral region are derived. Optimized structural parameters for a surface-relief grating adapted to the spectrum of an intended THz pulse are deduced. The effect of a structure fabricated into Topas® by a single-point diamond-turning process is demonstrated.
©2007 Optical Society of America
The THz spectral range is broadly defined as the frequency range from 0.1 to 10 THz corresponding to wavelengths from 30 μm to 3 mm . THz pulses comprise a broad fraction of this spectrum: typically they reach from 0.1 to 3 THz corresponding to wavelengths from 100 μm to 3 mm [2,3]. The requirements for an antireflection treatment in the THz spectral range arise from the large wavelengths and from the broad spectral bandwidth of the radiation.
Conventional antireflection coatings consist of mono- or multi-layer systems whose function is based on interference. Electromagnetic waves are partly reflected and partly transmitted at the interfaces between the individual layers. A correct combination of the amplitudes and appropriate phasing leads to destructive interference in reflection in the coating and thus a reduced reflection. With conventional multi-layer systems low reflectivity values are easily realized for a relative small spectral region, i.e. up to one octave. On the contrary, it is a challenging task to design multilayers suited for broadband antireflection applications.
A minimum requirement for a broadband antireflection coating is that within a spectral region larger than one octave the reflection values are lower than the reference value, i.e. the value without an antireflection treatment. With laterally homogeneous layers, a broadband antireflection effect can be achieved when the refractive index of the layers increases continuously from air to the substrate material .
The simplest version of a broadband antireflection coating is a quarter-wave layer. For the design wavelength, reflection is reduced to extremely low values (ideally to zero). For higher wavelengths, reflection approximates asymptotically against the reference value, but never exceeds it. A typical material used in THz optics is Topas® with a frequency independent refractive index of 1.5, which was determined by own measurements. To AR coat Topas®, the demands on the quarter-wave layer are a refractive index of 1.22 and a thickness of 6.12 μm already for the shortest wavelength in the THz spectrum (30 μm). On the one hand, there are no technical adequate materials with a refractive index below 1.3 in the THz spectral region . On the other hand, coating a surface by conventional deposition techniques with a homogeneous thickness of 6.12 μm will be very expensive.
Another approach achieving a broadband antireflection effect are surface-relief gratings with a grating period smaller than the incident wavelength. The grating structure generates a continuous gradient of the refractive index from the surrounding medium (typically air) to the substrate material. These subwavelength surface-relief gratings are also known as moth-eye structures. The fabrication and the effect of such structures are widely known for the visible, infrared and solar spectrum [5,6]. Surface-relief gratings have also been applied in the microwave region [7–11]. In the THz region, however, due to the structural parameters necessary conventional fabrication techniques for surface-relief gratings cannot be used . Specially adapted manufacturing methods are required.
THz imaging and spectroscopy are associated with the transfer of information [13–16]. In many applications, it is necessary that only the zeroth diffraction order is able to propagate, i.e. the directly reflected and transmitted light. The propagation of higher diffraction orders would be connected with a loss of information. This is in contrast to the demands on an antireflective structure in the solar spectral region (UV-VIS-NIR), where a maximum energy transfer to the solar cell shall be achieved. For UV-VIS-NIR higher diffraction orders can contribute to the energy deposit as well and do not need to be omitted [17,18].
The structural period of surface-relief gratings is determined by the shortest wavelength of the spectrum, i.e. about 10 μm for the THz region. The structural depth is specified by the largest wavelength of the spectrum, i.e. about 1 mm. The resulting aspect ratio of 100 for an antireflective structure for the whole THz spectral region is neither producible nor mechanical stable.
In the following sections, the effect of several broadband antireflective structures for pulsed THz radiation is investigated and an optimized antireflective structure for THz pulses is proposed.
2. Theoretical background
2.1. Zeroth-diffraction-order grating
For a 1D binary grating (Fig. 1) the condition for a zeroth-diffraction-order grating is:
with Λ – grating period, λ – wavelength in vacuum, ni – refractive index of the incident medium, ns – refractive index of the substrate, θi – the polar angle of incidence and ϕ – the azimuthal angle of incidence.
Equation (1) is deduced from the grating equation. An arbitrary angle of incidence, i.e. conical refraction, constrains the grating period to be:
From Eq. (2), for the shortest wavelength of the THz region (30 μm) and a substrate refractive index, ns = 1.5, a maximum grating period of 12 μm is required. For perpendicular incidence (θi = 0°), the constraint on the grating period is less tight:
For the shortest wavelength of the THz region Eq. (3) yields a maximum period of 20 μm for ns = 1.5.
The determination of the diffraction efficiency in the single diffraction orders of a grating with arbitrary unit cell occurs by the Rigorous Coupled Wave Approach (RCWA) .
The efficiency of the grating is strongly dependent on the depth d of its structure [21,22]. Fig. 2(a) shows the reflectance against the ratio d/λ for a 1D grating with an aspect ratio of structural depth to structural period d/Λ = 2 (Fig. 2(b)) with ni = 1 and ns = 1.5. An aspect ratio of 2 ensures mechanical stability and producibility by single-point diamond turning. The reflectance reaches a first minimum at d/λ ≈ 0.4. For increasing d/λ the value oscillates within a falling envelope. For d ≫ λ the reflectance is effectively zero. Applied to the large wavelength boundary of the THz region (i.e. 3 mm) a depth d of about 1 mm is required to achieve d ≫ λ.
2.2. Antireflective structure determined by the shortest wavelength of the spectrum (100 μm)
In the following section, it is investigated which spectral bandwidth can be achieved with a 1D surface-relief grating with triangular cross-section as shown in Fig. 2(b). For example, a structural period of 50 μm and a structural depth of 100 μm were chosen. The refractive index of the substrate material is 1.5. Transmittance and reflectance are determined by RCWA for perpendicular incidence (see Fig. 3). The curves of Fig. 3 show that the suppressed reflection is connected with an increased transmission, i.e. R + T = 1. This means that only the zeroth diffraction order is able to propagate and no energy is diffracted into higher diffraction orders. For a broad spectral range from (i.e. from 0.75 to 3 THz) a transmittance of over 99 percent can be achieved. This is broader than one octave, the achievable bandwidth for the quarter-wave layer or a multi-layer coating: the ratio of the highest frequency to the lowest frequency is approximately 4:1. Although a relative broad spectral region is covered by this structure, the effect becomes less pronounced when the frequency increases from 0.1 to 0.75 THz, which is again a frequency ratio of 7.5:1. This shows that the parameters of the structure have to be optimized for the intended THz spectrum.
The inset of Fig. 3(a) shows the reflectance of a quarter-wave layer for the transition from air to a substrate medium with n = 1.5 for a design wavelength of 300 μm (f = 1 THz). For the layer a thickness of 61.2 μm and a refractive index of 1.22 were supposed. For the design frequency reflection is reduced to zero. Reflection is also zero for frequencies that obey f = f0(2N+1), with f0 – the design frequency and N – a nonnegative integer. For other frequencies reflection varies between zero and the reference value without a coating. As simplest realization of a broadband antireflection coating the quarter-wave layer can be used as reference for the optimized surface-relief gratings.
2.3. Antireflective structure determined by the largest wavelength of the spectrum (3 mm)
As a next step the effect of a surface-relief grating with the required depth for the largest wavelength of the THz range (3 mm) was investigated. For the 1D structure with triangular cross-section a structural period of 0.5 mm and a structural depth of 1 mm were chosen. Fig. 4 shows that a high transmission can be achieved only for low frequencies. For frequencies from 0.1 to 0.4 THz transmittance is over 99.5 percent. But transmission is drastically reduced for frequencies higher than 0.4 THz. Transmittance and reflectance are only shown for the zeroth diffraction order. Comparison of both curves shows that most energy is scattered into higher diffraction orders. Thus, this grating period is connected with a loss of information for frequencies higher than 0.4 THz.
2.4. Effect of a 2D structure
To demonstrate the difference between a 2D and a 1D structure the same parameters as in Sec. 2.2 (Λ = 50 μm and d = 100 μm) were used to simulate reflectance and transmittance (Fig. 5). The 2D structure is pyramidal and can be generated by rotating the 1D grating by 90° about the z-axis and ablating the 1D structure again. In general, no new effect appears in the reflectance and transmittance curves. Because the structure has the same period in x and y direction, reflectance and transmittance are equal for the TE and TM polarization. In comparison to the 1D structure the bandwidth of the 2D antireflective structure is slightly smaller: transmittance is greater than 99 percent for frequencies above 0.8 THz. But between 1.15 THz and 3 THz transmittance is higher than 99.75 percent. One reason for the difference in the progression of the curves of the 1D and 2D structure are the different material fractions and thus the different gradient of the effective refractive index from air to the substrate material.
3. Realization of a surface-relief structure
3.1. Adaptation of the structural parameters to the intended THz pulse
The spectrum of a typical THz pulse reaches from 0.1 – 2 THz [3,23,24]. Thus, the shortest wavelength is 150 μm. For perpendicular incidence, according to Eq. (3), the maximum grating period is Λ = 100 μm. An aspect ratio of 2 yields a depth of d = 200 μm. Figure 6 shows the theoretical progression of the curves for reflectance and transmittance.
3.2. Manufacturing by a single-point diamond-turning process
The structure was realized on Topas® 8007 plates measuring 70 × 70 × 2 mm3. Manufacturing of the structure was performed by a Precitech Nanoform® 350 machine by means of single-point diamond turning at the IOF . Thus, a subwavelength grating of radial symmetry with the required structural parameters (period 100 μm, depth 200 μm) was generated. The samples were structured on both sides. At single-point diamond turning the deepest structural depth can be realized with a v-groove tool. There, the removal of the material is accomplished by grooving, i.e. the shape of the tool is formed in the material. The realizable aspect ratio is dependent on the aperture angle α of the tool:
The tool used for manufacturing the structures had an aperture angle of 28°. Thus, an aspect ratio d/Λ = 2 could be realized. It is also possible to generate structures with nearly straight grooves. For this, the sample is clamped off-axis a long distance (about 150 – 200 mm) from the rotation axis. Figure 7 shows a structured Topas® sample (a) and microscope pictures of its cross-section (b) and (c). For the cross-section pictures the sample was cut by a wafer saw at the dashed line shown in Fig. 7(a). Figure 7(b) shows the cross-section from a part of the outer region of the turned structure. There the structure has a high contour accuracy. The chippings are due to the sawing process. Figure 7(c) shows the cross-section of the center of the sample that coincides with the rotation axis of the turning process. In a region with a diameter of about 1.5 mm the height of the structure decreases continuously until it is zero in the center. This is caused by the low cutting speed around the rotation axis.
4. Measurements and results
For the measurements a THz-TDS setup was used [3,23]. The samples were placed in the collimated beam between two off-axis parabolic mirrors of diameter 50.8 mm. The dimensions of the samples were chosen in the way that no additional diffractional effects were introduced to the propagating beam. Thus, all radiation that passed the samples was collected and refocused to the detector by the second off-axis parabolic mirror.
The determination of the performance of the structured sample occurred in comparison to an unstructured sample of same dimensions. A measuring cycle comprised the measurement with the structured sample and the measurement with the unstructured sample. At first the properties of a single sample were investigated. A single surface between air and a medium with ns = 1.5 has a transmission of 96 percent for perpendicular incidence. Thus, a single sample with two surfaces has a transmission of 92.16 percent if interference effects are not included. If destructive interference occurs transmission is reduced to 84 percent. Also the effect of two both-sided structured samples was investigated. The two samples were placed into the setup with a distance of 24 mm. Two samples, i.e. four surfaces, have only a transmission of 84.93 percent if interference effects are not included.
4.1. Single sample transmission
Figure 8(a) shows the averaged waveforms of 10 measuring cycles. The pulses are superimposed in the delay time axis. The water absorption in air causes the oscillations after the main pulse. The structured sample shows a maximum transmission amplitude of 0.967 a.u. ± 0.7 %. The unstructured sample has a maximum amplitude of 0.935 a.u. ± 1.1 %. The curve of the unstructured sample shows a pulse copy with clearly enhanced amplitude. There, the transmission amplitude of the maximum at the pulse copy of the structured sample is 0.028 a.u. ± 1.6 %. The amplitude of the unstructured sample is 0.061 a.u. ± 0.9 % at this place. This pulse copy is due to reflections within the sample. It experienced two reflections and was then transmitted in the direction of the detector. The time delay between the main pulse and this pulse copy is 20.64 ps corresponding to a distance of 4.128 mm in Topas® (n = 1.5). This is twice the sample thickness. Figure 8(b) shows the average spectral intensity of the 10 measuring cycles. Two effects are apparent for the structured sample: the transmission is increased and the modulation of the spectrum caused by the reflection echo inside the sample is reduced.
Figure 9 shows the measured and theoretical ratio of the transmittance of the unstructured to the structured sample. To suppress the modulations in the spectra of the measured curves the pulses were cut after the main pulse before applying FFT. Thus, only the directly transmitted radiation is considered. To obtain the transmittance on passing a number of surfaces without consideration of back reflections, the single surface transmittance has to be taken to the power of the number of passed surfaces m. At the radial symmetrical structure the effective local transmittance lies between the value of the TE and TM transmittance predicted in Sec. 3.1. Thus, for the frequency dependent transmittance T(f) of the structured surface the average between the TE and TM transmittance is chosen. For the unstructured surface transmittance is 0.96 at perpendicular incidence. Thus, the theoretical ratio Rtheo of the transmittance of the unstructured to the structured surface is given by:
There are two regions where the structured sample has a higher antireflective effect than predicted: Around 0.2 and 0.9 THz the transmittance of the unstructured sample is only about 90 and 82 percent, respectively, of the transmittance of the structured sample. But the structured sample has hardly any effect to frequencies around 0.55 THz. Here, the transmittance of the structured sample is below the theoretical predicted. For frequencies above 1.2 THz noise dominates.
There are several reasons for the deviation of the intensity transmission of the structured sample from reference measurement: First, the difference could be due to the deviation from the ideal form of the structure. The cross-section pictures (Fig. 7(b) and (c)) show that the structure has a high contour accuracy in the outer region and a form deviation in a small area around the center of the sample. The quasi-optical setup with two off-axis parabolic mirrors possesses a frequency dependent beam waist in the collimated beam . Thus, the influence of the form deviation to the effect of the structure to the single frequencies is different. But it should be pointed out that the structure is not deformed such that it works as a quarter-wave layer. Then, a next minimum in the curve was expected at 0.6 THz.
Second, the insertion of the sample into the quasi-optical setup causes a shift of the back focal length in the optical path. This leads to a shift of the focus at the detector position, which was the same for all measurements.
Furthermore, the rays are not ideally collimated and thus not all perpendicular on the sample surface.
Finally, cross-polarization effects caused by the radial symmetry of the structure could have a strong influence on the measuring result [11,27]. The THz radiation is horizontally polarized. Dependent on the orientation of the incident field vector to the local grating vector, a vertically polarized field component can be generated. Because the detector only measures the horizontally polarized field components, the contribution from the vertically polarized field components cannot be included.
4.2. Two samples transmission
Fig. 10(a) shows the averaged waveforms of 6 measuring cycles. The pulse copy caused by reflections within the material is more pronounced than in case of a single sample. The first maximum in the curve of the structured sample has an transmission amplitude of 0.948 a.u. ± 0.7 %, whereas the amplitude at the first maximum of the unstructured sample lies only at 0.873 a.u. ± 0.9 %. At the place of the pulse copy the maximum transmission amplitude of the structured sample is 0.028 a.u. ± 5.1 %. The amplitude of the unstructured sample is 0.093 a.u. ± 1.6 %. The reason for this is that on the one hand the main pulse is weaker because it passes two samples and on the other hand this pulse copy is the sum of the pulse reflected on the second surface of the first sample and directly transmitted through the second sample and the pulse directly transmitted through the first sample and reflected at the second surface of the second sample. Both pulses experience the same temporal delay (see the inset of Fig. 10). Other possible pulse copies from reflections inside the samples with comparable amplitude have a too large delay and were not detected. Fig. 10(b) shows the average spectral intensity of the 6 measuring cycles. The two effects described for the single sample are amplified: the structured sample causes an increase in the transmitted intensity and a reduction of the modulations in the spectrum caused by pulse copies. This corroborates that the effect described in Sec. 4.1 is due to the structure of the sample.
Figure 11 shows the measured and theoretical ratio of the transmittance of the unstructured to the structured samples. Again, there are two regions where the structured samples have a clearly enhanced transmittance with respect to the unstructured samples: around 0.3 THz and 1.1 THz the transmittance of the unstructured samples is about 75 percent of the transmittance of the structured samples. There, transmittance of the structured sample is above the predicted one of the theoretical curve. But around 0.7 THz the structure does not work as required. There, the transmittance of the structured samples is slightly decreased with respect to the unstructured sample.
The measured curve of the two samples correlates with the measured curve of the single sample. Again, the difference from the expected progression of the curve could be due to the form deviation, the non-perpendicular incidence of the radiation, the back focal shift and cross polarization effects.
The principal effect of a broadband antireflective surface-relief structure for the THz spectral region is demonstrated for the first time, particularly in the time domain. The progression of the experimental curves does not perfectly correspond to the theoretical curves. There are two spectral regions where the structure works very well. One of these spectral regions coincides with the region of maximum intensity of the pulse spectrum. This is the reason for the clear appearance of the antireflection effect in the time domain. The antireflective structure has two effects: an increase of overall transmission, and a reduction of modulation in the spectrum caused by pulse copies from reflections within the samples. With the suggested triangular cross-section of the surface-relief grating a broader bandwidth can be achieved than with a quarter-wave layer, although attention must be paid to the information loss that occurs for wavelengths smaller than the grating period. A structure with an aspect ratio of 2 was generated on the surface of the Topas® samples by a single-point diamond-turning process. Only in a small area around the rotation axis was there a form deviation caused by the low cutting speed. To suppress scattered radiation from this area the turning process could be omitted in the center. The introduced turning process for manufacturing a radial symmetrical grating is suited for an application to curved surfaces, e.g. THz lenses. For plane surfaces the subwavelength grating can also be realized as nearly straight lines. For this the sample has to be clamped off-axis a long distance from the rotation axis.
This research was supported by the Fraunhofer Gesellschaft Internal Programs under Grant No. MAVO 813907.
References and links
1. D. Mittleman, Sensing with Terahertz Radiation (Springer, Berlin Heidelberg, 2003).
2. M. van Exter and D. R. Grischkowsky, “Characterization of an Optoelectronic Terahertz Beam System,” IEEE Trans. Microwave Theory Tech. 38,1684–1691 (1990). [CrossRef]
3. G. Matthäus, T. Schreiber, J. Limpert, S. Nolte, G. Torosyan, R. Beigang, S. Riehemann, G. Notni, and A. Tünnermann, “Surface-emitted THz generation using a compact ultrashort pulse fiber amplifier at 1060 nm,” Opt. Commun. 261,114–117 (2006). [CrossRef]
4. Lord Rayleigh, “On Reflection of Vibrations at the Confines of two Media between which the Transition is Gradual,” Proc. Lond. Math. Soc. 11,51 (1880). [CrossRef]
5. M. Karlsson and F. Nikolajeff, “Diamond micro-optics: microlenses and antireflection structured surfaces for the infrared spectral region,” Opt. Express 11,502–507 (2003).http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-5-502 [CrossRef] [PubMed]
6. A. Gombert, K. Rose, A. Heinzel, W. Horbelt, C. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Sol. Energy Mater. Sol. Cells 54,333–342 (1998). [CrossRef]
7. E. M. T. Jones and S. B. Cohn, “Surface matching of dielectric lenses,” IRE International Convention Record 2,46–53 (1954). [CrossRef]
8. D. G. Bodnar and H. L. Bassett, “Analysis of an Anisotropic Dielectric Radome,” IEEE Trans. Antennas Propag .23,841–846 (1975). [CrossRef]
9. R. Padman, “Reflection and Cross-Polarization Properties of Grooved Dielectric Panels,” IEEE Trans. Antennas Propag. 26,741–743 (1978). [CrossRef]
10. J. Y. L. Ma and L. C. Robinson, “Night moth eye window for the millimetre and sub-millimetre wave region,” Optica Acta 30,1685–1695 (1983). [CrossRef]
11. P. F. Goldsmith, Quasioptical Systems (IEEE Press, New York,1998). [CrossRef]
12. C. Brückner, B. Pradarutti, S. Riehemann, O. Stenzel, R. Steinkopf, A. Gebhardt, G. Notni, and A. Tünnermann, “Moth-eye structures for reduction of Fresnel losses at THz components,” Proc. SPIE 6194,61940N (2006). [CrossRef]
14. D. M. Mittleman, M. Gupta, R. Neelamani, R. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68,1085–1094 (1999). [CrossRef]
15. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11,2549–2554 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-20-2549 [CrossRef] [PubMed]
16. H. Zhong, H. Redo-Sanchez, and X. Zhang, “Identification and classification of chemicals using terahertz reflective spectroscopic focal-plane imaging system,” Opt. Express 14,9130–9141 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-20-9130 [CrossRef] [PubMed]
17. B. Bläsi , Holographisch hergestellte Antireflexoberflächen für solare und visuelle Anwendungen (Albert-Ludwigs-Universität, Fakultät für Physik, Freiburg i. Br., Diss., 2000).
18. A. Gombert, B. Bläsi, C. Bühler, and P. Nitz, “Some application cases and related manufacturing techniques for optically functional microstructures on large areas,” Opt. Eng. 43,2525–2533 (2004). [CrossRef]
19. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am A 11,2695 –2703 (1994). [CrossRef]
20. M. Neviere and E. Popov, Light Propagation in Periodic Media (Marcel Dekker, New York, Basel, 2003).
21. P. B. Clapham and M. C. Hutley, “Reduction of Lens Reflection by the ‘Moth Eye’ Principle,” Nature 244,281–282 (1973). [CrossRef]
22. S. J. Wilson and M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Optica Acta 29,993–1009 (1982). [CrossRef]
23. B. Pradarutti, G. Matthäus, C. Brückner, S. Riehemann, G. Notni, S. Nolte, and A. Tünnermann, “Electrooptical sampling of ultrashort THz pulses by fs-laser pulses at 1060 nm,” Appl. Phys. B 85,59–62 (2006). [CrossRef]
24. B. Pradarutti, G. Matthäus, C. Brückner, S. Riehemann, G. Notni, S. Nolte, V. Cimalla, V. Lebedev, O. Ambacher, and A. Tünnermann, “InN as THz emitter excited at 1060 nm and 800 nm,” Proc. SPIE 6194,61940I (2006). [CrossRef]
25. F. v. Hulst, P. Geelen, A. Gebhardt, and R. Steinkopf, “Diamond tools for producing micro-optic elements,” Industrial Diamond Review 3,58–62 (2005).
26. A. Gürtler, C. Winnewisser, H. Helm, and P. U. Jepsen, “Terahertz pulse propagation in the near field and the far field,” J. Opt. Soc. Am A 17,74 –83 (1999). [CrossRef]
27. T. D. Drysdale, R. J. Blaikie, H. M. H. Chong, and D. R. S. Cumming, “Artificial Dielectric Devices for Variable Polarization Compensation at Millimeter and Submillimeter Wavelengths,” IEEE Trans. Antennas Propag. 51,3072–3079 (2003). [CrossRef]