Imaging in the terahertz (THz) range of the electromagnetic spectrum is difficult owing to the lack of high-power sources and efficient detectors. For decades, there has been tremendous effort to fashion focal plane arrays for THz imaging owing to the great number of potential applications. Here, we propose and demonstrate an alternative approach which utilizes all-dielectric metasurface absorbers that act as universal converters of radiation. Incident THz waves are absorbed by the metasurface, converted to heat, and subsequently detected by an infrared camera. We realize a metasurface consisting of sub-wavelength cylindrical resonators that achieve diffraction-limited imaging at THz frequencies without cooling. The low thermal conductivity and diffusivity significantly limit the thermal conduction between neighboring pixels, thus improving the spatial resolution and imaging time. Similar to conventional metallic-based metamaterials, our all-dielectric metasurface absorber can be scaled to other bands of the electromagnetic spectrum, offering a blueprint to achieve novel uncooled bolometric imaging.
© 2017 Optical Society of America
Metamaterial (MM) electromagnetic wave absorbers have been shown across much of the electromagnetic spectrum  and exhibit the ability to tailor the frequency-dependent emissivity  and absorptivity . In the traditional design paradigm, MMs obtain their electromagnetic properties from individual metallic sub-wavelength unit cells, and a relatively complex response may be achieved through a bottom-up approach [4–6]. Indeed, metamaterial absorbers (MMAs) have shown polarization-dependent and -independent responses, broadband behavior, angular tuning, precise wavelength dependence [3,6,7], increased effective absorption coefficients , and tailored spatial-dependent responses [2,9]. More generally, electromagnetic MMs utilize highly conducting metals to achieve high- inductive-capacitive resonances: for example, with split-ring resonators (SRRs). Many other geometries may be utilized for tailored and responses, and the catalog of MM resonator shapes is expansive and flexible enough to provide innovative solutions to obtain nearly any desired electromagnetic property.
Traditional MMs, however, are based on metals, and, as such, one often chooses the highest electrically conducting materials in order to maximize performance. Indeed, the frequency dependence of the conductivity—and its subsequent reduction in the infrared and visible ranges—is what limits MMs from shorter wavelength operations. Thus, the performance of traditional MMs is strongly tied to the electrical conductivity. Although this may be a suitable dependence for many areas of investigation , it nonetheless presents a restriction that may limit potential applications. For example, the ratio of the electronic contribution of the thermal conductivity () to the electrical conductivity () is a constant and independent of any particular metal. This fundamental relationship—termed the Wiedemann–Franz law—is usually characterized by the Lorenz number given as the ratio , which is found to be independent of any material constants, i.e., it does not depend on the number density () or the effective mass of carriers (), but rather is a ratio of universal constants . Thus, for MM studies where thermal properties are important, the availability of a metal-free substitute would enable an alternative and less fundamentally restrictive design approach. Here, we present a metasurface absorber fashioned entirely from sub-wavelength dielectric resonators [11–14], which act as isolated “metamaterial atoms.” Since many dielectric materials exhibit thermal conductivities that are roughly three orders of magnitude smaller than those for good metals, our approach breaks the fundamental connection between thermal and electrical conductivity.
In order to highlight the usefulness of an all-dielectric metasurface absorber, we developed a technological demonstration of an uncooled THz imaging system. Though microbolometric arrays and thermally sensitive materials have been employed for THz imaging , the key component of our apparatus is a metasurface consisting of an array of sub-wavelength silicon cylinders on an ultra-thin PDMS substrate. Incident THz radiation is strongly absorbed solely within the cylindrical resonators, converted to heat, and directly detected by an infrared camera. Our metasurface is supported by a low thermal conductivity substrate, and the absorbed energy is isolated within the sub-wavelength particles, thus providing both high spatial resolution and thermal management. Our architecture is thus distinct from other metamaterial absorber designs, which typically use a metallic ground plane . High absorption is achieved when two conditions are simultaneously fulfilled: impedance matching to free space and a large extinction coefficient . Here, we describe the dielectric cylindrical resonators as waveguides where we independently tune effective hybrid magnetic () and electric () dipole modes, based on the geometry. Impedance matching is achieved by merging both the resonance frequency and amplitude response of the lowest-order and modes [8,17]. For materials with relatively high dielectric constants (), the surfaces can be approximated as perfect magnetic walls.  Under these conditions, the dimensions of the dielectric resonator are determined only by the resonance wavelength () and refractive index () of cylinders . The HE magnetic dipole mode has no cutoff and exists for all frequencies for a given size. Thus, in order to obtain high absorption at a given frequency, the critical criterion is to find the cutoff conditions for the EH mode. Prior studies have shown that for a cylindrical dielectric particle with an index of refraction of (), radius (), and height (), the EH cutoff condition is given by
Due to the specifically designed geometry using Eqs. (1) and (2), the overlap of the magnetic dipole and electric dipole resonances is established, and the absorption is significantly enhanced in the structure—reaching near unity—although the bulk material only possesses relatively small loss.
Here, we utilize silicon as the dielectric material, since it exhibits a relatively large dielectric value across the THz range, as well as the capability to achieve a variable loss tangent () through doping. We chose a target frequency of 600 GHz, and thus, Eqs. (1) and (2) predict dimensions of a diameter of and a height of . We use a support substrate, however, and thus, the optimal values determined by the numerical simulations differ slightly, with and for silicon with material parameters of a plasma frequency of and a collision frequency of . For the experimental implementation, we utilize an extremely thin sub-wavelength substrate to support the cylinder array, as shown in Fig. 1(c). Consideration of the conservation of energy allows us to describe the increase in temperature of the metasurface asSupplement 1.
Since our composite metasurface is supported by a substrate, we must also consider its thermal properties. The thermal diffusivity determines how much the absorbed heat spreads in the substrate—thus limiting the spatial resolution—and may be described by , where is the thermal conductivity, is the density of the material, and is the specific heat capacity. We choose PDMS as our support substrate, which possesses ideal thermal diffusive properties, i.e., is nearly five times smaller than that of polyimide . The imaging system is depicted in Fig. 2(a), and we note that the back side of the support substrate is facing the IR camera. Thus, another important consideration is the substrate’s IR emissivity, which we want to be large in order to achieve optimal imaging fidelity, i.e., maximize the image resolution while reducing noise. Indeed, PDMS realizes a relatively large average emissivity of approximately 75% between 8–13 μm. (See Supplement 1 for more details.)
The dielectric absorber was fabricated using a silicon-on-insulator (SOI) wafer with an 85 μm device layer thickness. The resistivity of the n-type device layer is approximately 2.2 Ω-cm, as determined by a four-point probe measurement. The array was patterned by deep reactive ion etching (DRIE), resulting in cylinders with a diameter of 212 μm and a periodicity of 330 μm [see Fig. 1(a)]. The cylindrical array was then transferred to a free-standing 8 μm PDMS substrate supported by a 1-mm-thick PDMS frame. The total area of the metasurface is , consisting of cylinders. An oblique view of the cylinder array on PDMS is shown in Fig. 1(b).
The transmittance and reflectance of the sample were characterized with a fiber-coupled THz-TDS system (Hübner Group). Transmittance measurements were referenced to free space at normal incidence, while the reflectance—also at normal incidence—was normalized to a gold mirror using a beam-splitter configuration. In both the and measurements, the THz waves were incident on the cylinder side of the metasurface. The absorbance characterized from both sides of the metasurface (see Supplement 1) is nearly identical, owing to the low permittivity of PDMS in the THz range, as well as the sub-wavelength thickness . The measured , , and from the cylinder side are shown in Fig. 1(d), and our all-dielectric metasurface realizes a peak absorption of 96% at a frequency of approximately of . Figure 1(e) shows the simulation results, which obtain a good match to the experiment. The dielectric properties of PDMS were modeled with a permittivity of 1.72 and a loss tangent of 0.15 around 600 GHz . Simulation indicates (not shown) that approximately 94% of the total absorbed power is dissipated within the silicon cylinders [see Fig. 1(c)], even though the loss tangent of silicon is relatively small, i.e., at .
Having verified the highly absorptive properties of our all-dielectric absorber, we next turn toward the demonstration of a room-temperature THz imaging system. Our source consists of a continuous-wave (CW) transmitter module (Virginia Diodes AMC) with a tuning range from 580–620 GHz. The use of a 2.4 mm aperture diagonal horn antenna produces a Gaussian beam with a full 3-dB beamwidth of about 10°. The imaging setup—depicted in Fig. 2(a)—consists of two 50.8 mm diameter 90° off-axis parabolic (OAP) mirrors. The source is placed at the focal point of the first mirror, OAP1, with an effective focal length of , which produces a collimated Gaussian beam with a 3-dB diameter of 33 mm. The second OAP2 mirror () is placed about 550 mm away from mirror OAP1 and forms a conjugate image on the dielectric absorber. We use a 75 μm thick black polyethylene sheet as an IR filter to block the thermal radiation from the source; see Supplement 1. The THz images formed on the metasurface are absorbed and converted to heat. Thus, in order to produce an image, we focused an uncooled microbolometer IR camera with a spatial resolution of 25 μm (FLIR T640sc) on the backside (PDMS substrate side) of the metasurface, thereby imaging the dissipated THz power.
We first characterized the noise performance of our imaging system, where all source power is focused into a diffraction-limited spot on the metasurface and modulated at a frequency of 0.25 Hz. Figure 2(b) shows the 3D and 2D temperature profiles obtained with the IR camera. A cross-section temperature profile across the center spot is shown on the 2D plane, and we observe that the peak temperature increase is about 5.4 K above the ambient temperature. The spot size at the full width at half-maximum (FWHM) is approximately 1 mm. The CW source produces a power of 2.1 mW at 603 GHz, and we find that approximately half of the source power is incident on the metasurface absorber when all the losses of the system are accounted for; see Supplement 1. Thus, assuming a Gaussian beam profile, we find the power incident on the center unit cell to be 11.9% of the source power, i.e., 250 μW. We can determine the responsivity of the absorber as the increase in temperature per unit of the incident power and find a value of . Measuring the thermal response of a heated cylinder via the IR camera, we found the noise spectral density of the imaging system was . This translates into a imaging system noise-equivalent power (NEP) of .
Figure 3 highlights the dynamic and frequency-dependent properties of the all-dielectric metasurface absorber. In Fig. 3(a), the black curve shows the frequency dependence of the CW source, which peaks at a frequency of approximately 615 GHz and maintains values above 90% over the range from 595 to 615 GHz. In Fig. 3(a), we also plot (red circles) the normalized peak-to-peak temperature change of the metasurface absorber while modulating the source. As can be observed, the relative source power determined by matches the power of the source (black curve), although the absorber does exhibit some frequency dependence across the range shown (blue curve). Further dynamic response measurements were performed via directly applying a modulation signal to the source. The inset of Fig. 3(b) displays the waveform of the temperature change via the IR camera with modulation frequencies of 1/16 Hz. From Fig. 3(b), the rise time and fall time of the thermal response in the range of 10% to 90% of maximum modulated temperature are estimated to be about 1.4 and 0.4 s, respectively. The longer rise time is attributed to the forced heating process, which takes more time to be stable, while the faster fall time is led by the free cooling process. For comparison, we also measured the thermal response on a bare 8 μm PDMS thin film (not shown here). The average peak-to-peak temperature change observed in PDMS is only about 6% of the maximum temperature occurring within the dielectric absorber. This is comparable to our simulation results, which showed only 6% of the incident THz power was absorbed by the PDMS substrate. Due to the low thermal conductivity and the very thin layer of PDMS, the thermal conductance of the dielectric absorber is negligible and about two orders of magnitude smaller than that of a metallic metasurface absorber with a 400-nm-thick aluminum ground plane . As a result, the absorbed THz power is highly localized in the center region of the cylindrical array, consisting of about cylinders. On the other hand, our device is not housed in a vacuum, and thus, the heat transfer is dominated by convective and radiative loss, leading to a response time longer than most commercial infrared bolometric detectors, in which the heat transfer is dominated by thermal conduction. The time constant of the absorber determined at the 3 dB point of the normalized temperature change is about 1 s, as shown in Fig. 3(b).
Imaging experiments were performed with the setup depicted in Fig. 2(a). The objects used for imaging consisted of metallic apertures, each with a minimum feature size of 5 mm (see insets to Fig. 4), and were back-illuminated by the CW source. The object distance was , and a thin layer of black polyethylene was used as an IR filter (IRF2) and placed after the object. The image distance was , and thus, our imaging system had a magnification of . We used a source frequency of 605 GHz and a power of 1.09 mW, which correspond to an average intensity of at the imaging plane, i.e., on the metasurface absorber. The object minimum feature size of 5 mm was demagnified to a size of 565 μm at the image plane, which is approximately 1.7 times larger than the metasurface lattice parameter of 330 μm. However, our system operates close to the Rayleigh diffraction limit of 620 μm and uses OAP mirrors, thus producing slightly distorted images (see Supplement 1). In Fig. 4, we show the false-color THz images obtained with our imaging setup and produced by the IR camera. We realize relatively high image fidelity and an accurate reproduction of the original object. The peak image intensity is 0.3 K above the ambient temperature, as measured directly with the IR camera.
We next turn toward a discussion of the imaging results. In Supplement 1, we calculate the contribution of each of the loss terms responsible for conducting heat away from the dielectric absorber. We find that the main component of temperature loss in our system is convection and accounts for about 81% of the total heat loss in Eq. (3). Thus, an obvious way to improve our imaging results is to house our all-dielectric metasurface absorber in a vacuum. We analytically estimate (see Supplement 1) that this alone will increase our responsivity to , and there will be a corresponding improvement of NEP to at a modulation speed of 1/4 Hz.
In summary, we have successfully designed, fabricated, and demonstrated an all-dielectric metasurface for imaging through THz to infrared conversion. The use of an all-dielectric absorber supported on an ultrathin polymer permits a reduction of the thermal conductivity by three orders of magnitude in comparison to other metallic metasurface absorbers, thereby significantly localizing the absorbed heat. Our all-dielectric metasurface architecture achieves a responsivity such that an uncooled infrared camera can be utilized to image THz radiation. Our experimental results showed the absorbance of the all-dielectric metasurface was as high as 96% at a frequency of 603 GHz and achieved a thermal responsivity of at a modulation speed of 1/4 Hz. Our results demonstrated here can also be scaled to other frequencies, such as millimeter-wave and higher infrared ranges, presenting a new path for bolometric imaging.
U.S. Department of Energy (DOE) (DE-SC0014372); National Science Foundation (NSF) (ECCS-1542015).
This work was performed in part at the Duke University Shared Materials Instrumentation Facility (SMIF), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), supported by the National Science Foundation (NSF) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).
See Supplement 1 for supporting content.
1. C. M. Watts, X. Liu, and W. J. Padilla, Adv. Mater. 24, OP98 (2012). [CrossRef]
2. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, Phys. Rev. Lett. 107, 045901 (2011). [CrossRef]
3. K. Fan, J. Suen, X. Wu, and W. J. Padilla, Opt. Express 24, 25189 (2016). [CrossRef]
4. J. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996). [CrossRef]
5. J. Pendry, A. Holden, D. Robbins, and W. J. Stewart, IEEE Trans. Microw. Theory Tech. 47, 2075 (1999). [CrossRef]
6. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, Phys. Rev. Lett. 100, 207402 (2008). [CrossRef]
7. H. Tao, C. M. Bingham, D. Pilon, K. Fan, A. C. Strikwerda, D. Shrekenhamer, W. J. Padilla, X. Zhang, and R. D. Averitt, J. Phys. D 43, 225102 (2010). [CrossRef]
8. X. Liu, K. Fan, I. V. Shadrivov, and W. J. Padilla, Opt. Express 25, 191 (2017). [CrossRef]
9. C. C. Nadell, C. M. Watts, J. A. Montoya, S. Krishna, and W. J. Padilla, Adv. Opt. Mater. 4, 66 (2016). [CrossRef]
10. X. Liu and W. J. Padilla, Adv. Opt. Mater. 1, 559 (2013). [CrossRef]
11. Y. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, Adv. Opt. Mater. 3, 376 (2015). [CrossRef]
12. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015). [CrossRef]
13. Z. Ma, S. M. Hanham, P. Albella, B. Ng, H. T. Lu, Y. Gong, S. A. Maier, and M. Hong, ACS Photon. 3, 1010 (2016). [CrossRef]
14. D. Headland, E. Carrasco, S. Nirantar, W. Withayachumnankul, P. Gutruf, J. Schwarz, D. Abbott, M. Bhaskaran, S. Sriram, J. Perruisseau-Carrier, and C. Fumeaux, ACS Photon. 3, 1019 (2016). [CrossRef]
15. Y. Y. Choporova, B. A. Knyazev, and M. S. Mitkov, IEEE Trans. Terahertz Sci. Technol. 5, 836 (2015). [CrossRef]
16. S. A. Kuznetsov, A. G. Paulish, A. V. Gelfand, P. A. Lazorskiy, and V. N. Fedorinin, Appl. Phys. Lett. 99, 023501 (2011). [CrossRef]
17. I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, ACS Nano 7, 7824 (2013). [CrossRef]
18. R. K. Mongia and P. Bhartia, Int. J. Microw. Millim.-Wave Comput.-Aided Eng. 4, 230 (1994). [CrossRef]
19. K. Kurabayashi, M. Asheghi, M. Touzelbaev, and K. E. Goodson, J. Microelectromech. Syst. 8, 180 (1999). [CrossRef]
20. A. Podzorov and G. Gallot, Appl. Opt. 47, 3254 (2008). [CrossRef]