Equivalent-Circuit Interpretation of the Polarization ... - IEEE Xplore

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IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 6, NOVEMBER 2013

Equivalent-Circuit Interpretation of the Polarization Insensitive Performance of THz Metamaterial Absorbers David Shawn Wilbert, Student Member, IEEE, Mohammad Parvinnezhad Hokmabadi, Patrick Kung, Member, IEEE, and Seongsin Margaret Kim, Member, IEEE

Abstract—Polarization insensitive metamaterial perfect absorbers were investigated through finite element numerical method and a new equivalent-circuit electric model was proposed to interpret this polarization insensitivity. The devices were fabricated to validate the model and experimental measurements were shown to be in good agreement with the simulated results. This absorber device is suitable for future use in THz sensing and detection applications. Index Terms—Frequency selective surface, metamaterials, perfect absorber, polarization independent, reflection, resonance, terahertz (THz).

I. INTRODUCTION

N

EW RESEARCH areas in the terahertz (THz) gap (0.1–10 THz) of the electromagnetic spectrum have seen rapid growth as of late due to the significant number of potential applications ranging from fundamental science to imaging and sensing [1]–[5]. To realize such potential applications, the development of novel optics and devices that operate in the THz regime becomes critically important since the lack of many functional and active devices has hindered progress at these frequencies. Recently, metamaterials have been actively investigated due to their extraordinary electromagnetic properties such as an independently tunable permittivity, permeability, and refractive index. This raises great promise for novel active devices, such as sensors and detectors suitable for THz applications [6], [7]. In particular, a perfect metamaterial absorber (MMA) has emerged as an attractive approach to achieve high sensitivity and selectivity THz detection. MMA was first proposed by N. I. Landy [8] in the GHz range, then various structures and properties have been discovered including wide incident angle absorption [9], dual band absorption [10], as well as broadband absorption [11], [12] at THz frequencies. Polarization insensitive MMAs based on four-fold rotational symmetry have also been proposed for

Manuscript received July 01, 2013; revised September 30, 2013; accepted October 01, 2013. Date of publication November 08, 2013; date of current version November 22, 2013. This work is supported by the National Science Foundation under NSF BRIGE 0824452 and by NSF CAREER. The work of D. S.Wilbert was supported by NSF Graduate Research in Diversity program. The authors are with the Electrical and Computer Engineering Department, University of Alabama, Tuscaloosa, AL 35487-0286 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TTHZ.2013.2285311

TE- and TM-mode incident polarizations [13]–[16]. A more detailed review of the subject was published very recently [17]. Among them, to the best of our knowledge, Ma et al. are the only group to have presented experimental verification of polarization independence at polarizations other than TE and TM incident polarizations in MMA structures [13]. Their work included rotations of 30 and 60 in addition to the standard TE 0 and TM 90 polarizations. In this work, we present simulation and experimental results of a fourfold symmetric THz MMA whose response is insensitive to any polarization angle with near perfect absorption. We propose a new electrical equivalent-circuit model that interprets the nature of the polarization independent absorption behavior at the resonance frequency. This model arises from the 3D finite element method (FEM) simulation of these THz MMA structures. In this model, the detailed electric field and induced surface current excited by incident THz radiation were considered to determine the inductances arising from induced electric current paths and capacitances between dipoles that appear at resonance. The absorption spectra from simulation and experimental measurements were shown to match well both in terms of absorption peak frequency and magnitude. The fourfold symmetry arises from a frequency selective surface (FSS), which is composed of an array of resonant elements where each unit cell contains a square closed ring with four plates arranged 90 from one another inside the ring. These plates form 45 gaps in order to generate an electric response at any incident field polarization. II. THEORY AND SIMULATION RESULTS The absorber structure consists of a plane of patterned resonant structures with a four-fold rotational symmetry [the FSS, Fig. 1(a)], a dielectric spacer and a metal plane sequentially as described in our previous work [18]. The simulation has been done through COMSOL Multiphysics by using FEM analysis in 3D. In the original design of our perfect absorber structures, we used COMSOL’s standard material library for the material parameters, including a copper and polyimide conductivity of S/m, respectively. 6 10 S/m and 6.67 10 was used The polyimide complex permittivity of in our simulations, which was empirically determined by both ellipsometry and THz time domain spectrometry. For the finite element simulation, the total number of free tetrahedral mesh elements was about 786 971. In our 3-D simulations, we used a continuous plane-wave source at normal incidence onto the structure, periodic boundary

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WILBERT et al.: POLARIZATION INSENSITIVE PERFORMANCE OF THZ METAMATERIAL ABSORBERS

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Fig. 1. (a) Diagram of a resonant element unit cell with labeled dimensional parameters. (b) Optical microscope picture of an individual resonant element from a frequency selective surface array. (c) Optical image of the final device of absorber arrays.

conditions for the side walls of the volume considered, and scattering conditions for the front and back walls (perpendicular to the wave propagation). Absorption calculation was accomplished using Poynting theory. The incident power density was , where and are the incident electric field intensity and free space intrinsic impedance, respectively. Since the metal back plane reflects all waves, the transmission is zero and we can define the absorption simply by , where the ratio (R) of the reflected power to the incident power was calculated through a surface in front of the structure. Various size dimensions were swept to achieve a structure that showed a near perfect absorption (99.5%) for the zero angle of polarization, that was insensitive to the angle of polarization, and exhibited an absorption resonance near 1 THz (targeted frequency). Fig. 2 illustrates the electric field and current density distribution on the FSS and backplane, along with the corresponding circuit model for the FSS at 0 , 20 , and 45 polarization angles. For clarity, the white arrows labeled in Fig. 2(a), 2(d), and Fig. 2(g) and black arrows in Figs. 2(c), 2(f), and Fig. 2(i) have been added to show the current directions on the FSS and backplane respectively. When a current passes through a rectangular metallic bar in the FSS, it produces a self-inductance in the corresponding bar. The inductance is proportional to the length of the bar. By considering this, in conjunction with the symmetry of current densities on the FSS, we can develop an equivalent-circuit model for the FSS as shown in Fig. 1(b), 1(e), and 1(h) for the corresponding polarizations. The origin of the capacitances corresponding to the different polarizations is of major importance. These capacitances come from the interaction of poles induced on the FSS. In other words, they are the capacitances associated with the formed dipoles, and vary for each polarization because the locations of the poles vary with the polarization of the incident wave. For clarity, we have added closed red curves inside Fig. 2(a), 2(d), and 2(g) to show the effective pole locations. The electric field distribution on the metal back plane demonstrates more clearly the induced poles. According to the distribution of these poles at different polarizations, the corresponding capacitance of the model will be different. By comparing the 0 and 20 configurations, we can see that increasing the angle of polarization leads to an increase in the effective interaction area of poles while the effective distance between them (red double-headed arrows in Fig. 2(d)) deceases. At 45 , the effect is so dramatic that the corresponding capacitance originates from the gaps between the plates of the “T”

Fig. 2. (a), (d), (g) Electric field and current density distribution on FSS, white arrows show the current direction, red closed curves show the locations of effective poles and the labels V and H have been added to indicate to horizontal and vertical legs. (b), (e), (h) FSS circuit model and (c), (f), (i) electric field and current density on back plane with black arrows indicating current paths for clarity.

TABLE I EQUIVALENT INDUCTANCE AND CAPACITANCE OF FSS

structure in the FSS (labeled and ), which is the smallest possible distance between poles [red arrows in Fig. 2(g)]. With this interpretation, the capacitance for a 45 polarization should be greater than for a 20 polarization, which should in turn be greater than , or in other words . We have summarized the equivalent-circuit inductances and capacitances for the 0 , 20 , and 45 polarizations in Table I. Similarly, it can be clearly observed that . This is due to the reduction in current path lengths as the polarization angle is rotated from 0 to 45 , leading to a reduced inductance. The resonance frequency of the absorber is therefore determined predominantly by the geometry of the FSS elements. Based on the aforementioned reasoning, any reduction in inductance is correspondingly compensated by an increase in capacitance at different polarizations such that the resonance frequency, ,will be conserved at all polarizations. The equivalent-circuit interpretation we are proposing therefore confirms the polarization insensitive nature of our THz metamaterial absorber design. The electric dipole on the FSS induces an oppositely directed dipole on the metal back plane. This back plane dipole generates

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TABLE II FSS ELEMENT UNIT CELL DIMENSIONS

Fig. 3. (a) Time-domain THz pulse waveform and (b) subsequent absorption spectrum after fast Fourier transform and division by reference. TABLE III EXPERIMENTAL RESULTS

a current anti-parallel to that on the FSS as illustrated with black arrows in Fig. 1(c), 1(f), and 1(i). We refer to the back plane dipole and corresponding back plane current as the image dipole and image current, respectively. The irradiated electromagnetic field out of this image dipole will subsequently undergo multiple reflections inside the cavity formed by the FSS and back plane. If the thickness and refractive index of the spacer are chosen properly, the electromagnetic wave irradiated from the image dipole can be made exactly out of phase with the irradiated reflected wave from the FSS itself resulting in zero total reflection and therefore perfect absorption at resonance frequency. III. EXPERIMENTAL RESULTS AND DISCUSSION To validate both the simulated absorber design and the equivalent-circuit model, several absorber arrays were fabricated and their THz absorption responses measured following experimental procedures reported earlier [18], [19]. The final array size was and the dimensions of the various FSS investigated experimentally are summarized in Table I. Typical images of both resulting individual FSS and arrays of FSS are shown in Figs. 1(b) and 1(c). Initial characterization of these arrays consisted of reflection mode THz TDS measurements at normal incidence and 0 polarization angle, as shown in Fig. 3. We experimentally verified that no wave transmitted through the absorber arrays. Arrays A and B exhibited nearly indistinguishable time domain amplitude signals Fig. 3(a), while array C only differed in the ringing, i.e., small modulation, after the main peaks, which is directly related to the phase of the reflected waves. Based on the dimensions in Table II, we can infer that the parameters and , which are the only ones that changed from A to B, cause very little effect on the time domain pulse or the subsequent ringing. Comparing arrays B and C, even though the lengths and both decrease further, it is the reduction in the outer length of the elements that causes a considerable compression in the time domain ringing, which leads to a corresponding increase in the absorption resonance frequency, as shown in Fig. 3(b). From the frequency-domain response in Fig. 3(b), arrays A, B, and C exhibited absorption of 83%, 97%, and 91%, respectively. Both arrays A and B had very close resonance frequencies near 0.85 THz, separated by only 25 GHz, due to an identical parameter. Both had a bandwidth or full-width at halfmaximum (FWHM) of 140 GHz. By contrast, array C had a resonance frequency of 0.970 THz, which was 120 GHz blue

shifted from that of array B due to a reduction in both and parameters, and a larger FWHM of 200 GHz. These initial measurement results are summarized in Table III. For all three arrays, we also observed second-order resonance peaks at a high frequency, as shown in Fig. 3(b). The parameters and have the strongest impact on the resonance frequency among the parameters listed in Table II, but the combination of and can have a significant impact as well, because these two parameters work in conjunction to set the 45 gap between two adjacent plates in the FSS. Although it does not have a major influence on the resonance frequency, the dielectric thickness parameter sep is also important because it determines the strength of the absorption. We now focus our discussion on array B, which exhibited the highest experimental absorption and provides a basis for direct comparison with simulation of Section II. Its absorption bandwidth was nearly 100 GHz larger than what was expected from simulation (blue dash–dotted line) and the resonance frequency was also lower, as depicted in Fig. 4(b). We believe this significant broadening could be due to a lower metal conductivity in the actual fabricated arrays. To prove this, we simulated the same absorber design as array B but swept the Cu conductivity. Fig. 4(a) shows the absorption strength versus Cu conductivity and frequency. We can readily see that reducing the Cu conductivity increases the bandwidth considerably and redshifts the absorption peak. We found that a Cu conductivity of 1 10 S/m yields a perfect match between simulation and experiment, as shown in Fig. 4(b) by the red dash line matching the experimental black solid curve. This is 6 times less than the bulk Cu conductivity used in COMSOL’s standard material library for the material parameters. Such a reduction in conductivity might be due to the thin nature of the metal layer, which makes carrier scattering by lattice defects much larger than scattering by phonons [20]. A similar bandwidth increase due to reduced Cu conductivity has also been reported using a transmission line model and dispersion engineering of the FSS [21], [22]. Impedance for this absorber B, was calculated from the reflection and transmission coefficients using the method presented

WILBERT et al.: POLARIZATION INSENSITIVE PERFORMANCE OF THZ METAMATERIAL ABSORBERS

Fig. 4. (a) Absorption versus Cu conductivity and frequency. The white indi10 S/m conductivity, which leads to a match between simulation cates a and experiment. (b) Absorption spectra of simulation with 1 10 S/m (red dash) and 6 10 S/m(blue dash-dot) for Cu conductivity, and experimental measurement of array B (black solid).

Fig. 5. (a) Absorption (black solid), real part (blue dash-dot) and imaginary part (red dash) of calculated relative impedance for absorber B. (b) Absorption (black solid), real part (blue dash-dot) and imaginary part (red dash) of calculated relative impedance for the perfect case of absorber B with Cu conductivity of 6 10 S/m.

by Smith et al. [23]. Since the transmission is zero in our absorber design, the complex relative impedance of the device becomes: (1) where is the complex reflection coefficient. Theoretically, if gets close to 1, impedance matching will occur between air and the absorber structure, which results in a zero reflection and 100% absorption. Fig. 5(a) shows the calculated impedance from the simulation data that matches the measured absorption of array B (i.e., Cu conductivity of 1 10 S/m). The relative impedance at resonance was found to be 0.73 -j0.37 which is reasonable with an absorption of 96.5%. We have also compared this with the impedance for array B when a Cu conductivity of 6 10 S/m was used (which gave rise to near perfect absorption at 0.9 THz). The calculated impedance at 0.9 THz was found to be where the absorption is 99.95%, almost close to unity. Fig. 6(a) compares the results of the absorption spectra of the array B measured at different polarization angles. Measurements were performed by rotating the arrays in plane and under normal incidence about the THz beam path. Due to the symmetry of the structure, the arrays have rotational periodicity of . The resonance shows almost no changes in frequency

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Fig. 6. (a) Comparison of absorption measured and simulated spectra of array B as a function of polarization angle. For simulation all spectra for various polarizations overlap onto each other (not shown in the figure), (b) Absorption maximum as a function of polarization from both measurement (dark circles) and simulation (open circles). Simulation shows perfect absorption through the rotation angles.

through the rotations as expected from our design for polarization independence. The experimental absorption near resonance was already shown to match the simulation results well in Fig. 4(b). However, measurements did exhibit a monotonous decrease of the absorption strength of about 16% over the course of the rotation as shown in Fig. 6(b). One possible cause for this may be the placement of the array during rotation which, unless perfectly centered, would cause beam walking. This means that, at each rotation, a slightly different set of individual elements from the array would be exposed, so single element defects could cause a non-negligible change in the absorption strength. As the array is further rotated, it could become out of the focal point that was established at zero degrees. Furthermore, the changes in absorption strength were not accounted for in the simulation, so we can speculate that there could be an additional current path length which would lead to additional resistive losses that depend on the polarization of the incident wave. IV. CONCLUSION We have designed polarization insensitive metamaterial absorber structures with a resonance near 1 THz by finite element numerical simulation, and developed an equivalent-circuit model that interprets their polarization insensitive nature based on the induced electric current paths leading to inductances and capacitances arising from the formed dipoles. Several absorber arrays based on this design were fabricated and their characteristics experimentally measured. The independence of the absorption response versus the polarization of the incident wave was confirmed. Matching between simulation and experiment of both the resonance frequency and strength required considering a lower conductivity of the metal used in the fabrication of the absorber structure. These devices could be useful for future frequency selective detection applications. REFERENCES [1] J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applicationsExplosives, weapons and drugs,” Semicond. Sci. Technol., vol. 20, pp. S266–S280, 2005.

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David Shawn Wilbert received the B.S. and M.S. degrees in electrical engineering from the University of Alabama, Tuscaloosa, AL, USA, in 2009 and 2011, respectively, and is currently working toward the Ph.D. in electrical engineering at the same university. His research interests include spectroscopic imaging techniques, THz generation and detection technologies, metamaterial devices, and nanoscale fabrication technology.

Mohammad Parvinnezhad Hokmabadi was born in Tabriz, Iran, in 1982. He received the B.Sc. degree in biomedical engineering from Amirkabir University of Technology, Tehran, Iran, and the M.Sc. degree in electronics engineering from the University of Tabriz, Iran, under supervision of Professor Ali Rostami. He is currently working toward the Ph.D. degree in electrical engineering at the University of Alabama, Tuscaloosa, AL, USA, under supervision of Professor Kim, while continuing his research on metamaterials with a focus on terahertz metamaterial device design and characterization. He has worked on nonlinear properties of metamaterials and high resolution imaging by metamaterials. His master’s thesis resulted in publishing two articles.

Patrick Kung (M’08) received the Diplôme d’Ingénieur from the École Polytechnique, Palaiseau, France, in 1993, and the Ph.D. degree in electrical engineering from Northwestern University, Evanston, IL, USA, in 2000. From 2000 to 2007, he was a Research Assistant Professor in the Department of Electrical Engineering and Computer Science, Northwestern University. He is currently an Associate Professor in the Department of Electrical and Computer Engineering, The University of Alabama, Tuscaloosa, AL, USA, and an Adjunct Professor in the Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA. He has been involved in the area of compound semiconductors and devices, advanced material characterizations, including atom probe tomography, and radiation hardened electronics. He has 62 publications. Prof. Kung is a member of APS, AVS, SPIE, and IFES.

Seongsin Margaret Kim (M’04) received the B.S. degree in physics from Yonsei University, Seoul, Korea, in 1992, and the M.S. degree in physics, and Ph.D. degree in electrical and computer Engineering from Northwestern University, Evanston, IL, in 1994 and 1999, respectively. From 2003 to 2007, she was a Research Associate at Stanford University after having worked at both Samsung (Korea) and Agilent Technologies, San Jose, CA, USA. She joined at the University of Alabama in 2007, and is currently an Associate Professor in the Department of Electrical and Computer Engineering, The University of Alabama, Tuscaloosa, AL, USA. She has been involved researches in the area of semiconductor quantum dots, nanowires, optoelectronics, and Terahertz science and technologies, including generation, detection, spectroscopy, biomedical imaging, near field imaging and THz metamaterials. She has over 100 peer-reviewed publications including 47 journal articles, 5 book chapters, and holds one U.S. patent. Prof. Kim is also a recipient of NSF CAREER award at 2010 and a member of SPIE, and Society of Women Engineers (SWE).