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ACCEPTED MANUSCRIPT Tunable reflectionless absorption of electromagnetic waves in a - composite structure

To cite this article before publication: Nolan Uchizono et al 2020 Plasma Sources Sci. Technol. in press https://doi.org/10.1088/1361- 6595/aba489

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1 2 3 4 5 6 7 8 9 10 Tunable Reflectionless Absorption of 11 Electromagnetic Waves in a Plasma-Metamaterial 12 13 Composite Structure 14 15 16 Nolan M. Uchizono, Stephen A. Samples, and Richard E. Wirz 17 University of California, Los Angeles, Department of Mechanical and Aerospace 18 Engineering, Los Angeles, CA, 90043 19 20 E-mail: [email protected], [email protected] 21 22 June 2020 23 24 Abstract. We present the first experimental demonstration of a tunable reflectionless 25 absorption resonance in a metamaterial integrated with a plasma discharge. A 26 one-dimensional metamaterial structure excites transverse magnetic slow-wave modes 27 known as “spoof” surface . When interfaced with an argon 28 plasma discharge, the metamaterial-induced “spoof” plasmon mode is converted to a 29 30 plasmon mode confined to the plasma/ interface. The reflectionless 31 absorption band that manifests in the metamaterial’s spectral response exhibits a 32 dependency on the plasma’s density that agrees well with theory. 33 34 35 36 Keywords: plasma-, polariton, tunable metamaterial, 37 38 plasma waves 39 40 Submitted to: Plasma Sources Sci. Technol. 41 42 43 44 45 1. Introduction 46 47 A metamaterial is an engineered structure designed to exhibit extraordinary properties, 48 49 such as zero or negative refractive index [1, 2]. Such unique properties have been 50 used to develop “cloaking” [3, 4], super lenses [5, 6, 7], and enhanced antennas [8, 9]. 51 Metamaterials are characterized by periodic features spaced at intervals much shorter 52 53 than the of a given excitation wave. The dependency of a metamaterial’s 54 spectral response on its geometry, shape, orientation, and size limits its expression of 55 unique properties to a narrow spectrum. Recent research efforts have focused 56 57 on overcoming the inherent bandwidth limitations by developing metamaterials with a 58 tunable frequency response [10]. Tunable metamaterials have improved functionality, 59 60 Accepted Manuscript AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1 Page 2 of 11

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 2 4 5 Spoof-SPP Coupling SPP

6 Plasma (εp < 0) 7 8 - - - -++ ++ (ε > 0) 9 Dielectric d 10 z 0 < v < c v = 0 Metamaterial 11 x g g 12 13 Figure 1: Qualitative description of spoof-SPP to SPP conversion in the plasma- 14 metamaterial structure. In the absence of the plasma (shown to the left), the device generates 15 16 spoof-SPPs, which are surface waves that have a longitudinal electric field. Spoof-SPPs 17 propagate along the surface of the metamaterial with a group velocity (vg) much lower than 18 the . In the presence of a plasma (shown to the right), these spoof-SPPs couple 19 to the free in the plasma, producing surface plasmon polariton (SPP) modes along 20 the plasma/dielectric interface, which have a group velocity of zero. 21 22 23 24 enabling broader adoption for mainstream applications, such as communication systems 25 [11], terahertz-band technologies [12, 13], and sensing [14, 15]. 26 One promising approach to achieving tunable metamaterials is through the 27 integration of gas discharges into resonant structures to create plasma-metamaterial 28 29 composites [16, 17, 18, 19, 20]. The response of a plasma-metamaterial composite is 30 easily controlled by tuning gaseous discharge parameters, such as electron density or 31 neutral gas . Bounded plasmas express many types of resonances in response to 32 33 electromagnetic excitation [21, 22, 23, 24]. Numerical simulations have predicted plasma 34 resonances induced by metamaterial structures, yet this phenomenon has 35 not been observed experimentally [25, 20]. In the presented work, we report the first 36 37 empirical observations of reflectionless absorption caused by coupling between plasma 38 and metamaterial resonances, thus demonstrating a new method of tuning the spectral 39 response of a metamaterial. 40 41 When considering the interface between plasmas, , and metamaterials, it 42 is germane to discuss the concept of surface waves. A surface plasmon polariton (SPP) 43 describes a surface plasma density oscillation that is coupled to an electromagnetic wave. 44 45 SPPs occur at the interface of a conductor and dielectric at visible and near- 46 (∼200-800 THz) in metals [26], and frequencies (∼0.1-100 GHz) 47 in gaseous discharges [27, 28, 29], where they are occasionally referred to as “gaseous 48 49 plasmon polaritons” [30]. Pendry et al. demonstrated an excitation analogous to SPPs 50 that has been termed a “spoof-SPP”, which can be excited at sub-terahertz frequencies 51 using a metamaterial [31]. SPPs and spoof-SPPs exhibit similar characteristics, such 52 53 as nonlinear and longitudinal electric field. Both embodiments of plasmonic 54 excitation exhibit a characteristic resonance defined as the frequency where 55 asymptotically approaches infinity. However, spoof-SPP excitation manifests as a result 56 57 of interactions between incident electromagnetic waves and the metamaterial’s periodic 58 structure, rather than the motion of surface charges as described by SPPs [31, 32]. The 59 presented work demonstrates how the analogous behavior between SPPs and spoof- 60 Accepted Manuscript Page 3 of 11 AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 3 4 (a) (b) (c) 5 6 Vacuum Chamber 14 mm 10 mm 7 z 8 Anode Transmit x 9 Helmholtz 10 Coils 11 Network 12 Analyzer 5.5 mm 13 Probe 14 15 14 mm 16 Receive 17 18 Cathode 19 20 21 Figure 2: (a) Image of experimental operation of the metamaterial immersed in a 22 magnetized DC plasma discharge during Langmuir probing. (b) Diagram of the UCLA 23 Plasma-Metamaterial Interactions Facility. A thermionic cathode and copper anode produce 24 a magnetized plasma column. The uniform DC magnetic field is produced by a 10-inch 25 Helmholtz coil. (c) Dimensions of the corrugated metamaterial. 26 27 28 29 SPPs may be exploited to couple electromagnetic energy from a metamaterial to the 30 free electrons in a plasma. Significant effort has been invested into the research of 31 spoof-SPP excitation in metamaterials due to their practical application in microwave 32 33 to terahertz frequency electronics [33, 34, 35]. Hence, the novel spoof-SPP to SPP 34 coupling phenomena presented here opens new possibilities for useful application of 35 metamaterial tuning. A diagram that qualitatively illustrates the spoof-SPP to SPP 36 37 coupling in the presented experimental geometry is shown in figure 1. 38 To excite an SPP, a photon must have the same wavenumber and frequency as the 39 surface plasmon. Free-space photons cannot excite an SPP, and so a dispersive medium 40 must be used as a coupling mechanism. Wavenumber matching is typically achieved with 41 42 a prism or grating [26], yet metamaterials that can excite spoof-SPPs are also dispersive 43 media (often referred to as slow-wave structures), which reduce the group velocity of 44 incident waves. The presented experiment uses a planar metamaterial as a dispersion 45 46 medium to couple to a nearby DC plasma discharge. Since wavenumber matching is 47 a key condition for excitation of SPPs, the dispersion relations of our metamaterial 48 structure (defined later in the Results & Discussion section) are instrumental for 49 50 analyzing our presented results. 51 In the following sections, we discuss the methods and diagnostics used in the 52 experiment, the results that demonstrate tunable reflectionless abosorption in a 53 54 metamaterial, and our analysis that leads us to conclude that this behavior manifests 55 as a results of spoof-SPP to SPP resonant coupling. 56 57 58 59 60 Accepted Manuscript AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1 Page 4 of 11

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 4 4 5 2. Experiment Methods 6 7 The presented study employed a 150 mm long corrugated microstrip as a metamaterial. 8 Corrugated are a class of slow-wave metamaterial that have been the subject 9 10 of extensive study for their ability to excite spoof-SPPs at relatively low frequencies 11 (∼0.3 - 300 GHz) [32, 36]. The corrugations on the microstrip are periodic reactive 12 elements, where the periodicity controls the metamaterial’s characteristic resonance 13 14 frequency. The presented microstrip metamaterial was comprised of a two-sided 15 FR4 printed circuit board (PCB), with corrugations etched onto the top plane. An 16 illustration detailing the dimensions and specifications of the metamaterial is shown in 17 18 figure 2(c). 19 A vector network analyzer (VNA) measured the scattering parameters of the 20 metamaterial using an excitation signal with a peak power of 250 µW . The waves 21 22 produced by the network analyzer are transverse electromagnetic (TEM) polarized and 23 are guided to the metamaterial by an RG-58 coaxial cable . The coaxial cable 24 directly interfaces to the microstrip using an SMA-to-PCB connector, rather than using 25 26 antennas to launch free-space propagating waves at the metamaterial-of-interest. From 27 the SMA port, TEM waves are directly coupled to the microstrip, which then transforms 28 them to a transverse magnetic (TM) polarization. 29 30 A direct-current, axially-magnetized, thermionic discharge was used as the plasma 31 source. The cathode was held at ground potential while the anode was biased to 32 45 V. The axial magnetic field was produced by a Helmholtz coil, and measured to 33 34 be approximately 7.25 mT. The metamaterial and plasma source were integrated inside 35 of a vacuum chamber to complete the plasma-metamaterial composite device. A 0.5 mm 36 sheet of mica (εd = 4.4) covered the face of the metamaterial, serving as an insulator 37 38 from the plasma and as the dielectric medium for SPP propagation. Figure 2(a) shows 39 the DC plasma source operating with the plasma column positioned along the surface 40 of the metamaterial. The vacuum chamber was evacuated to 4 µTorr, and backfilled 41 42 with argon. Pressure was held at 0.7 mTorr for the two lower plasma density conditions 43 and 4 mTorr for the two higher plasma density conditions. Variation in plasma density 44 was achieved by changing the background pressure and cathode current. The complete 45 46 experimental setup is illustrated in figure 2(b). 47 A cylindrical tungsten Langmuir probe with tip dimensions of 0.5 mm diameter 48 by 4 mm length was used to measure the plasma properties. The tip of the probe was 49 spaced 0.5 mm away from the metamaterial, oriented tangent to the metamaterial’s 50 51 surface and orthogonal to the axis of the plasma beam. The probe was swept at 50 Hz 52 using a Kepco BOP-100 amplifier driven by an NI function generator. At each setpoint, 53 a series of 200 current-voltage (I-V) trace sweeps were recorded for averaging to mitigate 54 16 −3 55 noise. A characteristic I-V trace for the ne = 2.94 × 10 m test condition is shown in 56 figure 3. The probe data were analyzed using Bernstein-Rabinowitz-Laframboise (BRL) 57 transitional-sheath theory as outlined by Lobbia and Beal, and Chen et al. [37, 38]. 58 59 Electron densities at the four test conditions are shown in the legend of figure 4. Due 60 Accepted Manuscript Page 5 of 11 AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 5 4 Characteristic I-V Trace 5 4 6 7 3 8 9 2 10 11 1 12 13 0

14 Langmuir Current [mA] 15 -1 -100 -50 0 50 100 16 17 Bias Voltage [V] 18 Figure 3: A characteristic Langmuir probe I-V trace obtained at at the lowest-density 19 setpoint tested (n = 2.94 × 1016 m−3). The plotted data are averaged over 200 sweeps 20 e 21 obtained at a 50 Hz sweep rate. 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Figure 4: (Top) Absorptivity and (Bottom) Reflectivity of the metamaterial exposed 48 to a range of plasma conditions. Emerging absorption bands accompanied by unchanging 49 50 reflectivity suggest SPP coupling. 51 52 53 to the finite length of the probe, the measured electron densities represent spatially 54 averaged values across a 4 mm span tangent to the face of the metamaterial. 55 56 57 3. Results & Discussion 58 59 The absorptivity (A) and reflectivity (R) of the metamaterial are given by: 60 Accepted Manuscript AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1 Page 6 of 11

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 6 4 5 6 2 2 7 A = 1 − S21 − S11 (1) 8 R = S2 (2) 9 11 10 where S and S are the input-referenced reflection and transmission scattering 11 11 21 12 parameters measured by the vector network analyzer [39]. Figure 4 shows absorptivity 13 and reflectivity at the four different electron densities and at vacuum. The vacuum 14 condition shows that the metamaterial strongly attenuates at its characteristic frequency 15 16 of 2.4 GHz, demonstrating expected spoof-SPP behavior [20]. Activating the plasma 17 discharge results in a band of increased absorptivity. The absorption band center 18 frequency and bandwidth increase with electron density, while the reflectivity remains 19 20 unaffected. The observed reflectionless absorption behavior is a distinguishing feature 21 of SPP excitation in plasmas [27, 28, 29]. 22 To support the hypothesis of spoof-SPP coupling to plasma SPP modes, we pursue 23 24 an analysis similar to those discussed by Bliokh et al. and Wang et al. For an incident 25 electromagnetic wave to excite SPPs, three conditions must be satisfied: (1) The 26 of the plasma must be negative at the dielectric interface, (2) the incident 27 28 wave must be TM polarized, and (3) wavenumber matching must occur between the 29 electron density oscillations and the incident electromagnetic wave [26, 28, 27, 40]. 30 SPP excitation occurs at the interface of a conductor and a dielectric, where there 31 32 is a flip in the sign of the real component of permittivity. A conductor’s permittivity 33 can be obtained using the [26]: 34 35 ! 36 ω 2 ε (ω) = 1 − p (3) 37 p ω2 + iωγ 38 39 where ωp is the plasma frequency and γ is the electron-neutral collision frequency. 40 γ was estimated using empirical relationships, and found to be on the order of 10 MHz, 41 q 2 42 much less than the plasma frequency (ωp = nee /meε0), so we assume γ can be 43 neglected. To satisfy condition (1), the ratio of the electron density to the plasma’s 44 critical density must exceed unity, indicating an overdense plasma regime and therefore 45 2 2 46 negative permittivity. The critical density is given by nc = me0(ω) /e , where ω is the 47 angular frequency of the incident wave. Inserting the approximate range of frequencies of 48 the attenuation bands in the absorptivity plot shown in figure 4 gives 8.9 < n /n < 32.7, 49 e c 50 and therefore condition (1) is satisfied. 51 Condition (2) is implicitly satisfied due to the strong, TM surface confinement of 52 the spoof-SPPs generated by corrugated microstrips. While the incident waves from 53 54 the coaxial cable are TEM polarized, several published works have numerically and 55 experimentally demonstrated the transformation of TEM and quasi-TEM waveguide 56 modes to TM slow-wave surface modes in corrugated microstrips [41, 42]. 57 58 Examination of the dispersion relations of the metamaterial structure and of the 59 plasma are necessary to determine whether condition (3) is satisfied. The dispersion 60 Accepted Manuscript Page 7 of 11 AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 7 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Figure 5: Comparison of the dispersion relations of: the metamaterial operating in vacuum 39 (solid black line), the plasma-metamaterial composite (solid color lines), SPPs at representative 40 plasma densities (dashed color lines), and light propagating through a homogeneous medium 41 42 (dashed black line). Intersections between the metamaterial and SPP dispersion relations 43 indicate wavenumber matching, a necessary condition for resonant coupling. 44 45 46 relation of SPPs on a semi-infinite dielectric slab interfaced with a homogeneous plasma 47 slab is obtained by solving the Helmholtz equation at the plasma/dielectric interface 48 49 [26]: 50 s 51 ω εpεd 52 kx,p = (4) 53 c εp + εd 54 where kx,p is the wavenumber of the surface waves that travel along the 55 plasma/dielectric interface, ε is the dielectric permittivity, and ε is the Drude 56 d p 57 permittivity of the conductor given by (3). 58 The periodic structures along the length of the metamaterial produce passbands 59 and stopbands that behave like electronic filters [39]. The periodic, sub-wavelength 60 Accepted Manuscript AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1 Page 8 of 11

1 2 3 Reflectionless Absorption in Plasma-Metamaterials 8 4 5 features that exemplify a corrugated microstrip filter can be analyzed by treating the 6 microstrip as a one-dimensional crystal, where the unit cell is the impedance of a period 7 of corrugation. Several authors have reported on the retrieval of the dispersion relations 8 9 of a metamaterial from its scattering parameters [39, 43, 44]: 10 11   1 −1 1 − S11S22 + S21S12 12 kx,m = cos (5) 13 d S21 14 15 where kx,m is the wavenumber of the spoof-SPPs propagating along the 16 metamaterial, and d is the spatial periodicity of the corrugations. S11, S21, S12, and S22 17 are the 2-port scattering parameters measured by the the vector network analyzer in 18 19 the presented experiment. 20 The four plots in figure 5 each show the dispersion relations for light propagating 21 in vacuum, the metamaterial without plasma, the metamaterial with plasma, and 22 the analytical SPP dispersion at the measured electron densities. Since light 23 24 disperses linearly in vacuum and lies to the left of the SPP dispersion curves, 25 wavenumber matching cannot occur with unmodified electromagnetic waves. The 26 metamaterial structure exhibits nonlinear dispersion behavior, slowing the group 27 28 velocity (vg ≈ dω/dk) of the incident electromagnetic waves, enabling coupling 29 to the plasma. For the two high-density plasma tests, peaks are observed in the 30 plasma-metamaterial dispersion at frequencies that agree with the metamaterial/SPP 31 32 intersection points. The low-density plasma tests appear to intersect with a minimum in 33 the dispersion curve of the vacuum metamaterial, indicating a region of weak coupling 34 from spoof-SPP to SPP modes. Reduced attenuation in the absorptivity spectra for the 35 36 low-density plasma tests further support the notion of weak coupling. The wavenumber 37 matching frequencies show good agreement with the center frequencies of the attenuation 38 bands shown in figure 4, satisfying condition (3). Given the satisfaction of all three 39 40 criteria, the reflectionless absorption bands observed in the metamaterial’s spectral 41 response are clear evidence of resonant SPP excitation in the plasma/dielectric interface. 42 43 44 4. Conclusion 45 46 The presented plasma-metamaterial composite structure exhibits a reflectionless 47 48 absorption band in its spectral response, with a strong frequency dependence on the 49 plasma’s density. Such reflectionless absorption bands are typical indicators of SPP 50 excitation. An analysis of the results verified that spoof-SPP modes produced by the 51 52 metamaterial are capable of exciting SPP modes in the plasma/dielectric interface, 53 demonstrating how the metamaterial behaves as both a polarizing and dispersion 54 medium. Exploiting these phenomena can lead to several useful applications in fields 55 56 such as plasma diagnostics, gaseous electronics, and materials processing. For example, 57 the metamaterial’s spectral absorptivity peaks provide good estimates of electron density 58 in a plasma. Furthermore, the reflectionless absorption phenomena can be leveraged 59 60 Accepted Manuscript Page 9 of 11 AUTHOR SUBMITTED MANUSCRIPT - PSST-103817.R1

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