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Sensors and Materials, Vol. 35, No. 10 (2023) 3731–3741
MYU Tokyo

LETTERS & M 3447

Remote Monitoring of Deep-subwavelength Thickness Variation
Using Deformable Metamaterial Absorbers
Shenwei Yin,1 Xiubo Jia,2* Jiawen You,1 Yuebo Luo,1 and Zhixiang Tang1**
1School of Physics and Electronics, Hunan University, Changsha 410082, China
2Hunan Engineering Laboratory for Control and Optimization of PV Systems,

Hunan Vocational Institute of Technology, Xiangtan 411104, China(Received December 7, 2022; accepted September 5, 2023)

Keywords: deformable metamaterial absorber, deep subwavelength, thickness monitor

Interferometry, a typical phase-sensitive measurement, usually requires additional hardwareand complex signal processing to achieve subwavelength resolution. In this paper, we propose apotential thickness variation monitor, in which only reflection losses are needed to achieve deepsubwavelength accuracy. The proposed monitor is based on a sensitive thickness-dependent
metamaterial absorber (MMA), which is made of split copper rings periodically arranged in a
flexible and nonabsorbent thermoplastic polyurethane base. Experimental results showed thatthe frequency of the absorption peak increases almost linearly in the range from 6.655 to
6.755 GHz when the thickness of the MMA decreases from 25.625 to 24.833 mm with a step of
0.0417 mm, about a thousandth of the central wavelength of this frequency region. The effects of
two key geometry parameters, i.e., the distance from the split copper ring to the metal base andthe gap width of the split copper ring, on the absorption performance are investigated bynumerical simulation. Our results may provide a simple method of monitoring deepsubwavelength thickness variation in the far field.

1.

Introduction

Metamaterial absorbers (MMAs) have attracted considerable attention since Landy et al. first
proposed a nearly perfect microwave absorber using metamaterials in 2008,(1) owing to theirimportant applications in stealth cover,(2) chirality-selective absorption,(3) selective thermal
emitters,(4–6) solar energy harvesting,(7–11) and so on. Usually, the structures and sizes of these
MMAs are fixed, and the absorption characteristics can no longer be changed, lacking
adaptability and tunability.
To make up for this disadvantage, tunable MMAs have been proposed and extensively
studied in recent years.(12–24) The absorption characteristics of these MMAs can be changed bymechanical stretching,(18,19) photoexcitation,(20) electrical excitation,(21) and other external
physical fields.(22–24) For example, Li et al. demonstrated a resonance-frequency tunable MMA
working at terahertz frequencies, which was made of a planar arranged resonator on a highly*Corresponding author: e-mail: jiaxiubo@xlgy.com**Corresponding author: e-mail: tzx@hun.edu.cn

https://doi.org/10.18494/SAM4269

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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stretchable substrate.(18) The MMA experimentally showed a large frequency shift with a small
applied stretch. Additionally, Su et al. proposed a dual-band tunable MMA, in which thegeometric parameters of the particularly designed metal structure can be adjusted through theapplied pressure.(19) With increasing pressure, the absorption peak at low frequency gradually
increases, whereas the other absorption peak at high frequency decreases simultaneously.
MMA-based sensors exhibit significant promise owing to their high sensitivity, quality factor,
cost-effectiveness, and ease of fabrication, enabling the accurate measurement of physicalparameters. Islam et al. proposed a digit 8-shaped resonator-inspired metamaterial for measuring
the thickness of multilayered structures with an accuracy of 0.5 mm.(25) Using a singlemicrostrip transmission line with a pair of coupled circular complementary spiral resonators,
Sun et al. realized a subwavelength planar microwave sensor to measure thickness with anaccuracy of 0.1 mm and the permittivity of a dielectric sheet.(26) Here, we propose an MMA
made of a flexible base and split-ring resonators, which has potential in monitoring deepsubwavelength thickness variation in the far field.
Usually, to achieve subwavelength accuracy in the measurement, interferometry, which isone of the most effective methods, has been widely used.(27–30) For example, opticalinterferometry uses light interference to determine thickness with ensured reliability and highprecision.(31–33) Compared with the optical-based method, microwave and millimeter-wave
interferometries have advantages against harsh environments such as fogs, oils, and powders inpractical applications.(34–38) Using microwave integrates and monolithic microwave integrated
circuits, Kim and Nguyen realized a millimeter-wave sensor with a resolution of λ0/840, where
λ0 is the free space wavelength.(34) Using frequency and phase evaluation algorithms, Ayhan etal. developed a frequency-modulated continuous wave radar system for high-accuracy range
detection.(36) By combining several continuous wave radars with different operating frequencies,
the measurement accuracy of the radar system can be improved further.(37,38)
However, interferometry is a typical phase-sensitive measurement, which usually requires
additional hardware and complex signal processing to achieve reliable precision. In this paper,
we propose a potential thickness variation monitor with deep-subwavelength accuracy based on
the sensitive thickness-dependent absorption of the designed MMA. Experimental results
showed that the frequency of the absorption peak increases almost linearly with the decrease in
MMA thickness with a step of 0.0417 mm, about a thousandth of the wavelength. The effects of
two main geometry parameters of the MMA on the absorption performance have also been
investigated by numerical simulation.

2.

Structure and Experiment

A unit cell of the proposed MMA is schematically shown in Fig. 1. The unit cells are
periodically distributed in a square lattice with a lattice constant at 18 mm in the x- and y-directions. The split resonant ring (SRR), which is made of a split copper ring on top of a hard
FR4 plate, is obliquely held by a designed flexible base. When the top of the absorber is pressed
downward, the FR4 plate is expected to rotate around the x-axis, and the included angle θ
between the SRR and the flexible base decreases, i.e., the thickness of the absorber decreases.
The absorption characteristic of the MMA is mainly determined by the magnetic flux passing

Sensors and Materials, Vol. 35, No. 10 (2023)

Fig. 1.

3733(Color online) Sketch of a unit cell of proposed MMA.

through the SRR, which is sensitive to the SRR tilt angle. To lengthen the interaction time
between the incident electromagnetic wave and the SRR, an aluminum plate is placed at thebottom of the flexible base to totally reflect the incident wave back. The thicknesses of thealuminum plate and flexible base are c = 2 and d = 8 mm, respectively. The FR4 plate and copperring are cubic and their thicknesses are 0.8 and 0.035 mm, respectively. The copper ring isfabricated at the center of the FR4 plate, its two side lengths are a = 18 and b =16 mm, and its
width is p = 0.5 mm. The split of the copper ring is on the top side and the width of the gap is g =0.1 mm. The distance between the SRR and the flexible base is e = 4 mm. The initial value of θ
is 53.24°, so that the thickness of the whole absorber is h = 25.625 mm. The relative permittivitiesof the flexible material and FR4 plate are 1.5 and 4.4, respectively. The incident electromagnetic
wave propagates in the negative direction of the z-axis, with the electric and magnetic fields
polarized along the x- and y-directions, respectively. Note that the magnetic field is perpendicular
to the SRRs, guaranteeing that the induced currents in the split copper rings can be excitedeffectively.
For fabricating the proposed MMA, we use a 3D printer to print a flexible base with unit cells
arranged 10 by 10 on top of an aluminum slab of 180 × 180 × 2 mm3. The 3D printing material
used here is thermoplastic polyurethane (TPU), which is flexible and almost nonabsorbent in the
GHz band. To reduce the effective permittivity and enhance the flexibility of the printed base, alow filling ratio of 30% is adopted during the 3D printing process. Then, the SRRs are assembled
in the flexible base periodically as shown in the inset of Fig. 2(a). In the upper part of the softbase, a slot structure is printed, and FR4 plates are inserted into it to keep the FR4 plates
relatively fixed. Moreover, an acrylic plate with a set of acrylic bolt and nut is fixed with thebottom aluminum plate. The acrylic plate, which is placed on top of the MMA, can move
downward or upward by screwing the nut in or out, for changing the thickness of the MMA in
the absorption measurement ensuring consistency in the decrease in thickness across all cells,
minimizing individual differences and ensuring uniform absorption characteristics throughout
the MMA.

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(a)

(b)

Fig. 2. (Color online) Experimental results of thickness-dependent absorptions of proposed MMA. (a) Thickness hand thickness decrease Δh vs peak frequency of absorption. The inset is the fabricated MMA. (b) Measured
absorptions of fabricated MMA for three Δh values of 0.25, 0.50, and 0.75 mm.

The absorption of the proposed MMA is characterized by reflection loss and measured using
a vector network analyzer (CETC41 AV3672B-S). We set 800 points during a linear frequency
sweep from 5 to 9 GHz, suggesting a frequency resolution of 0.005 GHz. By screwing theacrylic nut downward with a step of 10°, the MMA thickness h decreases from 25.625 to 24.833
mm with a step of 0.0417 mm. For each thickness decrease, we record the frequency of theabsorption peak. The experimentally measured results are shown in Fig. 2(a). Here, we only
focus on the absorption in the frequency range from 6.0 to 7.0 GHz because all the absorption
peaks in this range are distinct and less than −15 dB. As examples, the absorption spectra forthree Δh values of 0.25, 0.50, and 0.75 mm are plotted in Fig. 2(b). Clearly, the absorption peakmoves to the high frequency when the thickness of the MMA decreases. More importantly,
according to the experimental results, the frequency shift is almost linear with respect to thedecrease in thickness, indicating a potential thickness variation monitoring. Furthermore,compared with the central wavelength λ0 in this frequency range, the step of the experimentallymeasured thickness change is about λ0/1100. To verify the experimental repeatability, three
MMAs were fabricated and each of them was subjected to individual experimentation. As
shown in Fig. 3, the results obtained clearly demonstrate that all three MMAs exhibit remarkably
similar absorption characteristics, showing an approximately linear variation of the absorption
peak within a specific frequency range.

3.

Theory and Numerical Simulation

For a better understanding of the experiment results, numerical simulation is performed
using the 3D finite-difference time-domain (FDTD) method.(39) To mimic a plane wave
perpendicularly incident to the proposed MMA, periodic boundary conditions are applied to theSensors and Materials, Vol. 35, No. 10 (2023)

Fig. 3.

3735(Color online) Experimental results of thickness-dependent absorptions of three fabricated MMAs.

four sides of the unit cell, which are perpendicular to the x- and y-axes, respectively. Moreover,perfect matching layers are employed along the z-axis. Moreover, a plane wave source is placed
on top of the SRR and a two-dimensional frequency-domain monitor is located behind thesource to record the reflected power.
Similar to the experimental measurement, in the numerical simulation, we only consider theabsorption of the MMA from 6.0 to 7.0 GHz. The simulation results are plotted (the blue linewith squares) and compared with the experimental results (the red line with diamonds) in Fig. 4.
It is clearly shown that the peak frequency of the simulated absorption increases linearly with thedecrease in MMA thickness, agreeing well with the experimental results except for a slightfrequency shift. This difference is mainly caused by two factors. First, a low filling ratio of 30%
was taken in the 3D printing process for the soft base, resulting in a slight difference from thesimulation. Second, in the frequency range of 1–15 GHz, the relative dielectric constant and loss
tangent of the FR4 plate tend to exhibit instability.(40) In the simulation, a relative dielectric
constant of 2.4 and a loss tangent of 0.01 were chosen for a frequency of 8.4 GHz based on Ref.
40. However, these simulation values may not precisely match the actual electromagnetic
characteristics of the 6.5–7 GHz frequency band in the experiment. Despite these differences,
the simulation results still effectively prove the feasibility of the MMA and its properties ofapproximately linear variation of the absorption peak in a specific frequency range.
For a thorough study, the effects of the geometry parameters of the unit cell on the absorption
peak of the MMA have been systematically analyzed. Here, we only consider two key geometry
parameters, i.e., the distance e between the SRR and the flexible base and the gap width g of the
SRR. The first one is the main factor in determining the magnetic flux passing through the SRR
and the induced current in the SRR. The second one plays an important role in dissipating theelectromagnetic waves efficiently. Figure 5 shows the thickness-dependent absorption of the
MMA for the distance e changing from 1 to 7 mm with a step of 3 mm. It is clear that the
distance e affects not only the absorption intensity considerably but also the dependence of thepeak frequency on the MMA thickness. As shown in Figs. 5(a) and 5(c), all of the simulated

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Fig. 4. (Color online) Thickness decrease vs peak frequency of absorption of proposed MMA. The red line withdiamonds and the blue line with squares denote the experimental and simulation results, respectively.

Fig. 5. (Color online) Effect of distance between SRR and soft base on absorption peak: (a) e = 1, (b) e = 4, and(c) e = 7 mm.

maximum absorptions are larger than −15 dB, and the peak frequency is almost invariant withthe thickness decrease for e = 1 and 7 mm. However, as presented in Fig. 5(b), for e = 4 mm, theabsorption peak moves clearly to the high frequency when the thickness of the MMA decreases.
Moreover, all the maximum reflection losses are less than −15 dB, indicating strong anddistinguishable absorptions.
Similarly, the effect of the gap width g of the SRR on the absorption is also investigated bynumerical simulation. As shown in Fig. 6, for every gap width g, the frequency of the absorption
peak increases when the thickness of the MMA decreases. For g = 0.5 and 1 mm, the peakabsorptions of the MMAs are clearly weaker than those for g = 0 and 0.1 mm. Comparatively,
both the frequency shift of the peak absorption and the maximums of the absorptions are mostsignificant for the gap width g = 0.1 mm.

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Fig. 6. (Color online) Effect of gap width of SRR on absorption peak: (a) g = 0 (b) g = 0.1, (c) g = 0.5, and(d) g = 1 mm.

Although the absorption mechanism for the MMA is always very complicated, here, we
present a simple theoretical model based on the equivalent circuit theory to understand thesimulation and experimental results. On the basis of the equivalent circuit theory,(41,42) our
deformable absorber can be roughly described by an RLC resonant circuit as shown in Fig. 7.
The resonance frequency fm of the MMA can be written as

fm =

1
2π LC

.

(1)

For our MMA, the effective capacitance C mainly originates from the resonant ring gap andis almost unchanged during the deformation of the MMA, since the gap width g is invariant andnegligible compared with the resonant ring lengths a and b. Therefore, the resonance frequency
fm is primarily determined by the effective inductance L, because the effective resistance is also
invariant.
As shown in Fig. 1, the magnetic f lux through the SRR is given by Φ= ∫ B ⋅ d S ≈ BS sin θ , where B and S are the magnetic field and area of the SRR, respectively.
For a harmonic incident wave with an angle frequency ω, the induced electric potential
difference in the SRR is V =−d Φ / dt =jωBS sin θ . Moreover, the effective inductance L can be
decomposed into two parts, the self-inductance Ls of the SRR and the mutual inductance LM
between the SRR and its image due to the ground metal plane beneath it. Specifically, the SRR3738

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Fig. 7.

Equivalent circuit of proposed MMA.

induces an SRR image with the same current given by I − = I + because the reflected magnetic
field is in the same direction as the incident one. The coupling between the SRR and its image
can be expressed in matrix form as

 Ls LM   I + V +   ,  = jω  LM Ls   I − V − (2)where V + and V −, and I + and I − are the induced voltage and current of the SRR and their images,
respectively. It can be readily shown that the eigen solutions of Eq. (2) have the inductance eigen
values of L = LS + LM and the corresponding eigen vectors [1, 1]T. Finally, substituting
V = jωBS sin θ into Eq. (2), we can see that the effective inductance L decreases as the angle θdecreases, whereas, according to Eq. (1), the resonant frequency increases.

4.

Conclusions

We have experimentally demonstrated a deformable MMA, which has potential in the remotemonitoring of deep-subwavelength thickness variation. Different from the widely usedinterferometry, which usually requires additional hardware and complex signal processing toachieve subwavelength resolutions, our proposed method only needs to measure the reflection
loss of the MMA. The proposed monitor is based on a very sensitive thickness-dependent
MMA, which is made of split copper rings obliquely held by a flexible and nonabsorbent TPU
base. The soft TPU base makes the SRR capable of tilting in one direction and reducing its
included angle with the TPU base to change the thickness of the MMA. The experimentallymeasured results showed that the frequency of the absorption peak increases almost linearly inthe range from 6.655 to 6.755 GHz when the thickness of the MMA decreases from h = 25.625 to
24.833 mm with a step of 0.0417 mm, about one-thousandth of the central wavelength of thisfrequency region. Numerical simulation has also been conducted to check this sensitive
thickness-dependent absorption. The simulation results agreed well with the experimental
results except a frequency shift. This discrepancy may be attributed to the fabrication errors andthe introduction of the acrylic parts in the experiments.

Sensors and Materials, Vol. 35, No. 10 (2023)

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Moreover, the effects of two key geometry parameters, i.e., the distance between the split
copper ring and the flexible base and the gap width of the split copper ring, on the absorption
performance have been investigated by numerical simulation. The simulation results showed thatthe maximum absorption of the MMA is sensitive to these two parameters. Our results may givea new way to monitor deep-subwavelength thickness variation in the far field. For example, the
MMA can be integrated in some mechanical and building structures for the precise and longterm monitoring of the fine variation of their thicknesses in the far field, especially in places thatare inaccessible to humans.

Acknowledgments
This research was funded by the Natural Science Foundation of Hunan Province, China(No. 2021JJ60051) and the Scientific Research Foundation of Hunan Education Department(No. 18C1446).

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About the Authors
Shenwei Yin received his B.S. degree in information & communicationengineering from Hunan University, Changsha, China, in 2022. He is currently
working toward his Ph.D. degree in electronic science and technology in the
School of Physics and Electronics, Hunan University, Changsha, China. His
research interests include metamaterials, nonlinear optics, and bound state in
the continuum. (yinsw@hnu.edu.cn)

Sensors and Materials, Vol. 35, No. 10 (2023)

3741

Xiubo Jia received her M. S. degree in materials engineering from Hunan
University in 2016. She is now an assistant professor in the School of New
Energy, Hunan Vocational Institute of Technology, Xiangtan, China. Her
research interest focuses on metamaterial absorbers. (jiaxiubo@xlgy.com)

Jiawen You received her B.S. degree in communication engineering from
Hunan University, Changsha, China, in 2022. She is currently working toward
her M.S. degree at the University of Electric Science and Technology of China,
Chengdu, China. Her research interests include microwave devices forcommunication applications and antennas. (jiawyou@163.com)

		Yuebo Luo received his B.S. degree in communication engineering from
Hunan University, Changsha, China, in 2020. He received his M.S. degree inelectric engineering from the University of Melbourne, Melbourne, Australia,
in 2022. His research interests include metamaterial and antenna.
(389865719@qq.com)

Zhixiang Tang received his Ph.D. degree in optical engineering from
Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academyof Science (CAS), China, in 2007. He then joined the faculty at Hunan
University in Changsha, Hunan Province, China. From Oct. 2013 to Oct. 2014,
he was a visiting scholar in the Department of Electrical and Computer
Engineering of the National University of Singapore. His research interests
include the linear and nonlinear optical properties of man-made nanostructures
such as photonic crystals and metamaterials. (tzx@hnu.edu.cn)