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 * ABSTRACT
 * DATA AVAILABILITY
 * REFERENCES

INVISIBILITY CLOAKING WITH PASSIVE AND ACTIVE HUYGENS'S METASURFACES

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Open Submitted: 29 December 2020 Accepted: 08 February 2021 Published Online: 18
February 2021
 * INVISIBILITY CLOAKING WITH PASSIVE AND ACTIVE HUYGENS'S METASURFACES
 * 


Appl. Phys. Lett. 118, 071903 (2021); https://doi.org/10.1063/5.0041996
Paris Anga), Gengyu Xu, and George V. Eleftheriades
more...View Affiliations
 * The Edward S. Rogers Sr. Department of Electrical and Computer Engineering,
   University of Toronto, Toronto, Ontario M5S 3G4, Canada
 * a)Author to whom correspondence should be addressed:
   paris.ang@mail.utoronto.ca

   Note: This Paper is part of the APL Special Collection on Metastructures:
   From Physics to Applications.

View Contributors
 * Paris Ang
 * Gengyu Xu
 * George V. Eleftheriades




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ABSTRACT

According to the Equivalence Principle, any distribution of electromagnetic
fields can be generated within a closed region by suitable electric and magnetic
sources lying on its bounding surface. In electromagnetic theory, these sources
have been used as fictitious analytical tools. However, this has changed in
recent years with the development of “Huygens's metasurfaces,” which are
subwavelength thin sheets of artificial active and/or passive elements. With
proper configuration, these elements can physically approximate the
aforementioned sources, enabling precise manipulation of electromagnetic waves
in extraordinary manners. Given their potential, this work aims to provide an
overview of Huygens's metasurfaces with a focus on cloaking applications. After
an exposition of general operation and design principles, both active and
passive Huygens's cloaks are described.
Considered a foundation of classical electromagnetics, the “Equivalence
Principle,” a generalization of the Huygens's principle, postulates that any
electromagnetic field distribution within a region can be represented by
equivalent electric and magnetic sources.11. R. Harrington, Time-Harmonic
Electromagnetic Fields ( Wiley-IEEE Press, 2001). Conventionally, these sources
are considered fictitious tools, which help describe wave behavior. However,
this has changed with recent advances in artificial materials and the
development of so-called Huygens's metasurfaces (HMSs).2,32. C. Pfeiffer and A.
Grbic, “ Metamaterial Huygens' surfaces: Tailoring wave fronts with
reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
https://doi.org/10.1103/PhysRevLett.110.1974013. M. Selvanayagam and G. V.
Eleftheriades, “ Discontinuous electromagnetic fields using orthogonal electric
and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429
(2013). https://doi.org/10.1364/OE.21.014409 Composed of subwavelength-scaled,
composite elements (“meta-atoms”) arranged into thin sheets, HMSs can either
actively or passively recreate the aforementioned sources. Along with providing
a physical analog to theory, the ability to recreate these sources on demand
enables HMSs to arbitrarily synthesize and control electromagnetic waves.
Here, we aim to present an overview of passive and active HMSs in the context of
a cloaking paradigm. This is fitting as some of the earliest reported HMS
concepts have focused on cloaking.44. M. Selvanayagam and G. V. Eleftheriades, “
An active electromagnetic cloak using the equivalence principle,” IEEE Antennas
Wireless Propag. Lett. 11, 1226–1229 (2012).
https://doi.org/10.1109/LAWP.2012.2224840 General theory and design principles
for HMSs are first formulated. These are then used to develop active and passive
electromagnetic cloaks capable of concealing various electromagnetic scatterers.
Finally, the effectiveness of these cloaks is verified through simulations and
experiments.
For simplicity, we will restrict the problem to two-dimensions (∂/∂z=0). The
HMS, denoted by the dashed line in Fig. 1, divides the problem into two regions.
These are labeled V1 and V2 and contain electromagnetic fields
{→E1,→H1} and {→E2,→H2}, respectively. Due to its deep subwavelength thickness,
the HMS can be theoretically modeled as an infinitesimally thin sheet of
spatially varying surface electric currents (→Js) and/or surface magnetic
currents (→Ms). These so-called “Huygens's sources” give rise to discontinuities
in the tangential electromagnetic fields according to22. C. Pfeiffer and A.
Grbic, “ Metamaterial Huygens' surfaces: Tailoring wave fronts with
reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
https://doi.org/10.1103/PhysRevLett.110.197401

→Js=ˆn×(→Ht,2−→Ht,1)≜ˆn×Δ→Ht,→Ms=(→Et,2−→Et,1)׈n≜Δ→Et׈n,

(1)

where the subscript t denotes the tangential field components.
FIG. 1. Schematic of the 2D, two-region problem.
   
 * PPT
   |
 * High resolution

The currents →Js and →Ms can also be related to the average tangential
electromagnetic fields across the HMS according to the Bianisotropic Sheet
Transition Conditions (BSTCs),55. C. Pfeiffer and A. Grbic, “ Bianisotropic
metasurfaces for optimal polarization control: Analysis and synthesis,” Phys.
Rev. Appl. 2, 044011 (2014). https://doi.org/10.1103/PhysRevApplied.2.044011

[→Js→Ms]=[ˉˉYseˉˉKemˉˉKmeˉˉZsm]·[→Et,av→Ht,av],→Et,av≜→Et,1+→Et,22, →Ht,av≜→Ht,1+→Ht,22,

(2)

where ˉˉYse and ˉˉZsm are 2 × 2 tensors defining the effective surface electric
admittance and surface magnetic impedance, while ˉˉKem and ˉˉKme characterize
the bianisotropic coupling.
The surface currents may interact with the electromagnetic fields to emit and/or
dissipate power. In that case, the HMS can be classified as active and/or lossy.
Conversely, passive and lossless HMSs are reactive and, thus, neither consume
nor generate real power. Such surfaces must satisfy55. C. Pfeiffer and A. Grbic,
“ Bianisotropic metasurfaces for optimal polarization control: Analysis and
synthesis,” Phys. Rev. Appl. 2, 044011 (2014).
https://doi.org/10.1103/PhysRevApplied.2.044011

Re{ˉˉYse}=Re{ˉˉZsm}=Im{ˉˉKem}=Im{ˉˉKme}=0.

(3)

Furthermore, a surface consisting of only reciprocal components must satisfy55.
C. Pfeiffer and A. Grbic, “ Bianisotropic metasurfaces for optimal polarization
control: Analysis and synthesis,” Phys. Rev. Appl. 2, 044011 (2014).
https://doi.org/10.1103/PhysRevApplied.2.044011

ˉˉYTse=ˉˉYse, ˉˉZTsm=ˉˉZsm, ˉˉKTem=−ˉˉKme.

(4)

For practical reasons, (4) is assumed throughout this review.
To design a general HMS for arbitrary wave manipulation, the desired fields on
either side of the device are first stipulated. Next, an appropriate design in
the form of implicit electric and magnetic currents or explicit surface
parameters can be found by solving (1) or (2), respectively.
To construct an electromagnetic cloak, we first assume that the HMS completely
encloses the target while isolating it from all external illuminations (known a
priori). Consequently, we have

→Et,2=→Eit, →Ht,2=→Hit, →Et,1=→Ett, →Ht,1=→Htt,

(5)

where the superscripts i and t denote incident and transmitted fields,
respectively. The absence of reflections renders the target undetectable from
all external observers.
There are two approaches to synthesize the field discontinuities described by
(5). These are examined subsequently, starting with the active approach,
followed by the passive alternative. For simplicity, we assume, henceforth, that
the electromagnetic fields are strictly TMz-polarized (→E=ˆzE). Cloaks that
generate nonradiative external reflections in the form of cross-polarized
surface waves66. D.-H. Kwon, “ Lossless tensor surface electromagnetic cloaking
for large objects in free space,” Phys. Rev. B 98, 125137 (2018).
https://doi.org/10.1103/PhysRevB.98.125137 are noted but not discussed further
in this paper.
According to (1) and (5), the HMS cloak needs to support the surface currents,

→Js=ˆn×(→Hit−→Htt), →Ms=(→Eit−→Ett)׈n.

(6)

In an active cloaking approach, these spatially varying continuous current
sheets are discretized into n electric (ρe=→Jslh) and magnetic (ρm=→Mshl) dipole
moments.77. D. A. B. Miller, “ On perfect cloaking,” Opt. Express 14,
12457–12466 (2006). https://doi.org/10.1364/OE.14.012457 Here, h represents the
target height, whenever applicable.44. M. Selvanayagam and G. V. Eleftheriades,
“ An active electromagnetic cloak using the equivalence principle,” IEEE
Antennas Wireless Propag. Lett. 11, 1226–1229 (2012).
https://doi.org/10.1109/LAWP.2012.2224840 Each moment can then be physically
realized by radiating sources,77. D. A. B. Miller, “ On perfect cloaking,” Opt.
Express 14, 12457–12466 (2006). https://doi.org/10.1364/OE.14.012457 such as
conventional antennas with inter-elemental spacing l, serving as the
constitutive meta-atoms. Although other antennas may be used, the most direct
means of realizing ρe and ρm are through current driven dipoles (Ie=ρe/h) and
loops (Im=ρm/(jωμA)) of area A [Fig. 2(a)].
FIG. 2. Possible physical meta-atom designs for (a) active and (b) passive HMS
cloaks.
   
 * PPT
   |
 * High resolution

The impressed sources of an active HMS cloak grant us full control over the
surface current densities regardless of the illumination. Therefore, with a
priori knowledge of →Eit and →Hit, we are at liberty to choose the fields in
volume 1. The most natural choice is to set →Ett=→Htt=0 such that the target
enclosed by the cloak, no matter its size, shape, and material parameters, will
not interact with any electromagnetic fields. Hence, it will not cause
scattering.
The inherent reconfigurability of their impressed sources allows active HMS
cloaks to be dynamically tuned in response to different illuminations. However,
this flexibility comes at the cost of constant power requirement and the need
for complex control circuits.
For applications involving fixed illumination, such as electromagnetic
interference reduction,88. Z. H. Jiang, P. E. Sieber, L. Kang, and D. H. Werner,
“ Restoring intrinsic properties of electromagnetic radiators using
ultralightweight integrated metasurface cloaks,” Adv. Funct. Mater. 25,
4708–4716 (2015). https://doi.org/10.1002/adfm.201501261 it is possible to
passively implement the HMS cloak without any active or lossy components,
leading to easier fabrication and integration processes.
Substituting (5) and (6) into (2), we obtain an underdetermined system of
equations that can be solved to assess the required surface parameters. For the
TMz problem considered herein, we can fix several superfluous degrees of freedom
by assuming bi-isotropy. However, this is still not sufficient to guarantee
passivity and losslessness. To do that, we can impose the additional constraint
of local (pointwise) power conservation on the tangential fields,99. A. Epstein
and G. V. Eleftheriades, “ Synthesis of passive lossless metasurfaces using
auxiliary fields for reflectionless beam splitting and perfect reflection,”
Phys. Rev. Lett. 117, 256103 (2016).
https://doi.org/10.1103/PhysRevLett.117.256103

Re{→Eit×(→Hit)*}=Re{→Ett×(→Htt)*}.

(7)

With the known incident fields, we can solve (7) for the required transmitted
fields to conserve local power. This now ensures that the surface parameters are
passive and lossless.
The required transmitted fields, as determined by (7), can be interpreted as
auxiliary fields, which balance the power flow at every point on the
metasurface.99. A. Epstein and G. V. Eleftheriades, “ Synthesis of passive
lossless metasurfaces using auxiliary fields for reflectionless beam splitting
and perfect reflection,” Phys. Rev. Lett. 117, 256103 (2016).
https://doi.org/10.1103/PhysRevLett.117.256103 These fields are permitted to
penetrate into the target if it consists of a dielectric material. As such,
interaction between the target and the auxiliary field is confined within region
1 and remains unobservable from region 2 [Fig. 3(a)]. In contrast, targets made
from perfect electric conductors (PECs) do not permit internal fields and, thus,
demand special treatment. One possible approach is to introduce a dielectric
coating between the cloak and the target. As depicted in Fig. 3(b), this
additional region admits nonzero transmitted fields {→Et,→Ht}, which facilitates
the satisfaction of (7) on the HMS, subject to the constraint of vanishing →Et
along the PEC.1010. G. Xu, G. V. Eleftheriades, and S. V. Hum, “
Discrete-Fourier-transform-based framework for analysis and synthesis of
cylindrical omega-bianisotropic metasurfaces,” Phys. Rev. Appl. 14, 064055
(2020). https://doi.org/10.1103/PhysRevApplied.14.064055
FIG. 3. Schematics of passive HMS cloaks for (a) penetrable dielectric targets
and (b) impenetrable PEC targets.
   
 * PPT
   |
 * High resolution

Regardless of the type of target, the theoretically derived surface parameters
can be realized using a modified version of the passive meta-atoms previously
used to construct planar HMSs.1111. G. Xu, S. V. Hum, and G. V. Eleftheriades, “
Augmented Huygens' metasurfaces employing baffles for precise control of wave
transformations,” IEEE Trans. Antennas Propag. 67, 6935–6946 (2019).
https://doi.org/10.1109/TAP.2019.2922945 This original planar design can also be
generalized to build curved surfaces.1010. G. Xu, G. V. Eleftheriades, and S. V.
Hum, “ Discrete-Fourier-transform-based framework for analysis and synthesis of
cylindrical omega-bianisotropic metasurfaces,” Phys. Rev. Appl. 14, 064055
(2020). https://doi.org/10.1103/PhysRevApplied.14.064055 As depicted by the
illustrative example in Fig. 2(b), the meta-atom consists of an asymmetric stack
of three curved electrically polarizable scatterers. In this particular design,
the outer layers behave like capacitors to z-directed electric fields, whereas
the middle layer can be inductive or capacitive depending on its geometry.
Notably, since each layer contains just a conductive pattern, the overall HMS
cloak does not require any active or lossy elements.
Finally, we note that the proposed approach is applicable to targets of all
electrical sizes, distinguishing it from the well-known passive mantle cloaks
intended to operate within the quasi-static regime.1212. A. Alù, “ Mantle cloak:
Invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
https://doi.org/10.1103/PhysRevB.80.245115
Having established the basic theory, we now present experimental measurements
and simulation results, which demonstrate the validity of both cloaking
approaches.
Figure 4 shows the 2D layout and corresponding experimental apparatus of an
active HMS cloak. Here, a metallic five-sided polygonal target (measuring:
L = 272.73 mm, W = 218.18 mm, h = 38 mm, and ϕ=45°) is illuminated at θ′=30°
incidence by a monopole positioned ρ′=600 mm from the target's center. Next, an
h = 38 mm wide parallel-plate waveguide is formed by sandwiching the target
between two 1626 × 1094 mm aluminum plates. This enforces 2D conditions and
suppresses any non-TEM modes as plate spacing is less than half a wavelength at
the operational frequency of 1.2 GHz. Finally, radiation boundaries are
synthesized by lining the waveguide's perimeter with absorbing foams.
FIG. 4. Active HMS cloak: layout and experiment.
   
 * PPT
   |
 * High resolution

The incident electric field radiated by the monopole source is a cylindrical
wave described by

→Eit=ˆzE0H(2)0(k|→ρ(xtar,ytar)−→ρ′|),

(8)

where H(2)0 is the zeroth-order Hankel function of the second kind, k the
free-space wavenumber, →ρ(xtar,ytar) an observation point on the target's
surface, and →ρ′ the source location.1414. P. Ang and G. V. Eleftheriades, “
Experimental active cloaking of a metallic polygonal cylinder,” in 2019
IEEE/MTT-S International Microwave Symposium-IMS (2019). Since the target is
conductive, all electric surface currents are shorted out (→Js=0), meaning that
only magnetic sources are required to realize the active HMS. Following the
formulation previously derived, the magnetic surface current required to cloak
the target is15,1615. P. Ang and G. V. Eleftheriades, “ Active Huygens' cloaks
for arbitrary metallic polygonal cylinders,” in 2018 IEEE/MTT-S International
Microwave Symposium-IMS (2018), pp. 337–340.16. P. Ang and G. V. Eleftheriades,
“ Active surface cloaking with patch antennas,” in 2018 IEEE International
Symposium on Antennas and Propagation (2018).

→Ms=−ˆn׈zE0H(2)0(k|→ρ(xtar,ytar)−→ρ′|).

(9)

To construct the cloak array, 15 evenly spaced monopoles are mounted 14 mm from
the target's surface.1313. P. Ang and G. V. Eleftheriades, “ Active cloaking of
a non-uniform scatterer,” Sci. Rep. 10, 1–11 (2020).
https://doi.org/10.1038/s41598-020-58706-z The close proximity of these
monopoles to the target results in their electric currents being mirrored across
the conductive plane, creating a virtual current loop.17,1817. A. M. H. Wong and
G. V. Eleftheriades, “ Active Huygens' metasurfaces for RF waveform synthesis in
a cavity,” in 2016 18th Mediterranean Electrotechnical Conference (MELECON)
(2016), pp. 1–5.18. P. Ang, A. M. Wong, and G. V. Eleftheriades, “
Equivalence-principle-based active metasurfaces,” in 2019 URSI International
Symposium on Electromagnetic Theory (EMTS) ( IEEE, 2019), pp. 1–4. This element
design also reduces the cloak's profile and improves robustness.
We plot the measured total electric field inside the waveguide, with and without
the HMS cloak, in Figs. 5(a) and 5(b), respectively. When the incident wave
impinges on the uncloaked object [Fig. 5(a)], the resultant scattering manifests
as distortion near the illuminated lower right surface of the target.
Additionally, a shadow region forms on the opposite side of the illuminated area
due to the target occluding the impinging wave. Conversely, enabling the cloak
cancels out scattering and restores the original incident field. This can be
seen in Fig. 5(b) where frontal/side distortion is reduced and the shadow region
has largely disappeared. To provide a quantitative performance metric, Fig. 5(c)
shows the measured bistatic radar cross section (RCS) of the target, referenced
to the frame depicted in Fig. 4. It can be seen that scattering suppression is
achieved over the entire azimuth with an average reduction of 8.6 dB.
FIG. 5. Experimental results for active cloaking of a polygonal aluminum
cylindrical target with 30° incidence: (a) cloak off, (b) cloak on, and (c)
bistatic RCS. Simulated results for an active multi-target cloak with the
polygonal target illuminated at 30° incidence: (d) cloak off, (e) cloak on, and
(f) bistatic RCS. Simulation results for passive cloaking of a quasitriangular
PEC cylinder: (g) cloak off, (h) cloak on, and (i) normal power density at the
HMS. Parts (a)–(c) reproduced with permission from P. Ang and G. V.
Eleftheriades, Sci. Rep. 10, 1–11 (2020).;1313. P. Ang and G. V. Eleftheriades,
“ Active cloaking of a non-uniform scatterer,” Sci. Rep. 10, 1–11 (2020).
https://doi.org/10.1038/s41598-020-58706-z Copyright 2020 Authors, licensed
under a Creative Commons Attribution (CC BY) license.
   
 * PPT
   |
 * High resolution

Another method of configuring this active cloak is to calculate the weights
directly from incident field measurements. This enables operation in complex
environments such as the simulated (in ANSYS HFSS) multi-target scenario in Fig.
5(d). Here, the same polygonal target is illuminated at θ′=30° incidence by a
monopole positioned ρ′=600 mm from its center. However, a second metallic,
circular target (r = 112 mm) is positioned 600 mm from the polygon's center and
cloaked with an additional 15 monopole elements. A simulated empty waveguide is
then used to obtain 30 incident field measurements at positions on the targets'
surfaces corresponding to cloak element locations. Figure 5(e) confirms that
weights calculated using this method are effective at hiding both targets with
an average combined scattering reduction of 15.3 dB [Fig. 5(f)].
Next, in order to substantiate the developed passive cloaking concept, we
present a local power-conserving bi-isotropic HMS cloak designed to conceal an
electrically large quasi-triangular metallic cylinder from the fields radiated
by an electric line source (with a frequency of 4.4 GHz). As hinted by a
previous work, the cross section of the HMS cloak need not match that of the
target.1919. G. Xu, G. V. Eleftheriades, and S. V. Hum, “ Approach to the
analysis and synthesis of cylindrical metasurfaces with noncircular cross
sections based on conformal transformations,” Phys. Rev. B 102, 245305 (2020).
https://doi.org/10.1103/PhysRevB.102.245305 In fact, it is sometimes beneficial
to have a differently shaped cloak, as its associated dielectric layer may
provide enhanced structural rigidity. Nonetheless, it is noted that a minimal
overall profile is achieved when the cross sections of the HMS and the target
are parallel.
As a proof of concept, we present a cloak with a quasi-square cross section. To
allow better visualization of the auxiliary fields, the permittivity of the
dielectric layer is selected to be 1; its thickness is also exaggerated,
resulting in an unnecessarily thick profile. The HMS is numerically implemented
in COMSOL Multiphysics using field-dependent electric and magnetic surface
current densities.1919. G. Xu, G. V. Eleftheriades, and S. V. Hum, “ Approach to
the analysis and synthesis of cylindrical metasurfaces with noncircular cross
sections based on conformal transformations,” Phys. Rev. B 102, 245305 (2020).
https://doi.org/10.1103/PhysRevB.102.245305
In Fig. 5(g), we show the simulated total electric field without the cloak. As
expected, the metallic target generates a significant amount of reflections and
casts a shadow. Figure 5(h) depicts the fields with the cloak present. Here, the
wavefronts emanating from the line source remain unperturbed. Despite the highly
intricate appearance of the transmitted auxiliary fields, an external observer
will not perceive any scattering. To explicitly demonstrate the passivity and
losslessness of the cloak, we plot the normal power density inside (S−) and
outside (S+) the HMS in Fig. 5(i), as a function of the azimuthal angle ϕ. A
perfect match between the two power profiles means that the total power density
Stot≜S++S− is identically zero. Hence, the surface neither generates nor absorbs
power.
To conclude, we presented a general overview on the theory of Huygens's
metasurfaces, along with their application to the design of active and passive
electromagnetic cloaks. Next, practical realization schemes for both classes of
HMSs were discussed. Experimental results for active cloaking and full-wave
simulation results for passive cloaking confirm the effectiveness and robustness
of HMSs for realizing electromagnetic invisibility.
This work was financially supported by the Natural Sciences and Engineering
Research Council of Canada (NSERC).
DATA AVAILABILITY

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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 1. © 2021 Author(s). All article content, except where otherwise noted, is
    licensed under a Creative Commons Attribution (CC BY) license
    (http://creativecommons.org/licenses/by/4.0/).







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