Supplementary Information
Experimental demonstration of a transparent graphene
millimeter wave absorber with 28% fractional
bandwidth at 140 GHz
Bian Wu1,3, Hatice M. Tuncer2, Majid Naeem1, Bin Yang1,4, Matthew T. Cole2,
William I. Milne2,Yang Hao1,*
1
School of Electronic Engineering and Computer Science, Queen Mary University of London,
London, E1 4NS, United Kingdom;
2
Department of Engineering, University of Cambridge, 9 JJ Thomson Avenue, Cambridge, CB3
0FA, United Kingdom;
3
School of Electronic Engineering, Xidian University, Xi’an, 710071, China;
4
Engineering, Sports & Sciences Academic Group, University of Bolton, Deane Road, Bolton,
BL3 5AB, United Kingdom.
*
Correspondence should be addressed to Y.H. (email: y.hao@qmul.ac.uk).
The Supplementary Information includes:
Supplementary Figures S1 – S6.
1
a
b
f0
0
3f0
5f0
180
Mag(S11) (dB)
90
-10
0
-15
-90
-20
-25
Arg(S11) (degree)
-5
0
50
100
150
Frequency (GHz)
-180
200
Figure S1 | Schematic diagram of typical resonant absorbers and the reflection
spectra of a single graphene-dielectric absorber. (a) Salisbury screen absorber and
Jaumann absorber, equivalent to a multilayer Salisbury screen. (b) Reflection spectra
of a single graphene-dielectric Salisbury screen absorber, which shows periodic
reflection zeros (absorption peaks) at zero-phase points, occurring at fi = (2i-1)f0. The
scattering rate and chemical potential of graphene are set to Γ = 5 meV and μc = 0.3 eV
at T = 300 K. The relative permittivity of the 1.3 mm thick dielectric slab is εr = 3.8.
2
a
Arg(S11) (degrees)
180
90
0
N=1
N=2
N=3
-90
-180
0
40
80
120
160
200
160
200
Frequency (GHz)
b
f0/3 f0/2
1.0
f0
3f0/2 5f0/3
Absorption
0.8
0.6
2f0
0.4
N=1
N=2
N=3
0.2
0.0
0
40
80
120
Frequency (GHz)
Figure S2 | Reflection phases and absorption spectra of N = 1-3 unit stacked
graphene-dielectric absorbers. (a) Reflection phase spectra show that the absorption
peaks occur at the zero crossing points as the phase changes from positive to negative
angles. (b) Absorption spectra showing the peak locations. The scattering rate and
chemical potential of graphene are set to Γ = 5 meV and μc = 0.2 eV at T = 300 K;
relative permittivity and thickness of the dielectric slabs are εr = 1.1 and h = 1 mm.
3
a
Mode B
Mode A
1.0
Mode C
Absorption
0.8
0.6
0.4
c=0.0eV
c=0.1eV
0.2
0.0
c=0.2eV
c=0.3eV
0
50
100
150
200
Frequency (GHz)
b
Mode B
Mode A
Mode C
E-field [V/m]
5.0e3
2.5e3
z
0.0e3
y
Figure S3 | Calculated absorption spectra of the 3-unit absorber and its electric-field
distribution at absorption peaks (modes). (a) Absorption spectra with varying
chemical potentials of the graphene sheets. There are three absorption peaks in the
first band, labelled as mode A, B, C, which are induced by the mutual coupling of the
three Fabry-Perot resonators (Γ = 5 meV, T = 300 K, εr = 1.1, h = 1 mm). (b) Electricfield distribution when μc = 0.2 eV; mode C has the shortest wavelength corresponding
to the highest resonant frequency. The E-field magnitude inside the absorber has
diminished due to high absorption.
4
a
1.0
Absorption
0.8
0.6
BW
0.4
r=1.1
r=2.7
0.2
r=3.8
0.0
0
30
90
60
120
150
180
Frequency (GHz)
b
1.0
Absorption
0.8
BW
0.6
0.4
h=1.0
h=1.5
h=2.0
unit:mm
0.2
0.0
0
30
90
60
120
150
180
Frequency (GHz)
Figure S4 | Influence of dielectric parameter variations on absorption spectra of the
3-unit graphene-dielectric absorber. (a) Impact on bandwidth (BW) and magnitude of
absorption is shown for various relative permittivity values for different materials;
foam (εr = 1.1), PMMA (εr = 2.7) and quartz (εr = 3.8) with the dielectric thickness set to
h = 1 mm. (b) Thickness variation at a fixed relative permittivity (εr = 1.1) has an impact
on bandwidth only.
5
a
1.0
Absorption
0.8
0.6
r=1.1
0.4
h=1.3mm
=5meV
c=0.2eV
O
TE 0
O
TE 30
O
TE 60
0.2
5L
0.0
0
b
100
50
150
Frequency (GHz)
200
1.0
Absorption
0.8
0.6
r=1.1
0.4
h=1.3mm
=5meV
c=0.2eV
O
TM 0
O
TM 30
O
TM 60
0.2
5L
0.0
0
50
100
150
Frequency (GHz)
200
Figure S5 | Absorption spectra of the 5-unit absorber at oblique incidence angles (εr =
1.1). (a) TE-polarization. (b) TM-polarization. The bandwidth increases with increasing
incidence angles for both polarizations. The absorption is reduced significantly and the
absorption magnitude variation is more prominent for θ > 60⁰ with TE-polarization.
6
a
1.0
Absorption
0.8
0.6
r=3.8
0.4
h=1.3mm
=5meV
c=0.2eV
O
TE 0
O
TE 30
O
TE 60
0.2
5L
0.0
0
b
50
100
150
Frequency (GHz)
200
1.0
Absorption
0.8
0.6
0.4
r=3.8
O
TM 0
O
TM 30
O
TM 60
0.2
h=1.3mm
=5meV
c=0.2eV
5L
0.0
0
50
100
150
Frequency (GHz)
200
Figure S6 | Absorption spectra of the 5-unit absorber at oblique incidence angles (εr =
3.8). (a) TE-polarization. (b) TM-polarization. The bandwidth increases, the absorption
is reduced and the absorption ripple variation is insignificant for θ > 60⁰ TEpolarization. For TM-polarization, absorption increases and the amplitude of ripples
decrease for increasing angle of incidence.
7