LAYERED GRAPHENE FOR ENHANCED

TRANSMISSION AT LOW TERAHERTZ

Alexander B. Yakovlev

Department of Electrical Engineering

University of Mississippi

1ST

WORKSHOP ON METAMATERIALS AND PHOTONIC

CRYSTALS, MEPHOC’2013

ARMENIA, COLOMBIA, SEPT. 30-OCT. 4, 2013

Introduction and Motivation

Graphene-Dielectric Stack

Dual Capacitive/Inductive Nature of Graphene Patches

Results and Discussions

Conclusions

2

OUTLINE

Enhanced Transmission at low-THz

3

Extremely thin conducting layers are almost opaque.

However, multilayer metal-dielectric PBG-like structures become

transparent within certain frequency bands in the optical regime.

I. R. Hooper et al., Opt. Express, 16, 17249 (2008)

M. R. Gadsdon et al., J. Opt. Soc. Am. B, 26, 734 (2009)

Induced transparency in the optical regime

BACKGROUND AND MOTIVATION (1)

4

Can a similar effect be observed at

microwaves??

The metal films are substituted by perforated metal layers

Microwave transmissivity of a metamaterial-dielectric stack

Butler et al., Appl. Phys. Lett., 95, 174101 (2009)

Yakovlev et al., 3rd Int. Congress on Advan. Electromag. Materi. in Microwa. and Optic.,(2009)

BACKGROUND AND MOTIVATION (2)

Scalora et al., Jour. App. Physics , 83, 2377–2383 (1998).

Feng et al., Phys. Rev. B. , 82, 085117(2005)

5 6 7 8 9 10 11 12 13 14 15 160

0.2

0.4

0.6

0.8

11

Frequency (GHz)

|S21|2

|S21|2 FEM model

|S21|2 Experimental

|S21|2 Analytical

A

B C D

BACKGROUND AND MOTIVATION (3)

Characteristic Band

What is the nature of these

resonances ??

can we tune them

can we predict the band

The number of transmission peaks is equal to the number of

layers (resonators)5

Butler et al., Appl. Phys. Lett. , 95, 174101 (2009)

Kaipa et al., Opt. Express, 18, 174101 (2010)

6

GRAPHENE-DIELECTRIC STACK

7

SURFACE CONDUCTIVITY OF GRAPHENE

220

2

2 2

0

1

, , ,

4

d d

c

d d

f fd

jje jT

f fd

j

Surface conductivity of graphene [Kubo formula]

, which at low-terahertz frequencies behaves as a low-loss

inductive surface.

1sZ

G. W. Hanson, J. Appl. Phys., 103, 064302 (2008)

1ln2

2

2

intra

Tk

B

cB BceTkj

Tkej

j

jje

c

c

2

2ln

4

2

inter

Intraband contributions Interband contributions

-e : charge of electron, T : temperature, : energy

: angular frequency, : reduced Planck’s constant

: chemical potential, : phenomenological scattering rate

2h

c

In the far-infrared regime, the contribution due to the interband electron

transition is negligible

,B ck T

8

Solid lines: approximate closed-form expressions (intraband + interband)

Dashed lines: numerical integration [Kubo formula]

SURFACE CONDUCTIVITY OF GRAPHENE

2 5

min

1/ 1.32 meV, 0.5 ps, 300 K

/ 2 6.085 10 S

T

e h

0.2 eVc 0.5 eVc

1 3 5 7 9 11 13 150

50

100

150

Frequency [THz]

Co

nductiv

ity

Re (/min

)

Im (/min

)

9Single sheet of graphene is highly reflective at low-THz frequencies

Behaves similar to an Inductive grid (metallic meshes) at microwaves.

Reflectivity and Transmissivity for normal incidence

FREE-STANDING GRAPHENE

1/ 1.32 meV

0.5 ps

300 K

1 eVc

T

10

TWO-SIDED GRAPHENE STRUCTURE

Thickness (h): 10 μm

Permittivity: 10.2

K 300 T ps, 0.5

meV 23.11

Transmission resonance appears at low frequencies

Graphene sheets effectively increase the electrical length

FP-type resonance of dielectric slab loaded with graphene sheets

μc = 0.5 eV

11

POWER TRANSMISSION SPECTRA

The number of transmission peaks is equal to the number of

dielectric slabs within the characteristic frequency band

Thickness (h): 10 μm

Permittivity: 10.2

K 300 T ps, 0.5

meV 23.11

h h

h h

1.0 eVc

I

II

12

POWER TRANSMISSION SPECTRA

Enhanced transmission at low-THz

Fabry-Perot resonances of the individual open/coupled cavities

Thickness (h): 10 μm

Permittivity: 10.2

K 300 T ps, 0.5

meV 23.11

4 layer graphene structure

- 4 dielectric slabs

- 5 graphene sheets

h h

h h

A

BC

D

13

ELECTRIC FIELD DISTRIBUTIONS

1.0 eVc

14

ELECTRIC FIELD DISTRIBUTIONS-ANIMATION PLOTS

0.005

0.078

0.370

0.443

0.881

1.173

Mode D

0.002

0.053

0.258

0.411

0.615

0.717

Mode B

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

d (degrees)F

requency (

TH

z)

15

PB -I

SB

PB -II

PB -I

PB -II

BRILLOUIN DIAGRAMS – PASSBANDS AND STOPBANDS

Thickness (h): 10 μm

Permittivity: 10.21.0 eVc

StopBand

Multi-layer graphene-dielectric stack

SB: StopBand

PB: PassBand

0 20 40 60 80 100 120 140 160 1803.5

4

4.5

5

5.5

6

6.5

d (degrees)F

requency (

TH

z)

16

Thickness (h): 150 μm

Permittivity: 2.21.0 eVc

3.5 4 4.5 5 5.5 6 6.50

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

PB -I

PB -II

PB -III

PB -IV

PB -I PB -II PB -III PB -IV

SB SB SB SB

GRAPHENE THICK SLABS BRILLOUIN DIAGRAMS

StopBand

StopBand

StopBand

StopBand

Four-layer graphene-dielectric stack

SB: StopBand

PB: PassBand

Exhibits a series of bandpass regions separated by bandgaps

A thick dielectric slab is sometimes needed for mechanical handling

17

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

N = 4

N = 10

N = 20

N = 40

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

N = 4

N = 10

N = 20

N = 40

μc = 0.5 eV μc = 1 eV

1r

z

x

y

mh 10

Number of peaks correspond to number

of layers (N)

With increase in ‘N’, all peaks lie in a

characteristic frequency band

Acts as a Wideband Bandpass filter

BROADBAND PLANAR FILTERS

18

h: 30 μm,

Period (D) = 20 μm,

Strip width (w) = 2 μm,

t = 0.4 μm,

Dielectric permittivity: 1

Graphene-air stack mimics the behavior of Fishnet-air stack at THz

Five-layer graphene/meshgrid stacks separated by free-space

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency [THz]

|T|2

Meshgrid

Graphene, c = 1eV

BROADBAND PLANAR FILTERS

low-terahertz frequenciesinductive surface reactance

capacitive surface reactance

low-frequency passband followed by

alternating stop and passbands as

frequency increases

inductive surface reactance

low-frequency stopband, followed

by alternating pass and stopbands as

frequency increases

Metallic mesh-grids

microwave/low-terahertz

frequencies

microwave/low-terahertz

frequencieslow-terahertz frequencies

Graphene sheets

low-loss inductive surface reactance

low-frequency stopband, followed

by alternating pass and stopbands as

frequency increases

low-terahertz frequencies

Combining the properties of the above

three structures in a single configuration

low-loss inductive and capacitive surface

reactance

Combined filtering properties of the above

three configurations

Advantage of the Graphene Metasurface

Metallic patches

LAYERED GRAPHENE PATCHES

19

20

For interior patches

For patches at top and

bottom interfaces

SURFACE IMPEDANCE OF GRAPHENE PATCHES

21

D = 10 μm; g = 1 μm; εr = 4;

μc = 0.5 eV

• For the graphene patches, the surface impedance changes from capacitive to inductive as frequency

increases

At low frequencies the behavior of graphene patches is similar to that of the metallic patches

(capacitive)

At high frequencies the behavior of graphene patches becomes similar to that of a graphene sheet

(inductive)

D = 10 μm; g = 1 μm; εr = 4;

μc = 1eV

SURFACE IMPEDANCE OF GRAPHENE PATCHES

22

D = 10 μm; g = 1 μm; εr = 4; h = 10 μm

Five-Layer Stack of Graphene Patches

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

Graphene Patch, c = 0.5 eV, Analytical

Graphene Patch, c = 0.5 eV, HFSS

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

Graphene Patch, c = 1 eV, Analytical

Graphene Patch, c = 1 eV, HFSS

The analytical results are in good agreement

with the full-wave simulations

μc = 0.5 eV

μc = 1 eV

TRANSMISSIVITY

23

D = 10 μm; g = 1 μm; εr = 4; h = 10 μm

Fig. 1

Fig. 2

Fig. 3Fig. 4

μc = 0.5 eV

μc = 1 eV

TRANSMISSIVITY

24

D = 10 μm; g = 1 μm; εr = 4; h = 10 μmAnalytical Results

• One can clearly notice the low passband (starting from zero frequency), followed by

a deep stopband, and then a second passband

• Also, it can be noticed that with an increase in the number of layers, the number of

transmission peaks which corresponds to the number of coupled layers increases,

still maintaining the same characteristic frequency bands

TRANSMISSIVITY VERSUS NUMBER OF LAYERS

25

Analytical Results The Brillouin diagrams perfectly predict

the passband and stopband regions of the

corresponding finite-layer structures

BLOCH-WAVE ANALYSIS

D = 10 μm; g = 1 μm;

εr = 4; h = 10 μm;

μc = 0.5 eV

• For mode B, the field value is low in the middle graphene

patch and is concentrated more near the remaining

graphene patches, which is consistent with the electric-field

distributions shown in the inset

For mode A, the field

value is zero near the

middle graphene patch,

which is consistent with

the electric-field

distribution shown in the

inset

26

ELECTRIC FIELD DISTRIBUTIONS

27

D = 100 nm; g = 10 nm; εr = 1; h = 166 nm Four-layer thin-metal patch-dielectric stack

The results are calculated using a fit based on measured data [1] for the permittivity,

utilizing an augmented Drude model [2]

1. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)

2. A. Vial and T. Laroche, J. Phys. D: Appl. Phys., 40, 7152 (2007)

SURFACE IMPEDANCE AND TRANSMISSIVITY

THIN-METAL PATCHES

28

CONCLUSIONS

Graphene patches have a dual (capacitive and inductive) nature at low-

terahertz frequencies

We mimic the enhanced transmission at optical frequencies with a

metal-dielectric stack and in the microwave regime with stacked-

metascreens, at low-THz using stacked-graphene

The range of frequencies where the peaks are expected for a finite

graphene-dielectric stacked structure can be analytically and

accurately estimated from the Bloch analysis

At low-frequencies, it behaves similar to that of the multilayer

stack of metallic patches (capacitive, wherein the geometric patch

capacitance dominates over the weak metal inductance), and at higher

frequencies similar to that of a multilayer stack of contiguous graphene

sheets (inductive due to a large kinetic inductance of the material),

thus combining both the properties in a single configuration