LOW-TERAHERTZ TRANSMISSIVITY

WITH A GRAPHENE-DIELECTRIC

MICRO-STRUCTURE

Chandra S. R. Kaipa, Alexander B. Yakovlev

George W. Hanson, Yashwanth R. Padooru

Francisco Medina, Francisco Mesa

IEEE MTT-S International Microwave Symposium

Montréal, Québec, Canada, 17-22 June 2012

TU2D: Applications of Carbon-Based RF Technology

Introduction and Motivation

Graphene-Dielectric Stack

Results and Discussions

Conclusions

2

OUTLINE

Enhanced Transmission at low-THz

Broadband Filters

Frequency of Enhanced Transmission (Excess Length

Concept)

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)

1ln22

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

2hc

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 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

)

9 Single 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

B C

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: 10.2 1.0 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: 2.2 1.0 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

0 2 4 6 80

0.2

0.4

0.6

0.8

1

Frequency [THz]

|T|2

Dielectric slab

Two sided graphene

nH 90169.0GL

h

x

z

y z = h

z = 0

Substrate thickness: 20 μm

Dielectric permittivity: 2.2

FP resonance of dielectric slab

FP resonance due to the presence of Graphene sheets

μm 40.272

Δ0η

cLh G

THz 15.2Δ2

r

T

hh

cf

Accurate when hh

EXCESS LENGTH

17

h (in μm ) fT (Approx.) fT (Calculated)

20 ≈ 2.15 THz 2.89 THz

40 ≈ 1.50 THz 1.75 THz

60 ≈ 1.16 THz 1.28 THz

80 ≈ 0.95 THz 1.01 THz

100 ≈ 0.8 THz 0.84 THz

• For larger separation between the Graphene sheets fT

calculated using the excess lengths gives

pretty close results to the analytical results

μc = 0.5 eV

Y YY Port 2 Port 1

h

18

BROADBAND PLANAR FILTERS

μc

(eV)

fLB

(THz)

fUB

(THz)

BW

(THz)

1 2.33 6.24 3.91

0.5 1.49 5.20 3.71

0.2 0.78 4.44 3.66

Graphene sheet

Dielectric slabs

h

ϵh

h

Thickness (h): 10 μm

Permittivity: 10.2

Broadband transmission

Can be tuned by varying the chemical

potential

19

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

20

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

21

CONCLUSIONS

Tunable structures can be designed using stacked graphene sheets

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

Excess length concept has been successfully demonstrated

Broadband planar filters have been realized using a stack of graphene

sheets in free-space