Passive THz metamaterials and light modulators · 5 DTU Fotonik, Technical University of Denmark ABBE School of Photonics, FSU, Jena 06/11/2012 2D Material space μ 0 ε II III IV

Andrei V. Lavrinenko

Passive THz metamaterials and light modulators

06/11/2012ABBE School of Photonics, FSU, Jena2 DTU Fotonik, Technical University of Denmark

I. Introducing DTU Fotonik

DTU Fotonik,

Department of Photonics Engineering

COM DTU,

Center for Communications, Optics and

Materials


200+ employees

40+ academic staff

90+ PhD students


People

Andrei Lavrinenko

Radu Malureanu

Sergei Zhukovsky

Maksim Zalkovskij

Alexandra (Sasha) Boltasseva

Andrei Andryieuski

Claudia Gritti

Viktoriia Babicheva

Andrey Novitsky


2D Material space

μ

ε0

II

III IV

I

1

1

Normal dielectrics,

abundant occurrence

E

H

k

Electric plasma, e.g. metals at

optical frequencies. Limited

natural materials like noble

metals.

Evanescent waves

Not naturally occuring.

H

Ek Evanescent waves

Magnetic plasma? Not

natural occuring at optical

frequencies.


Air, water and Coca-Cola (abnormal water)


Optical phenomena

The Dark Side of the Moon


Pendry, Contemporary Physics, 50(2009) 363

Natural bulk

medium,

properties are

defined by atoms

Metamaterials,

properties are

defined by

”artificial” atoms

– building units

of the structure

Metamaterials are engineered composites tailored for specific

electromagnetic properties that are not found in nature and not observed in

constituent materials


THz metamaterials

1. Hypothesis generation

2. Hypothesis verification 3. Verification extension


Outline

• Fractal MM

• Transparent electrodes

• Transmission line approach

• Chiral MM

• Graphene hyperlens

• THz control over an optical waveguide

• Conclusion


Outline

• Fractal MM



• Chiral MM



• Conclusion


0.0

0.5

1.0

0 1 2 30 1 2 3

-180

-90

0

90

180

E//x

S11

S21

E//x

S11

S21

E//y

S11

S21

E//y

S11

S21

Phase [

deg]

Frequency [THz]

T/R

Fractal MMT

F. Miyamaru et al. Phys. Rev. B. 77, 045124 (2008)G.-Z. Zhao et al. Chin. Phys. Lett. 23, 1456 (2006)W. Wen et al. Phys. Rev. Lett. 89, 223901 (2002)X. Huang et al. Opt. Express 18, 10377 (2010)

2D metallic fractal structure

– Stop bands (positive structure)

– Transmission bands (negative structure)

– Insensitive to incidence angle

– Multi-level structure multiple bands

– supports TM and TE SPPs

– Superlensing effect (l/15 resolution) in GHz


THz membrane MM

R. Malureanu et. al., ICTON (Mo.C2.3) (2011)

In preparation

2 m thick

membrane

Initial stack of Si3N4/Si/Ti/Au

Membrane opening on the back side

Aligned UV-exposure

Photoresist development

Electrochemical growth of Ni

Photoresist removal

Back side etch of Si wafer and Au/Ti layer removal


Fractal MMT

5-level fractal


0.5 1.0 1.5 2.0 2.5-2

-1

0

1

2

Sample D12

0o

10o

20o

30o

40o

50o

60o

E//x

Ph

ase

ch

an

ge [

rad

ians]

Frequency [THz]

Fractal MMT

• THz-TDS measurement

• Frequency range 0.2 – 2.7 THz

• For E//x one resonance

• π-phase shift across resonance

• Tmin =0 @ 2.6 THz

• Abrupt phase change @ Tmin

• For E//y two resonances

• Transmission dip at antiresonance

• Sharp p phase shift

0.5 1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

1.0

Sample D12

0o

10o

20o

30o

40o

50o

60o

Tra

nsm

issio

n

Frequency (THz)

E//x

E//xE//y

0.5 1.0 1.5 2.0 2.5-2

-1

0

1

2

Sample D12

0o

10o

20o

30o

40o

50o

60o

E//y

Ph

ase

Ch

an

ge [

rad

ians]

Frequency [THz]0.5 1.0 1.5 2.0 2.5

0.01

0.1

1

0o

10o

20o

30o

40o

50o

60o

E//yTra

nsm

issio

n

Frequency [THz]

Sample D12

T < 5x10-3


Outline

• Fractal MM



• Chiral MM



• Conclusion


Transparent electrodes

Do we need transparent electrodes?

solar cells

touch panels

human-machine

interfaces

LEDs

electronic paper

etc…

conjugated polymers

colloidal semiconductors

carbon allotropes

transparent conductive oxides

- Indium-Tin-Oxide (ITO)

- AZO, GZO

Materials:



Only 20 % transmission

through C layer!

Our aim is to transmit in the most effective way electromagnetic waves through the metallic electrode (C layer) inwards the semi-infinite substrate.

100 % transmission

through C layer?!

add AB layer



Transmission as the function of relative permittivity

B and P/.

P

fixed values:

A = sub = 12

C = -40

wB = 0.1 0

dAB = dC = 0.02 0

R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen and AVL, “A new

method for obtaining transparent electrodes”, Optics Express, 2012, 20, 22770-22782



Silica

structures; (3) develop of photoresist and Al etch; (4)removal of the photoresist and

Deposition of 200nm Al on high-resistivity silicon wafer

UV lithography for defining the metallic pattern

Develop of photoresist and Al etch in inductive coupled plasma reactive ion etching

Deposition of 12.5msilica layer by plasma enhanced chemical vapor deposition

12.5 m of silica

200 nm of Al

200 nm of Al

200 nm of silica

530 m of silica


Transparent electrodes Due to the presence of a nonmetallic mesh, we assume that such MTMs can be

assigned with a Drudesimilar to the diluted metal concept [12]. In order to retrieve

their effective permittivities we first performed FDTD simulations to get the transmission

spectra. Then we fitted the simulation results with the Drude model. It resulted that the permittivities

of the MTMs B and C can be respectively described by e

3frequency in THz. For the f = 0:6THz these formulae

give us ethat designed MTMs can indeed mimic plasmonic

metals with the negative values of permittivity being in the desired range

C - layer

50m

AB and C - layers

20 m 40 m

100m

FDTD => transmission spectra => fit simulation

results with Drude model => effective permittivities

B = 3.85-(3.06/f)2 c = 3.85-(4.98/f)2

c - 65B - 22A 3.85



T-Ray 4000 THz TDS system

•Bandwidth: 0.05 – 1.9 THz

•Signal to noise ratio (50k waveforms):

3000 at 0.5 THz and 50 at 1.5 THz

•Scan rate: 100 Hz (50k waveforms in 9min.)



Transmission spectraTerahertz transient after the sample

Normalized to transmission through the Si substrate with 12.5m of silica.

Silica



Silica

Silica



R. Malureanu, M. Zalkovskij, Z. Song, C. Gritti, A. Andryieuski, Q. He, L. Zhou, P. U. Jepsen and AVL, “A new

method for obtaining transparent electrodes”, Optics Express, 2012, 20, 22770-22782


Outline

• Fractal MM



• Chiral MM



• Conclusion


Transmission line approach

27



Linear-elliptical polarization conversion

28

Linear polarization to circular polarization



• Transmission/reflection, single layer with TL analogy (PEC-PMC)

29

2

2

2

1

rR

tT

06/11/2012ABBE School of Photonics, FSU, Jena30 DTU Fotonik, Technical University of Denmark 30


• Impedance

– Wire => inductance with η = - ix

– Gap => capacitance with η = +ix

T1

R1



31

• Conclusion: maximum 50% conversion efficiency!

• For one polarization the MM should be inductive, for another capacitive

• Another option: employ resonances, then Z=-i [ωL-1/(ωC)]

• Conversion can be >50%

• Incidence through high-ε substrate

• For silicon-MM-air R=84%

• For γ=1, T=R=50%

R1

T1

06/11/2012ABBE School of Photonics, FSU, Jena32 DTU Fotonik, Technical University of Denmark 32

Reflectance is always 100%!


R2

T2



33



34

T1 50% Chin, et al APL 2008, 45% Strikwerda et al, OE, 2009 and 44% Roberts and Lin OL

2012

R1 40% in reflectance Pors, et al OL 2011.

T2 74% Weis, et al APL 2009, 25% Li, et al APL 2010, 80% Strikwerda et al, OE, 2009 and

50% KwonOE 2008

R2 96% Wang et al APL, 2012, ∼ 100% Strikwerda et al, Int. J. High Speed Electronics and

Systems 2011 and Hao, et al, PRL, 2007.

D. Markovich, A. Andryieuski, and AVL, submitted


Outline

• Fractal MM



• Chiral MM



• Conclusion


Chiral MM

3D chiral structures 2D chiral structures

R. Singh et. al., PRB. 36, 153104 (2009)

X. Xiong et. al., PRB. 81, 075119 (2010)

Bingnan Wang et. al., APL. 94, 151112 (2009)

N. I. Zheludev et. al., PRB. 18, 13425 (2010)Y. Ding et. al.,

Phys. Scr.. 85, 065405 (2012)


Chiral MM

1 2 0ˆ

eff d d d E

Effective permittivity tensor:

1

0ˆ ˆ

eff cell eff

I V

2

1,2 1,2 0 0 2,1ˆ k d E G R d

2 2 2ˆ j j j

j

j j j

f

i

D. Chigrin et. al., Opt. Lett. 36, 2278-2280 (2011)

Goal: To try an anti-rod structure with resonantly enhanced transmission!


Chiral MM

8 mm


Chiral MM


Chiral MM

0 degree

90 degree


Chiral MM

sam ref

ij ijE E Restore linearly polarized components:

90

90

xx yy

xy yx

sample

sample


Chiral MM

R. Singh et. al., PRB. 36, 153104 (2009)xx xy

yx yy

t t

t t


Outline

• Fractal MM



• Chiral MM



• Conclusion


Graphene hyperlens

• No natural → metamaterial

• Effectively homogenous → small period/λ

• 2 options:

– Metal-dielectric sandwich (optics/UV)

– Metal wires in dielectric matrix (MW/THz/IR)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, J. Opt. Soc. Am. A 24, A52 (2007).

P. Belov, Y. Hao, and S. Sudhakaran, Phys. Rev. B 73, 033108 (2006)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007)


• Free carriers – metal-like Drude behaviour

• Plasmons in THz

• Tunability (by electric field, magnetic field, optical excitation, chemical doping)

Graphene hyperlens

J. Mater. Chem. 22, 15863 (2012)


tts

s

s

EJ

JHHn

EEn

DDn

BBn

,

,0

,

,0

12

12

12

12

s

s

s

Znn

Znnr

Znn

nt

021

021

021

1 ,2

Ultrathin graphene layer is approximated by the impedance surface

Surface conductivity from

G. Hanson, IEEE Trans. Antennas Propag. 56, 747 (2008)

Graphene hyperlens


Linear regression analyses with R=0.95

ax × ay × az = 0.2 × 0.05 × 1μm3

zz

sak

m

t

tr

akqn

0

22

0

2

2

1arccos

1,sin

p

Metal + TOPAS (ε = 2.34)

22

r

q

C. Menzel, et al, Phys. Rev. B 77, 195328 (2008)

Graphene hyperlens


• Propagation constant

Graphene hyperlens


• Effective permittivity

Graphene hyperlens


Graphene hyperlens

25 periods in depth

06/11/2012ABBE School of Photonics, FSU, Jena51 DTU Fotonik, Technical University of Denmark6-Nov-12

f = 6 THz, λ = 50μm

with homogenized permittivities:

εr = −20.1 + 8.5i,

εθ = 2.73 + 0.0029i

Graphene hyperlens


A. Andryieuski, AVL, D. Chigrin, ” Graphene hyperlens for terahertz radiation”, Phys. Rev B Rapid Com., 86(2012),

121108

Graphene hyperlens

2 pulses sources at λ/5 = 10μm are resolved with thick system, R2 = 10 R1

2 CW sources at λ/5 = 10μm are resolved with thick system, R2 = 10 R1


Outline

• Fractal MM



• Chiral MM



• Conclusion


The thousands of THz field enhancement in the nanoslit

6-Nov-12

A. Novitsky, M. Zalkovskij, R. Malureanu, AVL,

“Microscopic model of the THz field enhancement

in a metal nanoslit”, Opt. Communic., 284 (2011)

5495-5500


A. Novitsky, A. Ivinskaja, M. Zalkovskij, R. Malureanu, P. U. Jepsen, AVL, “Microscopic model of the THz

field enhancement in a metal nanoslit”, J. Appl. Phys., 112(2012), 074318


Sketching the possible scheme

6-Nov-12


It would be nice

to increase nonlinearity due to the accumulative effect – propagation of optical mode along the slit

to decrease attenuation owing to the pulling optical mode out of the slitand using electrical polarization forbiddingexcitation of SPPs

at the same time, part of an optical mode in the slit should be significant



Mach-Zender scheme

A. Novitsky, M. Zalkovskij, R. Malureanu, P.U. Jepsen, AVL, “Optical waveguide mode control by

nanoslit-enhanced terahertz field”, Optics Letters, 37(2012), 3903-3905

06/11/2012ABBE School of Photonics, FSU, Jena60 DTU Fotonik, Technical University of Denmark6-Nov-12


Close-up look onthe fields

h=100 nmw=200 nmn(As3S2)=2.7


THz fields


Coupling coeffcient from THz to optical wave

Interaction

Kerr nonlinearity



M. Zalkovskij, C. Z. Bisgaard, A. Novitsky, R.

Malureanu, D. Savastru, A. Popescu, P. U. Jepsen, AVL,

Appl. Phys. Lett., 100 (2012), 031901


π-shift and e-decay versus frequency

X = 120nm, Y = 400nm, Δn = 0.001, Δh = 20nm


pp

D

LFOM 2/


cmkVcnn

n

GE

opt

THz

inc /1721

002

Δn = 0.001

n2 = 1.1 x 10-17 m2/W (optics range)

G = 100

Realistic numbers!!!

• A. Novitsky, M. Zalkovskij, R. Malureanu, P.U. Jepsen, AVL, “Optical waveguide mode control by

nanoslit-enhanced terahertz field”, Optics Letters, 37 (2012), 3903-3905

• K. Iwaszczuk, A. Andryieuski, AVL, X.-C. Zhang, and P. U. Jepsen, “Terahertz field enhancement to

the MV/cm regime in a tapered parallel plate waveguide”, Optics Express, 2012, 20, 8344-8355


Conclusions

Fractal MM



Chiral MM

Graphene hyperlens

THz control over an optical waveguide


Acknowledgements

Andrei Andryieuski, Claudia Gritti, Radu Malureanu, Andrey Novitsky, Maksim Zalkovskjj (Metamaterials group)

Peter Uhd Jepsen, David Cooke, Krzysztof Iwaszczuk (DTU Fotonik, Kgs. Lyngby)

Dmitry Chigrin, Christian Kremers (Bergische Universitat Wuppertal)

(ANU, Canberra)

Lei Zhou, Shiya Xiao, Zhengyong Song, Qiong He (Fudan University, Shanghai)

Falk Lederer, Carsten Rockstuhl, Arkadi Chipouline, Christoph Menzel(FSU University)

Thank you!

Projects: support from

THz COW project (Danish Research Council)

Abbe School of Photonics

website: http://www. fotonik.dtu.dk

Documents

Passive THz metamaterials and light modulators · 5 DTU Fotonik, Technical University of Denmark ABBE School of Photonics, FSU, Jena 06/11/2012 2D Material space μ 0 ε II III IV