Andrei V. Lavrinenko · 2 DTU Fotonik, Technical University of Denmark ABBE School of Photonics, FSU, Jena 06/11/2012 I. Introducing DTU Fotonik ... material for infrared”, J. of

Andrei V. Lavrinenko

Selected topics in plasmonics and metamaterials research: parameters restoration, light modulationand plasmonic coupler

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

I. Introducing DTU Fotonik

Technical University of Denmark

DTU Fotonik, Department of Photonics Engineering


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


Pulling forces and transformation optics

Switching of the force direction?

Andrey Novitsky, Cheng-Wei Qiu, Haifeng Wang, “Single Gradientless

Light Beam Drags Particles as Tractor Beams”, Phys. Rev. Lett., 2011,

v.107, 203601

Andrey Novitsky, Cheng-Wei Qiu, and AVL, “Material-independent

and size-independent tractor beams for dipole objects”, Phys. Rev.

Lett., 2012, v.109, 023902

A. V. Novitsky, S.V. Zhukovsky, L.M. Barkovsky, and

AVL, “Field approach in the transformation optics

concept”, Progress in Electromagnetics Research, 2012,

v.129, p.485-515.


Numerical methods: FDFD and nonlinear FDTD

0 0.2 0.4 0.6 0.8 1

3.99

4

4.01

4.02

/

a

s / a

0 0.2 0.4 0.6 0.8 110

0

101

102

103

104

105

106

107

108

109

Q f

acto

rmode one

mode two

Shift / a

A. M. Ivinskaya, AVL, and D. M. Shyroki, “Modeling of

Nanophotonic Resonators With the Finite-Difference

Frequency-Domain Method”, IEEE Transactions on

Antennas and Propagation, 2011, 59, p.4155-4161.

T. R. Nielsen, AVL and J. Mørk, “Slow light in

quantum dot photonic crystal waveguides”, Appl.

Phys. Lett., 2009, 94, 113111

I. S. Maksymov, A. A. Sukhorukov, AVL and Y. S.

Kivshar, “Comparative Study of FDTD-Adopted

Numerical Algorithms for Kerr Nonlinearities”,

IEEE Antennas and Wireless Propagation Letters,

2011, 10, 143-146


THz optics and metamaterials

Lecture on Monday, 05.11.2012, 13-30, Inst. Appl. Phys.


Outline

1. Restoration of effective parameters

2. Light modulation

3. Plasmonic couplers

4. Plasmonic photovoltaics


Outline


2. Light modulation




Effective parameters

S-parameters or NRW: Nicolson (1968), Smith (2002); Chen (2004); Menzel (2008), ….

Field averaging: Smith & Pendry (2006); Lerat (2006, 2007)

Polarization vector: Simovski, Belov (2003), Tretyakov

Fitting by surrounding media: Sun (2009)

Bloch modes methods: Zhang (2006), Smigaj (2007), Rockstuhl(2008), Mortensen (2009), Lalanne (2010, 2011)

Wave propagation: Popa & Cummer (2005), Andryieuski (2009)

And many others: Silveirinha (2007-2011), Shvets (2009), Vinogradov, Tsukerman (2010-2011), …


Restoration of effective parameters

Wang, et al., J. Phys. D, 42 (2009)Zhu, et al., MOTL, 51 (2009) Liu, et al., Appl. Phys. Lett, 90 (2007)



Cage ε<0 + split cube μ<0

Generic approach for isotropic NIM: Nested cubic structures

A. Andryieuski, R. Malureanu and AVL, “Nested structures approach in designing an isotropic negative-index

material for infrared”, J. of the European Optical Society-Rapid Publications, 4, 09003 (2009)

A. Andryieuski, C. Menzel, C. Rockstuhl, R.

Malureanu and AVL, “The split cube in a cage: bulk

negative-index material for infrared applications”, J.

Opt. A: Pure Appl. Opt., 11, 114010 (2009)

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R.

Malureanu, and AVL, “High symmetry versus optical isotropy of a

negative-index metamaterial,”, Phys. Rev. B, 81, 195123 (2010)



Row data: Ex distribution in the long fishnet – 100 unit cells

20 40 60 80 100

WPRM: restoration by inspecting propagation phenomena, e.g. by numerical modeling



A. Andryieuski, R Malureanu, and AVL, “Wave propagation retrieval method for metamaterials: unambiguous

restoration of effective parameters”, Phys. Rev. B, 2009, 80, 193101

A.Andryieuski, R. Malureanu and AVL, “Wave propagation retrieval method for chiral metamaterials”, Optics

Express, 2010, 18, p.15498-15503

Wave propagation retrieval method: WPRM

Bloch impedance



122 THz

132-0 THz

132-90 THz

150 THz

160 THz

170 THz

180 THz

200 THz



Wave parameters,

Bloch impedance

Material (Local) parameters,

Wave impedance

HBED 00

zn,r, t

Simovski and Tretyakov, PRB (2007);

Menzel et al., PRB (2008);

Simovski, Optics & Spectrosc. (2009)

Simovski, J. Opt. A (2011)



1. Calculate fields distribution 2. Retrieve dominating Bloch modes

3. Surface (a unit cell entrance) and volume averaging of positive wave

zaz

z

zSAVA adzzikzEE /)exp()(

zaz

z

zSAVA adzzikzHH /)exp()(

S

yxSA aadydxzyxEzE /),,()(

S

yxSA aadydxzyxHzH /),,()(

)exp()exp()()()(0

,0, zikiGpzEEE m

p

pmmm

rrr

)exp()exp()()()(0

,0, zikiGpzHHH m

p

pmmm

rrr

A. Sukhorukov et al. OE, 17, 3716 (2009); S. Ha et al. OL, 34, 3776 (2009),

S. Ha et al APL, 98, 061909 (2011)



Bloch impedance

Wave impedance

jSA

jSA

BHZ

Ez

,0

,

VA

VAW

HZ

Ez

0



Fundamental and 2nd Bloch modes



real

imaginary

S-parameters

Surface Averaging

Volume Averaging



real

imaginary

S-parameters

Surface Averaging

Volume Averaging



0

bh Micro-fields in SCT BbHh , Macro-fields

kS

reEkrde

VV

i

10 00

1EkB

0

2

0*

00

00

*

000

22

1

2

1

EkEkE

BES

J. Costa, M. Silveirinha, and A. Alu, Phys. Rev. B 83, 165120 (2011)



Mb

h 0

MuuBB

zzVASA ˆˆ00

00 SAVA

VA

BM

BH

SA

VA

VA

VAW

BZ

E

HZ

Ez

0

0

0

M. Silveirinha and C. Fernandes, Phys. Rev. E 75, 036613 (2007)



NRW method

EVA/BVA

EVA/BSA

ESA/HSA


Outline


2. Light modulation in plasmonicwaveguides




Light modulation in plasmonic waveguides

Advantages: compactness,field localization on nanoscalemetal plates serve as electrodes

Either you work with β’ (phase modulation) or with β’’ (loss modulation)

Any metal NP can be considered as a nanoantenna (N. Halas); any plasmonic waveguide can be considered as a modulator



Melikyan et al, Opt. Express, 2011

2

0

0

p

eff

e N

m

With 5% change of the carrier density ωp alters: 2.9x1015…2.9716x1015 s-1

εoff -εon = 0.28-i0.042



West et al, 2010,

Laser Photonics Rev.

is varied

onoff

off

α -αFoM =

α

εoff =0.83



λ=1.55 μm

ITO permittivity is optimal (ε∞ =6.4)

f=1

V. E. Babicheva, and AVL, “Plasmonic modulator optimized by patterning of active layer and tuning permittivity”, Opt.

Commun., 285 (2012), 5500-5507

f≠1



M. P. Nezhad, K. Tetz and Y. Fainman, Opt. Express 12 (2004) 4072;

I. Avrutsky, Phys. Rev. B 70 (2004) 155416;

S.A. Maier, Opt. Commun. 258 (2006) 295

D.B. Li and C.Z. Ning, Phys. Rev. B 80 (2009) 153304

S. Russev et al, Plasmonics, 7 (2012) 151



λ=1.55 μm

ε(Ag)=-128.7+3.44i

Gain medium In0.53Ga0.47As

ε’= 12.46, ε’’= -gn’/k0

g is material gain

gb: -0.6·104...0.6·104 cm-1

Modulation speed can be high because of enhancement of spontaneous emission due to the tight confinement of modes between two metal plates

L.A. Coldren and S. W. Corzine,

Wiley, N. Y. 1995

Y.C. Jun et al, Phys. Rev. B 78 (2008) 153111;

J.A. Dionne, et al IEEE J. Sel. Top. QE 16 (2010) 295.



Hill, et al. Opt. Express 17 (2009) 11107-11112

J.A. Dionne, et al, NL 6 (2006) 1928, NL 9 (2009) 897



“Off”: gb= -0.6·104 cm-1,

current is off, strong

loss;

gb1= 0.1·104 cm-1;

gb2= 0.34·104 cm-1;

gb3= 0.6·104 cm-1;

Insulator: ε’’= 0

(p): with n- and p-

doped layers

d: 20...400 nm

V. E. Babicheva, I. V Kulkova, R. Malureanu, K. Yvind and AVL, “Plasmonic modulator based on gain-assisted

metal-semiconductor-metal waveguide”, Photonics and Nanostructures: Fund. Appl., 10 (2012), 389-399



oneffoffeffoffonL kkLPP ImIm68.8/)/lg(10ER /

“Off”: current is off, gb=

-0.6·104 cm-1, strong

loss;

gb1= 0.1·104 cm-1;

gb2= 0.34·104 cm-1;

gb3= 0.6·104 cm-1;

Insulator: ε’’= 0

(p): with n- and p-

doped layers



gTM= 0.4·103...1.2·103 cm-1 gd1= 1·104 cm-1 and gd2= 5·104 cm-1

The QDs volume ratio in the 10-nm thick stack layer is ~ 9%.

bd1=0.9·103 cm-1 and bd2=4.5·103 cm-1

E.S. Semenova, et al, Appl. Phys. Lett. 99 (2011) 101106



gd1= 1·104 cm-1, gd2= 5·104 cm-1

bd1=0.9·103 cm-1, bd2=4.5·103 cm-1

The total core thickness

d = 50·N nm,

where N=1…5 is a number of columns



n- and p-doped layers (no gain)

QW thickness 5 nm (high gain)

Barrier thickness 5 nm (no gain)

d=10nm+5nm*NQW+5nm*Nbar+10nm



up to 25 QWs

gw1= 0.4·104 cm-1

gw2= 1·104 cm-1

J.D. Thomson, et al, APL 75 (1999) 2527

P. Blood, IEEE J. QE 36 (2000) 354


Outline






Plasmonic couplers

• Coupling difficulties : From optical single mode fiber, 8 µm core diameter to photonic

or plasmonic waveguide with core sizes < 1 µm

• Solutions:

– long tapered fibers

– silicon WGs to plasmonic WG

– plasmonic nanoantennas (NAs)

Delacour et al., NL 2010

Maksymov et al., APL 2011

Andrei Andryieuski and AVL, “Nanocouplers for infrared and visible

light”, Review accepted to Advances in OptoElectronics, 2012,

doi:10.1155/2012/839747


Plasmonic couplers

• Efficient nanoantenna coupler to a plasmonic slot waveguide

• Telecom wavelength (λ=1.55µm)

• Vertical arrangement of the fiber


Plasmonic couplers

42

Coupling efficiency

CE < 50% C. Balanis, Antenna theory: analysis and design, 2005

Effective area

Antenna figure-of-merit


Plasmonic couplers

Huang et al., NL 2009Wen et al., OE 2009

Experiment with CE=15% in: Wen et al., APL 2011

Fang et al., Plasm. 2010

Aeff = 0.086 µm2

λ = 1.550 µm

Aeff = 0.025 µm2

λ = 0.830 µm


Plasmonic couplers

44


Plasmonic couplers

• Idea of antenna nanocoupler

45


Plasmonic couplers

46


Plasmonic couplers

47

ExternalNA

Internal NA

NAGratings

Bow-tieNA


Plasmonic couplers

48


49

Plasmonic couplers


50

Plasmonic couplers


Gaussian beam excitation with the spot size

< 3 µm achievable with focused fibers

)1()(

exp)()( 2

21 RL

LSCE

P

Our focused spot is 2.5 µm in diameter

Focused spot in Wen et al APL 2011 is 0.9 µm in diameter

LP =2.8 µm

R = 0.036

Plasmonic couplers


CE=0.14%

CE=14%

CE=24-26%

with smaller spot – up to 40%

CE≈25%

CE=25%

Andrei Andryieuski, Radu

Malureanu, Giulio Biagi, Tobias

Holmgaard, AVL, “Compact

dipole nanoantenna coupler to

plasmonic slot waveguide” Opt.

Letters, 2012, 37, 1124-1126


Plasmonic couplers


54

Plasmonic couplers

06/11/2012ABBE School of Photonics, FSU, Jena55 DTU Fotonik, Technical University of Denmark 55

Plasmonic couplers


• Aalborg University

• King’s College, London

Plasmonic couplers

Without NA With 2-NA


without antenna with antenna

Plasmonic couplers


Not clear picture why such behavior is observed???

Plasmonic couplers


Outline






Plasmonic photovoltaics

M W Knight et al. Science 2011, 332, 702-704



Schottky junction with incorporated gold nanoparticles:

– L, D, material properties…

– L

L

DL

scattering absorption

to enhance light trapping

to create localized surface

plasmons

>photoemission

n-GaAs/ITO


The size is defining which process is dominant:

Cabs>Csca Electric field enhancement more localized and intense

If the LSP resonance results from absorption of photon of energy below the bandgap of the semiconductor it will extend the spectral range of the device.

contact area

[Yu E.T., “Nanoplasmonics for Photovoltaic Applications”, chapter 11, 391–421, CRC Press, 2010]




1,0 1,2 1,4

0,01

0,1

Tra

ns

mis

sio

n, T

Ab

so

rpti

on

, 1

-T-R

Wavelength (m)

A=1 - R - T

Transmission dip will reveal plasmon resonance.

A. Novitsky, A.V. Uskov, C. Gritti, I.E. Protsenko, B. Kardinal and AVL, “Photon absorption and photocurrent in

solar cells below semiconductor bandgap due to electron photoemission from plasmonic nanoantennas”, accepted to

Progress in Photovoltaics: Research and Applications, DOI: 10.1002/pip.2278

http://dx.doi.org.globalproxy.cvt.dk/10.1002/pip.2278


- Periodicity: 100nm-120nm

- Size: 30-50nm





100 and 120 nm pitch are pretty much in the same place – in agreement with measurements


Halo effect



pattern

Folding gold sheet not properly lifted off



SEM inspection revealed more complex conical-shaped form

1,0 1,2 1,4

0,1

1

h = 10 nm

L = 100 nm

Tra

nsm

issio

n T

Wavelength (um)

cylinder R =20 nm

cone Rmax

=20 nm, Rmin

=15 nm



Conclusions


2. Light modulation




Acknowledgements

Falk Lederer, Carsten Rockstuhl, Christoph Menzel, Rumen Iliew(Jena University)

Yuri Kivshar, Andrey Sukhorukov, Sangwoo Ha (ANU, Canberra)

Andrey Evlyukhin(LZH, Hanover)

Constantin Simovski (Aalto University, Helsinki and State University of Information Technologies, Mechanics and Optics, St. Peterburg)

Mario Silveirinha (University of Coimbra, Portugal)

Sergei Bozhevolnyi, Valentin Volkov, Ilya Rad’ko (Sud Dansk Universitet, Odense)

Jean-Sebastien Bouillard, Anatoly V. Zayats (King’s Colledge, London)

Giulio Biagi, Tobias Holmgaard (Aalborg University)

Irina Kulkova, Kresten Yvind (DTU Fotonik)

Beata Kardinal (Forschungszentrum Jülich)

Alexander Uskov, Igor Protsenko (FIAN, Moscow)



Acknowledgments

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

Projects: support from

NIMbus project (Danish Research Council)

THz COW project (Danish Research Council)

Linkage International Grant (Australian Research Council)

COST MP0702 action

Abbe School of Photonics

Thank you for attention!

Documents

Andrei V. Lavrinenko · 2 DTU Fotonik, Technical University of Denmark ABBE School of Photonics, FSU, Jena 06/11/2012 I. Introducing DTU Fotonik ... material for infrared”, J. of