Andrei V. Lavrinenkoiasprogram.ust.hk/201210/doc/HKUST-12-11-2012_for_pdf.pdf2012/11/12 ·...

Andrei V. Lavrinenko

Electromagnetic Approach in the Analysis of Structured Materials

19/11/2012Denmark ‐ Hong Kong Workshop on Metamaterials and Plasmonics, 12.11.2012

2 DTU Fotonik, Technical University of Denmark

People

Andrei LavrinenkoRadu

Malureanu

Sergei Zhukovsky

Maksim Zalkovskij

Andrei Andryieuski

Alexandra (Sasha) Boltasseva

Claudia Gritti

Viktoriia Babicheva

Andrey Novitsky



Outline

1. Restoration of effective parameters

2. Plasmonic nanoantennas

3. Field –based concept in TO

4. Graphene THz hyperlens

5. Pulling optical force

6. Plasmonic photovoltaics



Outline









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

250 nm

160 nm

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: unambiguousrestoration 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 μμεε 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

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

,0, zikiGpzEEE mp

pmmm ⎥⎦

⎤⎢⎣

⎡+= ∑

≠⊥⊥ rrr

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

,0, zikiGpzHHH mp

pmmm ⎥⎦

⎤⎢⎣

⎡+= ∑

≠⊥⊥ rrr

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

∫+

+−=zaz

zzSAVA adzzikzEE /)exp()(

∫+

+−=zaz

zzSAVA adzzikzHH /)exp()(

∫ +=S

yxSA aadydxzyxEzE /),,()(

∫ +=S

yxSA aadydxzyxHzH /),,()(

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

jSAB HZ

Ez

,0

,=

VA

VAW HZ

Ez0

=




Fundamental and 2nd Bloch modes




real

imaginary

S-parameters

Surface Averaging

Volume Averaging




0μbh = Micro-fields in SCT BbHh == , Macro-fields

kS =↑↑

reE krdeV V

i∫ −=1

0 001 EkB ×=ω

0

20*

0000

*0

00 221

21

ωμωμμEk

EkEBES =××=×=

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




Mb

h −=0μ

MuuBB××+≈ zz

VASA ˆˆ00 μμ

00 μμSAVA

VABMBH =−= ⊥

SA

VA

VA

VAW BZ

EHZ

Ez0

0

0

μ==

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

Andrei Andryieuski, Sangwoo Ha, Andrey A. Sukhorukov, Yuri S. Kivshar, and AVL, “Bloch-mode analysis for retrieving effective parameters of metamaterials”, Physical Review B, 2012, 86, 035127




NRW method

EVA/BVA

EVA/BSA

ESA/HSA

Andrei Andryieuski, Sangwoo Ha, Andrey A. Sukhorukov, Yuri S. Kivshar, and AVL, “Bloch-mode analysis for retrieving effective parameters of metamaterials”, Physical Review B, 2012, 86, 035127



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

A. 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

23

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

25



Plasmonic couplers• Idea of antenna nanocoupler

26



Plasmonic couplers

27



Plasmonic couplers

28

ExternalNA

Internal NA

NAGratings

Bow-tieNA



Plasmonic couplers

29


30 DTU Fotonik, Technical University of Denmark 30

Plasmonic couplers



Plasmonic couplers



Gaussian beam excitation with the spot size

< 3 µm achievable with focused fibers

)1()(

exp)()( 221 R

LLSCE

P

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

λλλ

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



Outline









• Method to get material parameters of a reqiured device using the coordinate transformation from virtual to physical space

Field –based concept in TO

L. Dolin, Izvestiya vuzov: Radiophysics 4 964 (1961)

J.B. Pendry et al, Science 312 1780 (2006)

U. Leonhardt, Science 312 1777 (2006)

D. Schurig et al, Science 314 977 (2006)



• Potential functions ψi (instead of coordinate transformation)


Papers-precursors

Tretyakov S A, Nefedov I S and Alitalo P, New J. Phys. 10, 115028 (2008)

Yaghjian A D and Maci S, New J. Phys. 10, 115022 (2008)

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.

tc ∂+∂

−=×∇)''''(1'' EHE βμ

tc ∂+∂

−=×∇)(1 EHE βμ

'r r

r')( rnr ⋅= iiψ

3322111 '

'' nnnr ⊗∇+⊗∇+⊗∇=⊗∇==

∂∂

= − ψψψJxx

Ji

j

ni – are arbitrary orthonormal vectors



• Fields and material tensors by means of ψi



∑=

− ∇==3

1

1 )'('i

iiJ EnEE ψ ∑=

− ∇==3

1

1 )'('i

iiJ HnHH ψ

)(

'

det'

321

3

1,

ψψψ

εεε∇×∇∇

⊗==∑ =ji jiij

T

JJJ aa

)(

'

det'

321

3

1,

ψψψ

μμμ∇×∇∇

⊗==∑ =ji jiij

T

JJJ aa

jiij nn '' εε =

213

132

321

,,

ψψψψψψ

∇×∇=∇×∇=∇×∇=

aaa

)( 321

3

1,

ψψψ ∇×∇∇

⊗=

∑ =ji iiJan



• Boundary conditions to define devices


Transparancy

Illusion

No penetrationor


Ssc

tinc

tSt |)(| EEE += Ssc

tinc

tSt |)(| HHH +=

Sinc

tSt || HH =Sinc

tSt || EE =

SBsc

tSinc

tSt ||| )(EEE += SBsc

tSinc

tSt ||| )(HHH +=

[ ]0|,0|,0|Re

===× ∗

SnSn

Sn

BDHE



– transparency


11|| S

inctSt HH =

11

11

11

|)(|)')((

,|)(|)')((

,|))((|

Sinc

iSii

Sinc

iSii

StiiSit

HnHnr

EnEnr

nr

=

=

=∇

β

β

βψ

11|),,(|),,(' 321321 S

incS xxxHH =ψψψ

11|),,(|),,(' 321321 S

incS xxxEE =ψψψ

11|| SiSi x

11|| S

inctSt EE =

=ψ

11|| SiSi x≠ψ1≠iβ

1=iβ



– cloaking

40


Transparancy

No penetration

11|| S

inctSt HH =

11|| S

inctSt EE =

[ ] 0|Re2=× ∗

SnHE

0|)(,0|)(,0|)(222 211332 =∇×∇=∇×∇=∇×∇ SnSnSn ψψψψψψ



Two-shell cloak concentrator-rotator

41


22|''| StSt HH =

22|''| StSt EE =

),,(|| 022zrA S

incS

in ϕϕ −= EE



• Connecting fields in TO lens with required fields after lens

42


axout

axxinc

x ==== == ||,|| 00 EEEE

axout

axxinc

x ==== == ||,|| 00 HHHH

)cos1(),( 0 yaeyaE aikout +=



• Planar cloaking slab – invisible curtain

43


Analysis of the tangential fields

singularity x=a

∞=),,( zyayyε

zxgyxfx )()(,)()(,)( 221 === rrr ψψψ

0)(,1)( == afxg

)ˆˆˆˆ(

ˆˆ1)(

)ˆˆˆˆ(2

xyyx

yyzzxx

dxdfy

f

ydxdf

f

eeee

eeeeee

⊗+⊗

−⊗+

+⊗+⊗== με




continuous E continuous H

non-singular


zxgyxfx )()(,)()(,)( 221 === rrr ψψψ

)()( xgxf =

yyzzyzyyzy fdxdfz

dxdfyf

dxdfz

dxdfy eeeeeeeeee ˆˆˆˆˆˆˆˆˆˆ ⊗+⊗+⎟

⎠⎞

⎜⎝⎛ −+⊗⎟

⎠⎞

⎜⎝⎛ −+== με



Outline



3. Field approach in TO






Graphene THz 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)

00 /,/ kkqkk r== θκ

122

=+r

qεκ

εθ

0,0 >< θεε r



• Free carriers – metal-like Drude behaviour• Plasmons in THz• Tunability (by electric field, magnetic field,

optical excitation, chemical doping)


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



( )( )( )( )

tts

s

s

EJJHHn

EEnDDnBBn

σ

ρ

==−×=−×=−⋅=−⋅

,,0,

,0

12

12

12

12

s

s

s

ZnnZnnr

Znnnt

σσσ

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)




Linear regression analyses with R=0.95

ax × ay × az = 0.2 × 0.05 × 1μm3

zzs ak

mt

trak

qn0

22

0

22

1arccos1,sin πϕκ ++−

±==

Metal + TOPAS (ε = 2.34)

22 κεεε θ

θr

q −=

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




• Propagation constant




• Effective permittivity





25 periods in depth


53 DTU Fotonik, Technical University of Denmark19-Nov-12

f = 6 THz, λ = 50μm

with homogenized permittivities:

εr = −20.1 + 8.5i,

εθ = 2.73 + 0.0029i




A. Andryieuski, AVL, D. Chigrin, ” Graphene hyperlens for terahertz radiation”, Phys. Rev. B Rapid Com., 86(2012), 121108


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









Pulling optical force

• Magnetodielectric particles in non-paraxial Bessel beam, propagating along z-axis

αe and αm - complex polarizabilities

J. Chen, J. Ng, Z. Lin and CT Chan, “Optical pulling force”, Nature Photonics, 5 (2011), 531-534

Andrey Novitsky, Cheng-Wei Qiu, Haifeng Wang, “Single Gradientless Light Beam Drags Particles as Tractor Beams”, Phys. Rev. Lett., 2011, v.107, 203601

⎟⎟⎠

⎞⎜⎜⎝

⎛+×−= + bbeeE 21

02 )ˆ(ˆ)( c

qc

qkcqrJe zzm

ziim ββϕ

⎟⎟⎠

⎞⎜⎜⎝

⎛+×+= + bbeeH 12

01 )ˆ(ˆ)( c

qc

qkcqrJe zzm

ziim ββϕ

2200 ,sin qkkq −== βα

[ ] )Re()Re()Re(3

||)Im(||)Im(2

4022

zmemez PkF ααααβ−+= HE

[ ]zzP ∗×= HE




µ = 3



⎟⎟⎠

⎞⎜⎜⎝

⎛×−∇+∇= ∗∗∗ mpBmEpF

32Re

21 4

0k


• Backward scattering

21

20

|| ckFz

3,1.00 === μεRk

HmEp me αα == ,

1212 , ciccic −==




c2 =1 c2 =i

1,,2,''12,1.0 120 ===+== mcicRk μεε

1,9.0/,1,1 010 ==== mkqcRk




• Recent works on nonparaxial light beams have suggested that a single beam can be a tractor beam, but in order to show that a pulling force is possible, one needs to wisely select the numerical aperture of the beam (nonparaxiality of the beam) and the particle’s permittivity and size.

• Can the pulling force be independent (at least quasi-independent) of an object’s material or size?

Andrey Novitsky, Cheng-Wei Qiu, and AVL, “Material-independent and size-independent tractor beams for dipole objects”, Phys. Rev. Lett., 2012, v.109, 023902

Dipole approximation valid: |a2|<0.2|a1|

µ = 1

a1 b1




Black line – exact multipole calculations

ε = 6, µ = 1 ε = 6 + i0.1, µ = 1

Scattering backward -Pushing force

Scatering forward -Pulling force

[ ] )Re(3

||)Im(||)Im(2

40220

zmemez PkkF ∗−+= ααααβ HE




Pulling force – shaded region

Pulling force, µ = 1.2

Andrey Novitsky, Cheng-Wei Qiu, and AVL, “Material-independent and size-independent tractor beams for dipole objects”, Phys. Rev. Lett., 2012, v.109, 023902

α >600

)Im()Im(3)Re(

||||)Im()Im(3)Re( 3

030

me

me

me

zme kPkαα

ααααααβ

∗∗

<<HE ))3/2(1/( )0(

,30

)0(,, mememe ki ααα −=

21cos <= αβ

µ = 1.0



Outline









Plasmonic photovoltaics

Thin film solar cells:<material >losses <efficiency

Metal nanoparticles implementation Metal nanoparticles implementation not for light trapping but to increase photoemission through plasmonic excitation

Atwater H. A., Polman A., Nat. Mater. , 9, 205 (2010).



Conclusions









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)Cheng-Wei Qiu, and Haifeng Wang (NUS, DSI, Singapore)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!

Andrei V. Lavrinenkoiasprogram.ust.hk/201210/doc/HKUST-12-11-2012_for_pdf.pdf2012/11/12 ·...

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