Happy Birthday Costascmp.physics.iastate.edu/wavepro/program/presentations/Kuzmiak.pdf · Happy...

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WavePro 2011, June 8-11, Rethymno, Crete Happy Birthday Costas !

Transcript of Happy Birthday Costascmp.physics.iastate.edu/wavepro/program/presentations/Kuzmiak.pdf · Happy...

Page 1: Happy Birthday Costascmp.physics.iastate.edu/wavepro/program/presentations/Kuzmiak.pdf · Happy Birthday Costas ! WavePro 2011, June 8-11, Rethymno, Crete Happy Birthday Costas !

WavePro 2011, June 8-11, Rethymno, Crete

Happy Birthday Costas !

Page 2: Happy Birthday Costascmp.physics.iastate.edu/wavepro/program/presentations/Kuzmiak.pdf · Happy Birthday Costas ! WavePro 2011, June 8-11, Rethymno, Crete Happy Birthday Costas !

WavePro 2011, June 8-11, Rethymno, Crete

Happy Birthday Costas !

NATO 1995 Elounda, WECS I Laguna Beach,

COST KTH Stockholm, Brussels

Hersonissos ,Agia Pelagia,….Rethymno 2011

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Transport Properties of One-way EM

waveguide formed at the interface between

metal and 2D photonic crystal

Vladimir Kuzmiak1 Sergey Eyderman1, Mathias Vanwolleghem2

1 Institute of Photonics and Electronics, Czech Academy of

Sciences, v.v.i., Prague, Czech Republic

2 Faculty Département MMS, Institut d’Electronique Fondamentale

(CNRS UMR8622), Université Paris-Sud, 91405 Orsay, France

COST MP0702, GA CR No. 0004632

WavePro 2011, June 8-11, Rethymno, Crete

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WavePro 2011, June 8-11, Rethymno, Crete

Outline

• Motivation

• Nonreciprocity – necessary conditions, role of the time-reverse symmetry breaking in nanodevices

• Nonreciprocal and one-way devices – concepts

• Spectral and transport properties of one-way waveguide

• Dependence of unidirectional behaviour on boundary conditions and when mg. field is modulated

• Discussion and conclusions

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Motivation

• To explore physical mechanisms that may lead to nonreciprocal devices

• Provide hints to design compact integrated optical analog to one-way electronic device such is diode or transistor to contribute to the effort to make photonics more realistic alternative to electronic solutions

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WavePro 2011, June 8-11, Rethymno, Crete

Nonreciprocity in the

context of the nanodevices

Effects of the disorder are

significantly influenced time-

reverse symmetry properties

the backreflection in the

presence of disorder may

constitute serious drawback

a new regime of photon transport

that supports only forward

propagating wave that is free of

disorder-induced backscattering

Reciprocal systems:

Non-reciprocal systems

with broken TR symmetry

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[1] I. Vitebsky, J. Edelkind, E. Bogachek, and Uzi Landman:, Phys. Rev. B 55, 12566, 1997.

[2] A. Figotin and I. Vitebsky, Phys. Rev. E 63, 066609, 2001.

Nonreciprocity ω(k) ≠ ω(-k)

To satisfy a sufficient condition to ensure spectral non-reciprocity

(-k) (k) requires breaking both space- and time-reversal

symmetry [1]

A generic 1D periodic arrangement of magnetic and dielectric

components that give rise to strong spectral asymmetry [2] has

been suggested

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Nonreciprocal devices - concepts

[3] F. D. M. Haldane and S. Raghu, arXiv:cond-mat/0503588v1.

[4] Z. Wang, et al.:, Phys. Rev. Lett. 100, 013905 (2008).

[5] Z. Wang, et al.:, Nature. 461, 772 (2009).

[6] H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).

[7] Z. Yu, et al.:, Phys. Rev. Lett. 100, 023902 (2008).

Design proposed in Ref. 3 employs photonic analogues

of quantum chiral edge states and relies on the

presence of a degenerate Dirac point in reciprocal

photonic crystal

Various designs of one-way waveguides operating at

microwave range proposed in Ref. [4]-[7].

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WavePro 2011, June 11-14, Rehytmo, Crete

One-way EM waveguide

(a) (b)

[8] Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100,

023902(2008).

[9] S. Eyderman, V. Kuzmiak, and M. Vanwolleghem, Proc. SPIE

Photonics Europe, Brussels, Belgium, April 2010, paper 7713-24.

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WavePro 2011, June 11-14, Rehytmo, Crete

Waveguide A

Dielectric permittivity of the metal:

)(

)(00

01

01

)()(

22

22

2

1

i

i

ii

ii

i

b

b

b

b

p

11 9.8diel

srad /10.1 14 sradp /10.1 16

nma 100 ad 2.0 nma 50

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WavePro 2011, June 8-11, Rethymno, Crete

Waveguide A

2B

SPSPL

2B

SPSPR

m

eBB

2

p

SP

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One-way waveguide concepts vs. Bloch theorem

In order to achieve true one-way property it is crucial that

within a certain frequency range there appears a photonic

band that has a single sign for its group velocity over the

whole Brillouin zone.

(/a) = (-/a)

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BAND STRUCTURE CALCULATION USING FURIER MODAL METHOD

BB B

… …

x

z

BB B

… …

BBBB BB

… …

x

z

x

z

Artificial periodization of the waveguide structure to be modeled (with

propagation along z). The dashed regions are the PML absorbers isolating the

“grating unit cells”. By a proper Fourier factorization in the x-direction the local

eigenmode basis can be described by discrete plane wave expansion.

out

in

S

inoutoutin

inoutoutin

in

out

B

F

TR

RT

B

F

,,

,,

in

ajk

in

inoutoutin

ajk

in

ajk

ininoutoutin

Be

F

TRe

Be

FRT

B

B

B

,,

,, 01

10 Af Bfl=

eigenmode scattering matrix S

S

Generalized eigenvalue problem with

applying Bloch boundary conditions which

allows to calculate band structures in the

frequency domain with frequency as the

independent parameter

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WavePro 2011, June 8-11, Rethymno, Crete

Waveguide A

The field plots show the z-component of the Poynting vectors at the

reduced frequency 0.7ωp inside one unit cell of the structure shown on

the left. Lighter shades indicate positive Sz. In the obtained dispersion

diagram a forward and a backward plasmonic mode are found at this

frequency. The field plots show that +z and –z propagating plasmonic

modes are guided at opposite metallic interfaces.

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ICTON 20010,June 27-July 1, Munich, Germany

Waveguide B

qualitative demonstration of the possibility to obtain similar

unidirectional regime by using a magnetic PhC and a nonmagnetic

metal with one way frequency range 0.366 < ω/ωp < 0.376

~ 363 nm < < 373 nm

Drude metal

fp = 2200 THz

= 1 THz

PML

garnet

13 p

erio

ds +

1 «

extr

laye

r

x

z

d/a 0.23 central gap c 0.396 2c/a

p/7.25 = 0.396 2c/aa = 0.396 7.25 2c/p

= 1.066 p

B

ad

xx = 6.25 xy = -yx = -i*g (g=0.1)

Drude metal

fp = 2200 THz

= 1 THz

PML

garnet

13 p

erio

ds +

1 «

extr

laye

r

x

z

d/a 0.23 central gap c 0.396 2c/a

p/7.25 = 0.396 2c/aa = 0.396 7.25 2c/p

= 1.066 p

B

ad

xx = 6.25 xy = -yx = -i*g (g=0.1)

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WavePro 2011, June 8-11, Rethymno, Crete

Theoretical model Surface plasmon polaritons propagating along the interface between

two semi-infinite homogenous slabs fabricated from BIG and Ag

00

0

0

ig

ig

2

2

1)(

p

1.0,25.6 gzzyyxx

sradp /10381.1 16

srad /1028.6 12

[10] T. Tepper and C. Ross, J. Cryst. Growth., 255, 324 (2003)

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WavePro 2011, June 8-11, Rehytmo, Crete

Dispersion relation Surface plasmon polaritons propagating along the interface between

two semi-infinite homogenous slabs fabricated from BIG and Ag

2222212

02

4)( xymxxm

x

KKkk

2321 4))(( xymxxmmmxxK

))(2(2 222 xxmxxmmxyiK

xxxyxx /2

2

2

1)(

p

[11] A. Boardman et al., New Journal of Physics 7 (2005) 191

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WavePro 2011, June 8-11, Rethymno, Crete

Dispersion relation Surface plasmon polaritons propagating along the interface between

two semi-infinite homogenous slabs fabricated from BIG and Ag

[10] A. Boardman et al., New Journal of Physics 7 (2005) 191

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WavePro 2011, June 8-11, Rethymno, Crete

Effect of Boundary Case conditions Case I

One-way propagation in the waveguide structure formed the interface

between metal and a MOPhC @ frequency ωc = ωp/√7.25 inside the band

gap: PML boundary conditions

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Effect of Boundary Case conditions Case II

ωc = ωp/√7.25 inside the band gap: Perfect conductor(PC) boundary

conditions

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Effect of Boundary Case conditions Case III

ωc = ωp/√7.25 inside the band gap: PC wall placed into middle of PhC

unit cell C

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Conclusions

• Improved one-way waveguide that assumes significantly reduced mg. field ~ 0.01 T

• Spectral and transport characterics have been studied

• Dependence on boundary conditions and temporal modulation of the mg. field

• Some new and interesting phenomena observed

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WavePro 2011, June 8-11, Rethymno, Crete

Conclusions

Future directions:

two major challenges to be addressed

1. reduce or completely avoid using mg. field,

2. scale operating wavelength to optical range

Costas !