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  • 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

  • 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

  • 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

  • WavePro 2011, June 8-11, Rethymno, Crete

    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

  • 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

  • WavePro 2011, June 8-11, Rethymno, Crete

    [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

  • WavePro 2011, June 8-11, Rethymno, Crete

    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].

  • 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.

  • 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  9.8diel

    srad /10.1 14 sradp /10.1 16

    nma 100 ad 2.0 nma 50

  • WavePro 2011, June 8-11, Rethymno, Crete

    Waveguide A

    2 B

    SPSPL

      

    2 B

    SPSPR

      

    m

    eB B 

    2

    p

    SP

      

  • WavePro 2011, June 8-11, Rethymno, Crete

    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)

  • 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

    in inoutoutin

    Be

    F

    TR e

    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

  • 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.

  • 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

    er io

    ds +

    1 «

    ex tr

    a »

    la ye

    r

    x

    z

    d/a  0.23 central gap c  0.396  2c/a

    p/7.25 = 0.396  2c/a a = 0.396  7.25  2c/p = 1.066  p

    B

    a d

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

    Drude metal

     fp = 2200 THz

      = 1 THz

    PML

    garnet

    13 p

    er io

    ds +

    1 «

    ex tr

    a »

    la ye

    r

    x

    z

    d/a  0.23 central gap c  0.396  2c/a

    p/7.25 = 0.396  2c/a a = 0.396  7.25  2c/p = 1.066  p

    B

    a d

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

  • 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