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Wave propagation in structures with left-handed materials

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... but resonator gaps Nonlinear surface waves Nonlinear dispersion of surface wave Localized ... (2000) Metamaterial The first experiment on LH media ... – PowerPoint PPT presentation

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Title: Wave propagation in structures with left-handed materials


1
Wave propagation in structures with left-handed
materials
  • Ilya V. Shadrivov
  • Nonlinear Physics Group, RSPhysSE
  • Australian National University, Canberra,
    Australia
  • http//rsphysse.anu.edu.au/nonlinear/
  • In collaboration with
  • Yu. S. Kivshar, A. A. Sukhorukov, D. Neshev

2
Outline
  • Introduction Left-Handed Materials (LHM)
  • Interfaces and surface waves
  • Nonlinear properties of LHM
  • Nonlinear surface waves
  • Giant Goos-Hänchen effect
  • Guided waves in a slab waveguide
  • Photonic crystals based on LHM
  • Presentations and publications

3
Left-handed materials
  • Materials with negative permittivity e and
    negative permeability µ
  • Such materials support propagating waves
  • Energy flow is backward with respect to the wave
    vector

4
Frequency dispersion of LH medium
  • Energy density in dispersive medium
  • Positivity of W requires
  • LH medium is always dispersive

5
The first experiment on LH media
  • D.R.Smith, W.J.Padilla, D.C.Vier,
    S.C.Nemat-Nasser and S.Schultz, Composite medium
    with simultaneously negative permeability and
    permittivity, Phys. Rev. Lett. 84, 4184 (2000)
  • Metamaterial

Effective medium approximation
Frequency range with elt0, µlt0 4 - 6Ghz
6
Negative refraction at LH/RH interface
RH
LH
7
Unusual lenses
LH lens does not have a diffraction resolution
limit Improved resolution is due to the surface
waves
  • V. G. Veselago Soviet Physics Uspekhi 10 (4),
    509-514 (1968)
  • J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)

8
Surface waves of left-handed materials
z
RHM
LHM
x
9
Guided modes
  • TE-polarization
  • TM-polarization
  • Solutions for guided modes

I. V. Shadrivov, A. A. Sukhorukov, Yu. S.
Kivshar, A. A. Zharov, A. D. Boardman, and P.
Egan, submitted to Phys. Rev. E (2003)
10
Energy flux at the interface
z
Total energy flux
RHM
LHM
P1
P2
PP1P2
Forward waves P gt 0 Backward waves P lt 0
11
Existence regions of surface waves
  • Parameters
  • No regions where TE and TM waves exist
    simultaneously
  • Waves can be both forward traveling and backward
    traveling

12
Dispersion of TE guided modes
Normalized frequency
Normalized wave number
  • Waves can posses normal or anomalous dispersion
  • Dispersion depends on the dielectric
    permittivity of RH medium
  • Dispersion control in a nonlinear medium?

13
Nonlinear properties of left-handed materials
  • Metallic composite structure embedded into the
    nonlinear dielectric

A. A. Zharov, I. V. Shadrivov, and Yu. S.
Kivshar, Phys. Rev. Lett. 91, 037401 (2003)
14
Nonlinear dielectric properties of the composite
  • Microscopic derivation in the effective medium
    approximation

Contribution from nonlinear dielectric
Contribution from metallic wires
15
Effective magnetic permeability
Effective medium approximation
16
Magnetic properties of composite materialwith
self-focusing dielectric
Frequency
17
Magnetic properties of composite materialwith
self-defocusing dielectric
Frequency
18
Effective magnetic permeability
19
Nonlinear properties management
  • Composite completely filled by nonlinear
    dielectric

20
Nonlinear properties management
  • Only resonator gaps are filled by nonlinear
    dielectric

21
Nonlinear properties management
  • Composite completely filled by nonlinear
    dielectric, but resonator gaps

22
Nonlinear surface waves
RHM
LHM
Self-focusing
Self-focusing
I. V. Shadrivov, A. A. Sukhorukov, Yu. S.
Kivshar, A. A. Zharov, A. D. Boardman, and P.
Egan, submitted to Phys. Rev. E (2003)
23
Nonlinear dispersion of surface wave
  • The dispersion is multi-valued
  • Two different types of surface waves

24
Localized polaritons
Vg - the group velocity d - the group velocity
dispersion ? - the nonlinear coefficient
Energy flow has a vortex structure
25
Energy flow in a pulse
26
Surface waves
  • We have revealed the unusual properties of
    linear surface waves
  • Both TE and TM modes exist at a LH/RH interface
  • Modal dispersion can be either normal or
    anomalous
  • Total energy flow can be either positive and
    negative
  • Wave packets have a vortex structure of the
    energy flow

27
Goos-Hänchen effect
A shift of the reflected beam from the position
predicted by geometric optics ? ltlt width of the
beam
28
Giant Goos-Hänchen effect
  • ? width of the beam

29
Giant Goos-Hänchen effect
LHM
30
Resonant beam shift
31
Energy flow at a negative beam shift
RHM
  • Vortex
  • surface wave excitation

Air
LHM
32
Possible application
  • Measure the angle of resonant shift
  • Determine surface mode eigen wave number
  • Calculate LH material parameters

33
Negative refractive index waveguide
z
RHM
RHM
LHM
x
L
-L
34
Guided modes in Negative Refractive Index
Waveguides
  • TE-polarization
  • TM-polarization
  • Solutions for guided modes

I. V. Shadrivov, A. A. Sukhorukov and Yu. S.
Kivshar, Phys. Rev. E. 67, 057602-4 (2003)
35
Dispersion of guided modes
  • Fast and slow modes
  • Fundamental mode may be absent
  • Normal and anomalous dispersion

36
Dispersion of guided modes
  • Fast and slow modes
  • Fundamental mode may be absent
  • Normal and anomalous dispersion

37
Sign-varying energy flux
PP1P2
Total energy flux
38
Energy flow in a pulse
39
Negative refractive index waveguide
  • We have revealed the unusual properties of
    guided modes in negative refractive index
    waveguides such as
  • Both fast and slow modes exist in LH slab
    waveguide
  • Modal dispersion can be either normal or
    anomalous
  • Total energy flow can be either positive or
    negative
  • Wave packets have a double vortex structure of
    the energy flow

40
Unusual lenses
  • V. G. Veselago Soviet Physics Uspekhi 10 (4),
    509-514 (1968)
  • J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)

41
Periodic structure witha left-handed material
Photonic band gap appears in periodic structures
with zero averaged refractive index. J. Li, L.
Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett.
90, 083901 (2003)
42
Reflection from periodic structures
Bragg resonant reflection f2 - f1 2pm,
m1,2,3
43
Band gap in 1D photonic crystal
Transfer Matrix Trace
Z-components of wavevectors in right- and
left-handed media
Wave impedances of right- and left-handed media
44
Band gap structure
I.V. Shadrivov, A.A. Sukhorukov and Yu.S.
Kivshar, Appl. Phys. Lett. 82, 3820 (2003)
45
Beam shaping
Gaussian beam oblique incidence
Vortex beam normal incidence
Vortex beam oblique incidence
46
Transmission properties of the layered structure.
  • We have analyzed transmission properties of a
    layered periodic structure with left-handed
    materials
  • We have shown the existence of narrow angular
    transmission resonances embedded into a wide band
    gap
  • We have suggested applications of the
    transmission resonances for the beam shaping

47
Oral presentations
  • Ilya Shadrivov, Andrey Sukhorukov, and Yuri
    Kivshar, Guided waves and beam transmission in
    layered structures with left-handed materials,
    K22.010, APS March Meeting, March 3-7, 2003
    Austin, Texas, USA
  • Ilya Shadrivov, Andrey Sukhorukov, and Yuri
    Kivshar, Guided modes in negative refractive
    index waveguides, CMM5, CLEO/QELS, June 1-6,
    2003, Baltimore Maryland, USA
  • Ilya Shadrivov, Andrey Sukhorukov, and Yuri
    Kivshar, Beam shaping by a periodic structure of
    left-handed slabs, QThN3, CLEO/QELS, June 1-6,
    2003, Baltimore Maryland, USA
  • I. V. Shadrivov, A. A. Sukhorukov, Yu. S.
    Kivshar, A. A. Zharov, A. D. Boardman, and P.
    Egan, Surface Polaritons of Nonlinear Left-Handed
    Materials, EB2-6-MON, CLEO/Europe EQEC 2003,
    22-27 June, 2003, Munich, Germany

48
Related publications
  • I. V. Shadrivov, A. A. Sukhorukov, and Yu. S.
    Kivshar, Phys. Rev. E 67, 057602-4 (2003)
  • A. A. Zharov, I. V. Shadrivov and Yu. S. Kivshar,
    Phys. Rev. Lett. 91, 037401 (2003)
  • I. V. Shadrivov, A. A. Sukhorukov, and Yu. S.
    Kivshar, Appl. Phys. Lett. 82, 3820 (2003)
  • I. V. Shadrivov, A. A. Sukhorukov, Yu. S.
    Kivshar, A. A. Zharov, A. D. Boardman, and P.
    Egan, submitted to Phys. Rev. E
  • I. V. Shadrivov, A. A. Zharov, and Yu. S.
    Kivshar, Submitted to Appl. Phys. Lett.
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