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Wave propagation in structures with left-handed materials

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. Outline.

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Wave propagation in structures with left-handed materials

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  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 ε 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 Wrequires • 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 ε<0, μ<0: 4 - 6Ghz

  6. Negative refraction at LH/RH interface RH LH

  7. Unusual lenses • V. G. Veselago Soviet Physics Uspekhi 10 (4), 509-514 (1968) • J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000) LH lens does not have a diffraction resolution limit Improved resolution is due to the surface waves

  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 P=P1+P2 Forward waves: P > 0 Backward waves: P < 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. +q + + + - - - -q Effective magnetic permeability Effective medium approximation

  16. Magnetic permeability Magnetic properties of composite materialwith self-focusing dielectric Frequency

  17. Magnetic permeability 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. z nonlinear RHM nonlinear LHM x 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. Normalized energy flow Normalized wave number Nonlinear dispersion of surface wave • The dispersion is multi-valued • Two different types of surface waves

  24. RHM LHM P1 P2 Localized polaritons Vg - the group velocity δ - 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 Δ << width of the beam

  28. Giant Goos-Hänchen effect Δ ~ width of the beam

  29. Excitation of forward surface wave results in a positive shift Excitation of backward surface wave results in a negative shift Giant Goos-Hänchen effect LHM

  30. Resonant beam shift

  31. Energy flow at a negative beam shift Vortex surface wave excitation RHM Air LHM

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

  33. Slab thickness 2L Negative refractive index waveguide z RHM LHM RHM -L L x

  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. TE Modes Dispersion of guided modes • Fastandslowmodes • Fundamental mode may be absent • Normal and anomalous dispersion

  36. TM Modes Dispersion of guided modes • Fastandslowmodes • Fundamental mode may be absent • Normal and anomalous dispersion

  37. LHM RHM RHM P1 P2 P2 Sign-varying energy flux P=P1+P2 Total energy flux

  38. 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

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

  40. 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)

  41. φ2 RHM LHM RHM 1 RHM 2 φ2 φ1 φ1 Nonresonant reflection φ2- φ1 = 0 Reflection from periodic structures Bragg resonant reflection φ2- φ1 = 2πm, m=1,2,3…

  42. K Kx LHM RHM Kz a b 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

  43. Gap Wave propagation Transverse wavenumber Transverse wavenumber Frequency Frequency Band gap structure I.V. Shadrivov, A.A. Sukhorukov and Yu.S. Kivshar, Appl. Phys. Lett. 82, 3820 (2003)

  44. Spatial filter Incident Reflected Transmitted Beam shaping Gaussian beam oblique incidence Vortex beam normal incidence Vortex beam oblique incidence

  45. 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

  46. 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

  47. 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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