Effect of nonlinearity on wave scattering and localization Yuri S. Kivshar Nonlinear Physics Centre, Australian National University, Canberra, Australia St. Petersburg University of Information Technologies, Mechanics & Optics, Russia http://wwwrsphysse.anu.edu.au/nonlinear/ http://phoi.ifmo.ru/metamaterials//
Costas in APS journals Search Soukoulis + xxx (full text) Anderson localization 55 Disorder -- 106 Photonic crystals -- 58 Metamaterials -- 41 Nonlinear 24 Solitons - 10
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Back to 1988 Yu.K. et al, Phys Lett A 125, 35 (1987) St. Pnevmatikos (1957-1990)
Suppression of Anderson localization Linear scattering Nonlinear scattering
Experimental demonstration
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Localized states in disordered structures x x exp 0 loc Anderson 1951 random dielectric medium Azbel 1983 What nonlinearity does to such a resonance? barrier cavity barrier Bliokh et al. 2004
618.9nm Bistable transmission
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Photonic Crystals www.rsphysse.anu.edu.au/nonlinear
Waveguide + defect coupling How can we use optical resonators to control light? 1 m Interference between different photon pathways Bandwidth modulation with small refractive index variation ( n/n<10-4 )
Fano resonance U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961) Ranked #3 in Top-100 Phys. Rev. articles! Ugo Fano (1912-2001) ε = ω ω / Γ 2 0 F ε = ε+ f 2 ε + 1 2 First published in Nuovo Cimento in 1935
Gustav Mie, 1868-1951 Mie resonances
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Microwave metamaterials from Canberra
Epsilon-near-zero channel Tunability of the ENZ channel
Arrays of nonlinear SRRs i n 2 (2 i n ) n ( n 1 n 1 2 n) t N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002). Bistability, modulational instability, switching waves, dissipative solitons,
Moving switching waves
Hysteresis of switching wave velocity V > 0 means widening of the region corresponding to the upper branch Mechanical analogy: static friction > rolling friction Bistability range: Not standard bistability! 0.0271 0.03135
Outline of today s talk Back to 1988 Disorder and nonlinearity Bistability of Anderson states Photonic crystals & Fano resonances Nonlinear metamaterials Self-trapped localized beams
Spatial optical solitons www.rsphysse.anu.edu.au/nonlinear
Self-trapping in BEC Th. Anker et al, PRL 94, 020403 (2005)
Novel broad gap states truncated nonlinear Bloch modes two types of modes
Nonadiabatic generation Nonadiabatic loading into a 1D optical lattice produces broad states t=0 t=25 ms V 0 4E R ; N ~10 3 V 0 T.J. Alexander et al, Phys. Rev. Lett. 96, 140401 (2006)
Experimental observation in optics
Summary Nonlinearity produces many interesting effects in wave propagation and scattering Many effects have been observed and verified experimentally We hope Costas will find more time to study nonlinear effects!!