Localized modes and solitons in nonlinear discrete …• Discrete systems offer a simple ground for the study of many fundamental effects in physics of nonlinear waves • Many novel

www.rsphysse.anu.edu.au/nonlinear

Localized modes and solitonsin nonlinear discrete systems

Yuri KivsharNonlinear Physics Centre

Research School of Physics and EngineeringAustralian National University


Outline

Solitons: historical remarksRecent advances: fields and conceptsOptical solitons in periodic structuresMulti-colour optical solitonsPlasmon solitonsControl of matter-wave solitons Self-trapped localized states


What is “soliton” ?


John Scott Russell (1808-1882)

Very bright engineer: invented an improved steam-driven road carriage in 1833. ``Union Canal Society'' of Edinburgh asked him to set up a navigation system with steam boats

During his investigations, 6 miles from the centre of Edinburgh,he observed a soliton for the first time in August 1834


“Solitons”

>1400 citations

(1925-2006)0

241

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Solitons

Nonlinear localized waves existing when nonlinearity is balanced by dispersion


sine-Gordon equation


The latest observation:a huge “soliton mode”


Recent advances

New media and materials: nonlinear optics: nonlocal media, discrete and subwavelength structures, slow light BEC: nonlinearity management nanostructures: graphene, carbon nanotubes

New types of localized modes: gap solitons, discrete breathers, compactons, self-trapped modes, azimuthons, etc

Importance of nonintergrable models


Self-focusing and spatial optical solitons


Photonic crystals and lattices

fabricated

Optically induced


How does periodicity affect solitons ?


Spatial dispersion and solitonsBulk media

Waveguide array

TIR GAPSPATIAL SOLITON

LATTICE SOLITON

Theory: Christodoulides & Joseph (1988), Kivshar (1993)Experiments: Eisenberg (1998), Fleischer (2003), Neshev (2003), Martin (2004)

TIR GAP

BR GAP


Effective discrete systems

Self-focusingnonlinearity

Defocusingnonlinearity

DISCRETE SOLITONS

GAP SOLITONS

z

Kx


Gap Solitons - defocusing case

low power 10nW high power 100WLiNbO3 waveguide array

TIR GAP

BR GAP

Opt. Exp. 14, 254 (2006)


Polychromatic solitons


Diffraction of polychromatic light

waveguides5 0 0 6 0 0 7 0 0 8 0 0

1 0 1

1 0 2

1 0 3

1 0 4

s u p e rc o n tin u u m in c a n d e s c e n t la m p

I(),

arb.

uni

ts

, n m


Theory: coupled NLS equations

Optically-controlled separation and mixing of colors

Power

Micro-scale prism Filtering of redWhite-light input and output


Experiment: polychromatic gap soliton

10W 6mW 11mW


Plasmon solitonsand oscillons

Nonlinear Kerr-type dielectric

2|E| linear

Nonlinear modes in planar metal-dielectric waveguidesV.M. Agranovich et al., JETP (1980), G.I. Stegeman et al., J. Appl. Phys. (1985), A.R. Davoyan et al. Opt Express (2008)

Plasmon-solitonTemporal plasmon solitons - A.D. Boardman et al. Phys. Rev. B (1986)

Spatial plasmon soliton in a slot waveguideE. Feigenbaum and M. Orenstein, Opt. Lett. (2007)

Nonlinear plasmonics

Heat

Collisions

Interband

Ponderomotive force

Drude model works in case of Au for IR

Negligible in short pulse operation

Spectral band limited

Metal nonlinearities

- 1 8 2 2= 3 1 0 [ m / V ]

Orenstein, 2010

V. Drachev, A. Buin, H. Nakotte, and V. Shalaev, Nano Lett. 4, 1535 (2004)

10 nm radius Ag spheres possess high and purely real cubic susceptibility

Currently, there is no reliable theoretical models describing nonlinear opticalresponse of metal nanoparticles, however experimental data shows that it depends on many factors, including duration and frequency of the external excitation as well as particle characteristics themselves (metal type and size)

Arrays of nonlinear metal particles

An array of metal particles in external electromagnetic field

Modulational instability and oscillons

“oscillons” –nonlinear localized modes in externally driven systemsH. Swinney et al, Nature 382, 793 (1996) H. Arbell et al, Phys. Rev. Lett. 85, 756 (2000)


Matter waves and BEC


Solitons in Bose-Einstein condensates

Bright solitons – attractive interaction, negative scattering lengthAchieved through self focusing, modulational instability, collapse

L. Khaykovich et al., Science 296, 1290 (2002); K. E. Strecker et al., Nature 417, 150 (2002); S. Cornish et al., PRL 96, 170401 (2006)


1D driven model for a BEC

All symmetries are broken, no damping

3D to 1D reduction due to trapping geometry

Normalization using typical scales of the system

T. Salger et al., PRL 99, 190405 (2007)


• Being initially at rest, the soliton starts moving provided N larger than a certain critical value

• Cumulative velocity depends on the soliton mass (particle number); this effect can be explained by the effective particle approximation

The first example of the mass-dependent soliton ratchet

Collisions of driven solitons

Initially different values of N Initially equal values of N

www.rsphysse.anu.edu.au/nonlinearThe driving initiates and controls the dynamics


Nonlinear self-trapped states


Self-trapping in BEC

Th. Anker et al, PRL 94, 020403 (2005)


Novel ‘broad’ gap states

two types of modes

truncated nonlinear Bloch modes

Darmanyan et al, 1999

Discrete NLSE

T.J. Alexander et al, Phys. Rev. Lett. 96, 140401 (2006)


Nonadiabatic generation• Nonadiabatic loading into a 1D optical lattice produces broad states

t=0

t=25 ms

V0 4ER ; N ~ 103

V0

Experimental observation in optics


Conclusions

• Discrete systems offer a simple ground for the study of many fundamental effects in physics of nonlinear waves

• Many novel types of localized waves discovered: compactons, azimuthons, etc

• Generalized concepts: nonlinearity management, ratchets, self-localized states

• Optical systems allows to observe and study many different types of nonlinear waves and solitons

Documents

Localized modes and solitons in nonlinear discrete …• Discrete systems offer a simple ground for the study of many fundamental effects in physics of nonlinear waves • Many novel