introduction to singular nonlinear optics · opt. letters 35, 3417 (2010) solitons in external...
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INTRODUCTION TO SINGULAR NONLINEAR OPTICS
FSU-Jena, Abbe School of Photonics’2011
LECTURE 1: Linear vs. nonlinear optics. Optical solitons.
LECTURE 2: Singular optical beams. Dark optical solitons– physics and applications.
LECTURE 3: Interactions between optical solitons.
LECTURE 4: Polychromatic spatial solitons.
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INTRODUCTION TO SINGULAR NONLINEAR OPTICS
Polychromatic spatial solitons.
FSU-Jena, Abbe School of Photonics’2011
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Polychromatic spatial solitons.
1. White light generation basics.2. Discrete diffraction and discrete polychromatic solitons.3. Polychromatic OVSs in photorefractive media.
4. White light optical vortices.5. Applications of optical vortices and concluding remarks.
FSU-Jena, Abbe School of Photonics’2011
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FSU-Jena, Abbe School of Photonics’2011
1. White light generation basics.
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FSU-Jena, Abbe School of Photonics’2011
Phys. Rev. Lett. 80, 4406 (1998).
General characteristics:* The spectral width depends on the NLM;* The polarization remains unchanged;* The Anti-Stokes broadening dominates
* The threshold is the same as for the self-focusing:
Physical mechanisms behind the WLC generation:* Self-phase modulation in space and time* Group-velocity dispersion* Parametric four-photon mixing* Raman and Brillouin scattering* Shock-wave formation* Ionization (stabilizing mechanism for the filaments)
1a. WL generation in a bulk medium (normal GVD)
20
0 2
3.778
GausscritP n n
λπ
=
( )2 20 0
2(1/ 2) 4 | | 1 ;SPM n ILQ Q Q
cωω τ±Δ = + ± − =
( )2
2 20
2( 1) 0eeo e
e Nnn m
πω υ
Δ = − <+
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FSU-Jena, Abbe School of Photonics’2011
Phys. Rev. Lett. 80, 4406 (1998).
1a. WL generation in a bulk medium (normal GVD)
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FSU-Jena, Abbe School of Photonics’2011
Nature 424, (2003).
1b. WL generation in photonic crystal fibers (anomalous GVD)
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FSU-Jena, Abbe School of Photonics’2011
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FSU-Jena, Abbe School of Photonics’2011
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FSU-Jena, Abbe School of Photonics’2011
500 600 700 800
101
102
103
104 supercontinuum incandescent lamp
I(λ),
arb.
uni
tsλ, nm
1b. WL generation in photonic crystal fibers (anomalous GVD)
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FSU-Jena, Abbe School of Photonics’2011
Phys. Rev. Lett. 88, 173901 (2002).
1b. WL generation in photonic crystal fibers (anomalous GVD)
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FSU-Jena, Abbe School of Photonics’2011
J. Lightwave Technol. 12, 3770 (2007).
1b. WL generation in photonic crystal fibers (anomalous GVD)
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FSU-Jena, Abbe School of Photonics’2011
Opt. Lett. 25, 1049 (2000).
1c. Coherence of the WLC
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FSU-Jena, Abbe School of Photonics’2011
Phys. Rev. Lett. 81, 3383 (1988).
2. Discrete diffraction and discrete polychromatic solitons.
Discrete diffraction - diffraction of light in the course of propagation light along periodic structure of strongly-coupled waveguides.
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FSU-Jena, Abbe School of Photonics’2011
Phys. Rev. Lett. 81, 3383 (1988).Optics and Photonics News, p. 41, December 2007.
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FSU-Jena, Abbe School of Photonics’2011
Optics and Photonics News, p. 41, December 2007.
2. Discrete diffraction and discrete polychromatic solitons.
Description by a system of coupled discrete NLSEs
21 1( ) 0n n n n n n
dai a C a a a adz
β γ+ −+ + + + =
β – propagation constant
C – coupling constant
0 2
eff
ncAωγ =
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FSU-Jena, Abbe School of Photonics’2011
Optics and Photonics News, p. 41, December 2007.
2. Discrete diffraction and discrete polychromatic solitons.
Description by a system of coupled NLSEs ν(x) – effective refr. index
σ – rel. photosensitivity
0 2
eff
ncAωγ =
22
2 210
2 ( ) ( ) | | 04
Mm m s m s
m m mms m
A z A zi v x A Az n x x M
λ π γ σ λπ λ =
∂ ∂ ⎧ ⎫+ + + =⎨ ⎬∂ ∂ ⎩ ⎭
∑
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete diffraction and discrete polychromatic solitons.
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete diffraction and discrete polychromatic solitons.
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FSU-Jena, Abbe School of Photonics’2011
Motivation
1 2 3 4 5 6, , , , ,λ λ λ λ λ λ1 3 5, ,λ λ λ
2 4 6, ,λ λ λ
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
cw laser -Nd:YVO4 / SHG
fs Ti:S-laser -Mira 900-F, Coherent,
0.5W / 76 MHz
PCF - 2m / 2 μmsolid core / 740 nm
zero GVD
LiNbO3 - 5.5cm / Ti indiffusion;
negative photorefractive
nonlinearity
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
Phys. Rev. Lett. 99, 123901 (2007).
Linear
Nonlinear
RGB
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.Linear
Nonlinear
RGB
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
Phys. Rev. Lett. 99, 123901 (2007).
Linear Nonlinear
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic solitons.
Phys. Rev. Lett. 99, 123901 (2007).
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FSU-Jena, Abbe School of Photonics’2011
2. Discrete polychromatic surface solitons.
Optics Express 16, 5991 (2008).
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FSU-Jena, Abbe School of Photonics’2011
3. Polychromatic OVSs in photorefractive media.
Opt. Lett. 33 , 1851 (2008).
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FSU-Jena, Abbe School of Photonics’2011
3. Polychromatic OVSs in photorefractive media.
Opt. Lett. 33 , 1851 (2008).
OVS (m=1) → Δλ~70nm
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FSU-Jena, Abbe School of Photonics’2011
3. Polychromatic OVSs in photorefractive media.
Opt. Lett. 33 , 1851 (2008).
OVS (m=2) → Δλ~180nm
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FSU-Jena, Abbe School of Photonics’2011
4. White light optical vortices.4.1. Experimental results in CaF2
CGH – d=80μmCaF2 - Egap=10.2 eV
Clark-MXR - 150-fs / 15 MW
This is the first experimental study of supercontinuum generation with beams of complex spatial and phase structure.
Optics Express 18, 18368 (2010).
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FSU-Jena, Abbe School of Photonics’2011
4.1. Experimental results in CaF2
Optics Express 18, 18368 (2010).
Low intensity
High intensity
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FSU-Jena, Abbe School of Photonics’2011
4.1. Experimental results in CaF2
Optics Express 18, 18368 (2010).
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FSU-Jena, Abbe School of Photonics’2011
4.1. Numerical results in CaF2
Journal of Optics 13, 064015 (2011).
NLM exit | / 1.125Diffz L =
Time-integrated energy-density OV beam profiles for 12 and 4 azimuthal modulation periods.
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FSU-Jena, Abbe School of Photonics’2011
4.2. Experimental results in Argon
Running experiment
50 fs / 1 kHz / 2.1 W / λc=795 nmAr pressure - 0.8 - 2.3 bar
Vortex lens – 16 steps
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FSU-Jena, Abbe School of Photonics’2011
4.2. Experimental results in Argon
Running experiment
400 500 600 700 800 900
102
103
104
input output
Inte
nsity
(arb
. uni
ts)
Wavelength (nm)
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FSU-Jena, Abbe School of Photonics’2011
Running experiment
TC transformation: → ; →211 2 ωωω −=s 122 2 ωωω −=s11121 =−×=sm 1122 1=−×=sm
500 nm
800 nm >900 nm
650 nm
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FSU-Jena, Abbe School of Photonics’2011
Running experiment
TC transformation: → ; →211 2 ωωω −=s 122 2 ωωω −=s11121 =−×=sm 11122 =−×=sm
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FSU-Jena, Abbe School of Photonics’2011
Running experiment
4.2. Experimental results in Argon
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FSU-Jena, Abbe School of Photonics’2011
Running simulations
4.2. Comparative numerical results
02)(2)( 22 =
⎭⎬⎫
⎩⎨⎧
+++Δ++∂∂ ∑
≠⊥ m
mnmnmmm
m
mmmDiff
m HAAAAAnnAkL
zAi γ
λλλλ
ω
ωω
)exp()exp(2 2*2
1*
2ω
δωωω
δωωδωδω DiffDiff zLkiAAzLkiAAAH Δ+Δ= +++−)exp()exp(2)exp(2 5
*2
242
*3
* ωδωδω
ωδωδωδω
ωδωδωωω DiffDiffDiff zLkiAAzLkiAAAzLkiAAAH Δ+Δ+Δ= ++−++−+
)exp()exp(2)exp(2 8*2
72*
62ω
δωωω
ωδωδωω
δωδωωδω DiffDiffDiff zLkiAAzLkiAAAzLkiAAAH Δ+Δ+Δ= −++−++)exp()exp(2 10
*29
*2
ωωδω
ωδωωδωδω DiffDiff zLkiAAzLkiAAAH Δ+Δ= ++−+
δωδωδωω −++ −−+=Δ kkkkk 21 2δωδωω −+ −−=Δ kkkk 22ωδωδω kkkk 23 −+=Δ −+
ωδωδωδω kkkkk −−+=Δ +−+24ωδωδω kkkk −−=Δ ++ 25 2
δωωδωδω +−+ −−+=Δ kkkkk 26δωωδω ++ −+=Δ kkkk 227
δωδωω +− −−=Δ kkkk 28δωδωδωω 29 +−+ −−+=Δ kkkkk
δωωδω 210 2 ++ −−=Δ kkkk
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FSU-Jena, Abbe School of Photonics’2011
Running simulations
4.2. Comparative numerical results
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FSU-Jena, Abbe School of Photonics’2011
Running simulations
4.2. Comparative numerical results
Topological charge transfer of vortex beams to white-light supercontinuum vortex beam trough nonlinear frequency conversion predicted and experimentally
demonstrated.
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FSU-Jena, Abbe School of Photonics’2011
5. Applications of optical vortices and concluding remarks.
Vortex coronograph
The relative contrast between a low-level near-axis light source and a high-intensity on-axis coherent source can be enhanced by many orders of magnitude.
This occurs because the on-axis coherent light under-goes destructive interfe-rence creating a dark vortex core, while the off-axis light from other sources diffracts into the core. Opt. Lett. 26, 497 (2001);
Optics Express 16, 10207 (2008)
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FSU-Jena, Abbe School of Photonics’2011
5. Applications of optical vortices and concluding remarks.
IEEE J. Quant. Sel. Topics in Quant. Electron. 6, 841 (2000);
Nature 424, 810 (2003).
A single colloidal particle trapped in the optical vortex travels around its circumference, driven by the orbital angular momentum of the helical beam.
(11 stages at 1/6 s intervals).
Optical tweezers
Intensity gradients in the converging beam draw small objects,such as a colloidal particle, toward the focus, whereas the radiation pressure of the beam tends to blow them down the optical axis.
Under conditions where the gradient force dominates, a particle can be trapped.
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FSU-Jena, Abbe School of Photonics’2011
5. Applications of optical vortices and concluding remarks.
Appl. Optics 46, 676 (2007).
Optica Applicata 39, 91 (2009).
Optical vortices interferometer
In the position changes of the optical vortices there is hidden information which makes possible to measure small rotation angles (from 10 arcsec to 2 degrees) of a small surface (~50×50 μm).
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FSU-Jena, Abbe School of Photonics’2011
5. Concluding remarks.
All-optical waveguidingOpt. Lett. 25, 55 (2000)Opt. Lett. 25, 660 (2000)
Material processingOpt. Letters 35, 3417 (2010)
Solitons in external potentials BECsPhys. Rev. Lett. 83, 2498 (1999)Physics Today 52, 37 (1999)
Spectroscopy – revision of the selection rulesNew J. of Physics 12, 083053 (2010)Optics Express 18, 3660 (2010)
Quantum information – generation of photons entangled in OAMNature Physics 3, 305 (2007)
MicromechanicsAppl. Phys. Lett. 78, 249 (2001)
MicrofluidicsOptics Express 12, 1144 (2004)
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FSU-Jena, Abbe School of Photonics’2011
Acknowledgements
Alexander von Humboldt Foundation Australian Research Council
Max Planck Society National Science Fund (Bulgaria)
Sofia University MPI for Quantum Optics
D. Neshev G. G. Paulus
J. Veltchev F. Lindner
K. Bezuhanov H. Walther
G. Maleshkov
The Australian National University Friedrich-Schiller-University, IOQ
Yu. Kivshar G. G. Paulus
W. Krolikowski P. Hansinger
D. Neshev
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There are so many open questions …
Thank you for your attention!
INTRODUCTION TO SINGULAR NONLINEAR OPTICSINTRODUCTION TO SINGULAR NONLINEAR OPTICS