INTRODUCTION TO SINGULAR NONLINEAR OPTICS · Opt. Letters 35, 3417 (2010) Solitons in external...

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.

INTRODUCTION TO SINGULAR NONLINEAR OPTICS

Polychromatic spatial solitons.


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.



1. White light generation basics.


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 = − <+


Phys. Rev. Lett. 80, 4406 (1998).

1a. WL generation in a bulk medium (normal GVD)


Nature 424, (2003).

1b. WL generation in photonic crystal fibers (anomalous GVD)


500 600 700 800

101

102

103

104 supercontinuum incandescent lamp

I(λ),

arb.

uni

tsλ, nm



Phys. Rev. Lett. 88, 173901 (2002).



J. Lightwave Technol. 12, 3770 (2007).



Opt. Lett. 25, 1049 (2000).

1c. Coherence of the WLC


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.


Phys. Rev. Lett. 81, 3383 (1988).Optics and Photonics News, p. 41, December 2007.


Optics and Photonics News, p. 41, December 2007.


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 =


Optics and Photonics News, p. 41, December 2007.


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 =

∂ ∂ ⎧ ⎫+ + + =⎨ ⎬∂ ∂ ⎩ ⎭

∑


Motivation

1 2 3 4 5 6, , , , ,λ λ λ λ λ λ1 3 5, ,λ λ λ

2 4 6, ,λ λ λ


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



Phys. Rev. Lett. 99, 123901 (2007).

Linear

Nonlinear

RGB


2. Discrete polychromatic solitons.Linear

Nonlinear

RGB



Phys. Rev. Lett. 99, 123901 (2007).

Linear Nonlinear



Phys. Rev. Lett. 99, 123901 (2007).


2. Discrete polychromatic surface solitons.

Optics Express 16, 5991 (2008).


3. Polychromatic OVSs in photorefractive media.

Opt. Lett. 33 , 1851 (2008).



Opt. Lett. 33 , 1851 (2008).

OVS (m=1) → Δλ~70nm



Opt. Lett. 33 , 1851 (2008).

OVS (m=2) → Δλ~180nm


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.



4.1. Experimental results in CaF2


Low intensity

High intensity


4.1. Experimental results in CaF2



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.


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



Running experiment

400 500 600 700 800 900

102

103

104

input output

Inte

nsity

(arb

. uni

ts)

Wavelength (nm)


Running experiment

TC transformation: → ; →211 2 ωωω −=s 122 2 ωωω −=s11121 =−×=sm 1122 1=−×=sm

500 nm

800 nm >900 nm

650 nm


Running experiment

TC transformation: → ; →211 2 ωωω −=s 122 2 ωωω −=s11121 =−×=sm 11122 =−×=sm


Running experiment



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


Running simulations



Running simulations


Topological charge transfer of vortex beams to white-light supercontinuum vortex beam trough nonlinear frequency conversion predicted and experimentally

demonstrated.


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)



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.



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).


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)


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

There are so many open questions …

Thank you for your attention!

INTRODUCTION TO SINGULAR NONLINEAR OPTICSINTRODUCTION TO SINGULAR NONLINEAR OPTICS

INTRODUCTION TO SINGULAR NONLINEAR OPTICS · Opt. Letters 35, 3417 (2010) Solitons in external...

Documents

Transcript of INTRODUCTION TO SINGULAR NONLINEAR OPTICS · Opt. Letters 35, 3417 (2010) Solitons in external...