Dipole and Vector Solitons
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Dipole and Vector Solitons in 2D Photonic Lattices. Jianke Yang Dept of Mathematics and Statistics, University of Vermont Igor Makasyuk, Anna Bezryadina, Zhigang Chen Dept of Phys. & Astronomy, San Francisco State University. Discrete solitons in waveguide arrays.

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Jianke Yang Dept of Mathematics and Statistics, University of Vermont

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Jianke yang dept of mathematics and statistics university of vermont

Dipole and Vector Solitons

in 2D Photonic Lattices

Jianke Yang

Dept of Mathematics and Statistics, University of Vermont

Igor Makasyuk, Anna Bezryadina, Zhigang Chen

Dept of Phys. & Astronomy, San Francisco State University


Jianke yang dept of mathematics and statistics university of vermont

Discrete solitons in waveguide arrays

D. N. Christodoulides et al., , Optics Letters 13, 794 (1988).

H. S. Eisenberg et al., , Physical Review Letters, 81, 3383 (1998).


Optically induced lattices in photorefractive crystals

Optically-induced lattices in photorefractive crystals

SBN

v

From multiple o-beam interference

Linear waveguides

Efremidis et al., PRE 2002

Fleischer, et al., PRL, Nature 2003

Nashev, et al., OL 2003

O-beam

E-beam

Spatial modulation of a partially coherent o-beam

Chen, et al. PRL2004

Amplitude mask


Jianke yang dept of mathematics and statistics university of vermont

So far, fundamental and vortex solitons in a 2D lattice have been reported:

Fleischer, et al., PRL, Nature 2003

Martin, et al., PRL 2004

Malomed and Kevrekidis, PRE 2001

Yang and Musslimani, OL 2003

Neshev, et al., PRL 2004

Fleischer, et al., PRL 2004

Yang, New J. Phys. 2004


Jianke yang dept of mathematics and statistics university of vermont

In this talk, we report both theoretically and experimentally

dipole and vector solitons

in a 2D photonic lattice


Dipole solitons in a 2d lattice

Dipole solitons in a 2D lattice

Theoretical model:

Here U: electric field; z: propagation distance;

E0 : applied DC field; D: lattice spacing;

I0: lattice intensity; r33: electro-optic coefficient;

k0= 2p/l0; k1= k0 ne;


Out of phase dipole solitons

Out-of phase dipole-solitons

Moderate intensity

High intensity

Low intensity

Lattice


In phase dipole solitons

In-phase dipole solitons

High intensity

Moderate intensity

Low intensity

Lattice

always unstable


Jianke yang dept of mathematics and statistics university of vermont

Note:

the above dipole solitons arise due to a balance of

discrete diffraction

nonlinearity, and

lobe interactions

They can not exist without the lattice.


Simulations of a pair of gaussian beams

Simulations of a pair of Gaussian beams

Output

Input

Out-of

phase

In-phase

Low NL High NL High NL

No lattice


Quadrupole solitons

Quadrupole solitons

Out-of-phase

In-phase

Always unstable

Can be stable


Jianke yang dept of mathematics and statistics university of vermont

Dipole solitons: experimental results

Output

Input

Out of

Phase

In Phase

Low NL High NL High NL

No lattice


Anisotropic effect out of phase case

Anisotropic effect: out-of-phase case

Output

Input

Low NL Low NL High NL

No lattice with lattice with lattice

These dipole solitons are robust against anisotropic effects


Anisotropic effect in phase case

Anisotropic effect: in-phase case

Output

Input

Low NL Intermediate NL High NL

These dipole solitons are sensitive to anisotropic effects


Vector solitons in a 2d lattice

Vector solitons in a 2D lattice

If we make the two beams of the dipole incoherent,

and launch into the same lattice site,

then we can study vector lattice solitons


2d vector lattice solitons experiment

2D vector lattice solitons: experiment

Input

Output

Expt.

results

Num.

results

Low NL High NL High NL

Coupled Decoupled

Mutually

Incoherent


2d vector lattice solitons theory

2D vector lattice solitons: theory

Vector solitons can be derived from scalar ones by a polarization rotation:

(x, y) : scalar lattice soliton;

: polarization

Scalar 2D lattice solitons have been studied before:

Yang and Musslimani, Opt. Lett. 2003

Efremidis, et al. PRL 2004


Dipole like vector solitons in a 2d lattice

Dipole-like vector solitons in a 2D lattice

If we make the two beams incoherent, and launch into different lattice sites,

then we can study dipole-like vector lattice solitons

Comb. input Low NL High NL 1st comp. 2nd comp.

Expt.

results

Num.

results


Conclusions

Conclusions

  • 1. We have demonstrated the formation of dipole,

  • quadrupole, vector, and dipole-like vector solitons in a

  • 2D photonic lattice for the first time.

  • 2. These solitons arise due to a balance of discrete

  • diffraction, nonlinearity, and lobe interactions.

  • 3. These solitons are stable in certain parameter regimes.


Jianke yang dept of mathematics and statistics university of vermont

A scalar lattice soliton

They are stable in a large parameter space


Dipole like vector solitons in a 2d lattice1

Dipole-like vector solitons in a 2D lattice

If we make the two beams incoherent, and launch into different lattice sites,

then we can study dipole-like vector lattice solitons

Comb. input Low NL High NL 1st comp. 2nd comp.

Expt.

results

Num.

results


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