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Jianke Yang Dept of Mathematics and Statistics, University of VermontPowerPoint Presentation

Jianke Yang Dept of Mathematics and Statistics, University of Vermont

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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

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

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

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

In this talk, we report both theoretically and experimentally

dipole and vector solitons

in a 2D photonic lattice

Dipole solitons in a 2D lattice experimentally

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;

In-phase dipole solitons experimentally

High intensity

Moderate intensity

Low intensity

Lattice

always unstable

Note: experimentally

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 experimentally

Output

Input

Out-of

phase

In-phase

Low NL High NL High NL

No lattice

Dipole solitons: experimental results experimentally

Output

Input

Out of

Phase

In Phase

Low NL High NL High NL

No lattice

Anisotropic effect: out-of-phase case experimentally

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 experimentally

Output

Input

Low NL Intermediate NL High NL

These dipole solitons are sensitive to anisotropic effects

Vector solitons in a 2D lattice experimentally

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 experimentally

Input

Output

Expt.

results

Num.

results

Low NL High NL High NL

Coupled Decoupled

Mutually

Incoherent

2D vector lattice solitons: theory experimentally

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 experimentally

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 experimentally

- 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.

A scalar lattice soliton experimentally

They are stable in a large parameter space

Dipole-like vector solitons in a 2D lattice experimentally

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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