Abstract

An optical medium whose nonlinearity can be spatially adjusted is considered to study beam reshaping. The concept is applied to perform adiabatic self-focusing of broad beams. Experimental results are obtained in a photorefractive lithium niobate crystal where the self-focusing nonlinearity is controlled over propagation by a temperature gradient. As a demonstration, gradual self-focusing is shown to transform an incoming beam into an output circular spot 10 times smaller over a 2cm long crystal submitted to a 30°C temperature gradient. Once formed, the adiabatic self-focused beam has inscribed a funnel waveguide in the crystal.

© 2011 Optical Society of America

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References

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    [CrossRef]
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2009 (1)

2007 (1)

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

2002 (1)

1998 (1)

I. Moerman, P. P. Van Daele, and P. M. Demeester, IEEE J. Sel. Top. Quantum Electron. 3, 1308 (1998).
[CrossRef]

1996 (2)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys Lett. 35, 25 (1996).
[CrossRef]

M. Segev, M. F. Shih, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

1994 (1)

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Agranat, J.

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

Bartholomaüs, T.

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Birks, T. A.

Boardman, D.

D. Boardman and A. P. Sukhorukov, Soliton Driven Photonics (Kluwer, 2001).
[CrossRef]

Buse, K.

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Chauvet, M.

Ciattoni, A.

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

DelRe, E.

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

Demeester, P. M.

I. Moerman, P. P. Van Daele, and P. M. Demeester, IEEE J. Sel. Top. Quantum Electron. 3, 1308 (1998).
[CrossRef]

Deuper, C.

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Devaux, F.

Knight, J. C.

Krätzig, E.

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys Lett. 35, 25 (1996).
[CrossRef]

Martin Man, T.-P.

Moerman, I.

I. Moerman, P. P. Van Daele, and P. M. Demeester, IEEE J. Sel. Top. Quantum Electron. 3, 1308 (1998).
[CrossRef]

Ortigosa-Blanch, A.

Palange, E.

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

Pierangelo, A.

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

Russell, P. St. J.

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys Lett. 35, 25 (1996).
[CrossRef]

Safioui, J.

Segev, M.

Shih, M. F.

Sukhorukov, A. P.

D. Boardman and A. P. Sukhorukov, Soliton Driven Photonics (Kluwer, 2001).
[CrossRef]

Valley, G.

Van Daele, P. P.

I. Moerman, P. P. Van Daele, and P. M. Demeester, IEEE J. Sel. Top. Quantum Electron. 3, 1308 (1998).
[CrossRef]

Wadsworth, W. J.

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys Lett. 35, 25 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

E. DelRe, A. Pierangelo, E. Palange, A. Ciattoni, and J. Agranat, Appl. Phys. Lett. 91, 081105 (2007).
[CrossRef]

Europhys Lett. (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys Lett. 35, 25 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

I. Moerman, P. P. Van Daele, and P. M. Demeester, IEEE J. Sel. Top. Quantum Electron. 3, 1308 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Phys. Status Solidi A (1)

T. Bartholomaüs, K. Buse, C. Deuper, and E. Krätzig, Phys. Status Solidi A 142, K55 (1994).
[CrossRef]

Other (1)

D. Boardman and A. P. Sukhorukov, Soliton Driven Photonics (Kluwer, 2001).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic configuration of the optical setup to realize an adiabatic self-focusing of a broad beam in a crystal whose PR nonlinearity distribution is controlled by a temperature gradient.

Fig. 2
Fig. 2

Pyroelectric spatial soliton width Δ x (FWHM) in LiNbO 3 versus a crystal temperature increase from equilibrium temperature Δ T .

Fig. 3
Fig. 3

Dynamics of dislocation of an extraordinary polarized 100 μm FWHM beam at λ = 532 nm propagating in a 20 mm long LiNbO 3 crystal homogeneously heated to Δ T 1 = Δ T 2 = 20 ° C .

Fig. 4
Fig. 4

Adiabatic self-focusing dynamics of an extraordinary polarized 100 μm FWHM beam at λ = 532 nm in a 20 mm long PR LiNbO 3 crystal controlled by a temperature gradient Δ T 1 = 10 ° C , Δ T 2 = 30 ° C .

Fig. 5
Fig. 5

Numerical calculation of a refractive index change induced by pyroelectric beam self-trapping for an extraordinary polarized beam in a 20 mm long crystal. Refractive index profile at (a) input and (c) output faces both along the x and z axis and refractive index distribution in the ( y z ) plane (b) Parameters: beam power : 40 μw , input beam FWHM : 100 μm , Δ T 1 = 10 ° C , Δ T 2 = 30 ° C .

Equations (2)

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E py = 1 ε 0 ε r p Δ T ,
Δ x = 2 λ π n e 2 r 33 ( E py E ph ) ,

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