Abstract

We theoretically predict and numerically demonstrate that narrow beams (of the width of few wavelengths) can be efficiently parametrically amplified in nonlinear photonic crystal (with χ(2) nonlinearity) tuned to subdiffractive (self-collimating) regimes. We derive relations and give analytic estimations for the efficiency of amplification.

© 2007 Optical Society of America

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  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
    [CrossRef]
  2. D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, Opt. Express 11, 1203 (2003).
    [CrossRef] [PubMed]
  3. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
    [CrossRef]
  4. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
    [CrossRef] [PubMed]
  5. K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  6. S. A. Achmanov and P. B. Chochlov, Problems of Nonlinear Optics (Viniti, 1963), in Russian.
  7. K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
    [CrossRef]
  8. K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
    [CrossRef]

2007 (1)

K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
[CrossRef]

2006 (2)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

2004 (2)

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Achmanov, S. A.

S. A. Achmanov and P. B. Chochlov, Problems of Nonlinear Optics (Viniti, 1963), in Russian.

Augustin, M.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Chen, C.

Chigrin, D.

Chochlov, P. B.

S. A. Achmanov and P. B. Chochlov, Problems of Nonlinear Optics (Viniti, 1963), in Russian.

de Valcarcel, G.

K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

de Valcárcel, G. J.

K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
[CrossRef]

Enoch, S.

Etrich, C.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Fuchs, H.-J.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Herrero, R.

K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

Iliew, R.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kley, E.-B.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Lederer, F.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Murakowski, J.

Nolte, S.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Peschel, U.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Prather, D. W.

Pustai, D. M.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Schelle, D.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Schneider, G.

Sharkawy, A.

Shi, S.

Sotomayor Torres, C.

Staliunas, K.

K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
[CrossRef]

K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tayeb, G.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tünnermann, A.

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

Venkataraman, S.

Appl. Phys. Lett. (2)

R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, Appl. Phys. Lett. 85, 5854 (2004).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

K. Staliunas, R. Herrero and G. J. de Valcárcel, Phys. Rev. A 75, 011604(R) (2007).
[CrossRef]

Phys. Rev. E (2)

K. Staliunas, R. Herrero, and G. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Other (1)

S. A. Achmanov and P. B. Chochlov, Problems of Nonlinear Optics (Viniti, 1963), in Russian.

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Figures (3)

Fig. 1
Fig. 1

Spatial dispersion curves (frequency isolines) in cases of (a) normal diffraction and (b) subdiffraction, as follows from [5]. The different wave components with k 1 and k 2 dephase in a propagation and are never simultaneously phase matched with the pump in case (a) but can be in case (b). The horizontal fuzzy line denotes (tunable) phase-matching condition.

Fig. 2
Fig. 2

Evolution of the highest intensity (a) and the width (b) of the large-scale envelope of the subharmonic beam in homogeneous (dashed curves) and spatially modulated (solid curves) OPAs, as obtained by numerical integration of Eqs. (2). Q = 0.6 , f = 0.1 , Γ = 0.002 , and Δ K = 0.052 ; the pump intensity is 1. The initial width of the beam Δ X = 20 .

Fig. 3
Fig. 3

Coefficient of parametric gain depending on the width of the crystal in homogeneous (dashed) and modulated (solid) OPAs, as reconstructed from numerical integration of Eqs. (2) in the linear regime. The parameters are as in Fig. 2.

Equations (6)

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A 1 z = i ( Δ k + 1 2 k 1 2 x 2 + U ( x , z ) ) A 1 + γ A 0 A 1 * ,
A 0 z = i 2 k 0 2 x 2 A 0 γ A 1 2 .
A 1 Z = i ( Δ K + 2 X 2 + 4 f cos ( Q Z ) cos ( X ) ) A 1 + Γ A 0 A 1 * ,
A 0 Z = i 2 2 X 2 A 0 Γ A 1 2 ,
Δ K ( K ) = D 0 + D 2 K 2 + D 4 K 4 + O ( K 6 ) ,
A 1 ( K ) Z = i ( Δ K + Δ K ( K ) ) A 1 ( K ) + Γ A 0 A 1 * ( K ) .

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