Abstract

We analyze light self-confinement induced by multiple nonlinear resonances in a two-dimensional χ(2) photonic crystal. With reference to second-harmonic generation in a hexagonal lattice, we show that the system can not only support two-color (1+1)D solitary waves with enhanced confinement and steering capabilities but also enable novel features such as wavelength-dependent soliton routing.

© 2007 Optical Society of America

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  1. Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).
  2. G. Assanto and G. I. Stegeman, Opt. Express 10, 388 (2002).
    [PubMed]
  3. W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
    [CrossRef]
  6. B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. G. Leo, A. Amoroso, L. Colace, G. Assanto, R. V. Roussev, and M. M. Fejer, Opt. Lett. 29, 1778 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. K. Gallo, C. Codemard, C. B. E. Gawith, J. Nilsson, P. G. R. Smith, N. G. R. Broderick, and D. J. Richardson, Opt. Lett. 31, 1232 (2006).
    [CrossRef] [PubMed]
  14. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
    [CrossRef] [PubMed]
  15. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
    [CrossRef]

2006

2004

2003

2002

2001

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

M. De Sterke, S. M. Saltiel, and Yu. Kivshar, Opt. Lett. 26, 539 (2001).
[CrossRef]

2000

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

1999

1998

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

1996

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

1995

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

1976

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Amoroso, A.

Assanto, G.

Baek, Y.

R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Barthelemy, A.

Berger, V.

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Boland, B.

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

Bourliaguet, B.

Broderick, N. G. R.

K. Gallo, C. Codemard, C. B. E. Gawith, J. Nilsson, P. G. R. Smith, N. G. R. Broderick, and D. J. Richardson, Opt. Lett. 31, 1232 (2006).
[CrossRef] [PubMed]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Chowdhury, A.

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

Codemard, C.

Colace, L.

Couderc, V.

De Angelis, C.

De Sterke, M.

Di Falco, A.

Fejer, M. M.

Fuerst, R. A.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Gallo, K.

Gawith, C. B. E.

Hagan, D.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Kivshar, Yu.

Kuech, T. F.

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

Lawrence, B. L.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Leo, G.

Mazilu, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

McCaughan, L.

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

Menyuk, C.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Mihalache, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Nilsson, J.

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Richardson, D. J.

K. Gallo, C. Codemard, C. B. E. Gawith, J. Nilsson, P. G. R. Smith, N. G. R. Broderick, and D. J. Richardson, Opt. Lett. 31, 1232 (2006).
[CrossRef] [PubMed]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

Roussev, R. V.

Saltiel, S. M.

Schiek, R.

R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Smith, P. G. R.

Sohler, W.

Staus, C.

A. Chowdhury, C. Staus, B. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 23, 1353 (2001).
[CrossRef]

Stegeman, G.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

G. Assanto and G. I. Stegeman, Opt. Express 10, 388 (2002).
[PubMed]

R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Torner, L.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Van Stryland, E.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Phys. Rev. Lett.

W. Torruellas, Z. Wang, D. Hagan, E. Van Stryland, G. Stegeman, L. Torner, and C. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Sov. Phys. JETP

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

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Figures (4)

Fig. 1
Fig. 1

QPM diagram for twin-beam SHG via the reciprocal lattice vectors G 1 and G 2 of a quadratic 2D NPC. QPM can be obtained in distinct directions and for distinct FF wavelengths.

Fig. 2
Fig. 2

Contour maps of the FF output versus mismatches δ β 1 and δ β 2 , calculated for γ = 5 and ζ = 6 . (a) Normalized beam waist ϖ FF = w out w 0 and (b) lateral displacement Δ ξ FF with respect to the input ( ξ = 0 ) . The dashed lines indicate the trajectories corresponding to Figs. 3, 4.

Fig. 3
Fig. 3

Symmetric TB-SHG for δ β 1 = δ β 2 . (a) Calculated FF beam waist ( ϖ FF ) and transverse displacement ( Δ ξ FF ) versus δ β 1 for γ = 5 , ζ = 6 (solid lines). The dashed line refers to conventional single-beam SHG. Inset: FF beam propagation at low power ( γ = 0.01 ) . Beam propagation of (b) FF and (c) SH components for δ β 1 = δ β 2 = 2 π , γ = 5 [point A in (a)].

Fig. 4
Fig. 4

Asymmetric TB-SHG for δ β 2 = δ β 2 + 10 π . (a) Normalized FF beam waist ( ϖ FF ) and transverse displacement ( Δ ξ FF ) versus δ β 1 for γ = 5 , ζ = 6 . (b), (c) Beam (FF) intensity propagation plots for (b) δ β 1 = 9 π ( δ β 2 = π ) , i.e., point B in (a) and (c) δ β 1 = π 2 ( δ β 1 = 10.5 π ) , i.e., point C in (a).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

a ζ + i σ 0 2 a ξ 2 = i γ a * b 1 i γ a * b 2 ,
b 1 ζ + ρ 1 b 1 ξ + i σ 1 2 b 1 ξ 2 + i δ β 1 b 1 = i γ a 2 ,
b 2 ζ + ρ 2 b 2 ξ + i σ 2 2 b 2 ξ 2 + i δ β 2 b 2 = i γ a 2 .
σ 0 = L d ( 2 β ( ω ) w 0 2 ) = 1 4 ,
σ 1 , 2 = L d ( 2 β 1 , 2 ( 2 ω ) w 0 2 ) 1 8 .

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