Abstract

Nonlinear photonic crystals formed by two-dimensional periodic poling of the quadratic susceptibility χ2 can support quasi-phase-matched harmonic generation. The frequency-conversion efficiency depends on the photonic crystal’s poling pattern through certain Fourier coefficients of the poling function. A procedure is described for finding those poling patterns that are most efficient for any specific quasi-phase-matched frequency-conversion scheme.

© 2003 Optical Society of America

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References

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  1. 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]
  2. N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
    [CrossRef]
  3. A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, Opt. Lett. 26, 1353 (2001).
    [CrossRef]
  4. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  5. S. Saltiel and Y. S. Kivshar, Opt. Lett. 25, 1204 (2000).
    [CrossRef]
  6. M. de Sterke, S. M. Saltiel, and Y. S. Kivshar, Opt. Lett. 26, 539 (2001). The results in this reference are incomplete, as two phase-matching conditions were overlooked. Figure 1 represents the complete QPM diagram for this FHG scheme.
    [CrossRef]
  7. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]

2002 (1)

2001 (2)

2000 (2)

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]

S. Saltiel and Y. S. Kivshar, Opt. Lett. 25, 1204 (2000).
[CrossRef]

1998 (1)

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

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Berger, V.

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

Boland, B. F.

Bratfalean, R. T.

Broderick, N. G. R.

N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
[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]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Chowdhury, A.

de Sterke, C. M.

de Sterke, M.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

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]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Kivshar, Y. S.

Kuech, T. F.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

McCaughan, L.

Monro, T. M.

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.

N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, J. Opt. Soc. Am. B 19, 2263 (2002).
[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]

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]

Saltiel, S.

Saltiel, S. M.

Staus, C.

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Figures (3)

Fig. 1
Fig. 1

QPM diagram for a collinear FHG scheme. Reciprocal NPC lattice vectors G1,-1 and G1,1 phase match second-harmonic wave vectors k2a and k2b. Lattice vectors G8,-2, G8,0, and G8,2 phase match the fourth-harmonic wave vector k4, which is collinear with the fundamental k1.

Fig. 2
Fig. 2

Surface Σ for the FHG scheme considered here. The two circles are those on which the poling merit, given by Eq. (6), is a global maximum.

Fig. 3
Fig. 3

Optimal poling patterns given by Eq. (7) for (a) ϕ=0 and (b) ϕ=π/2.

Equations (7)

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αp= p11*p112p80+p82*p80+p82,
px=a1=-a2=-pa1a2 expix·Ga1a2,
αμv>αv.
ρnx¯=signn·δx¯.
ρnx¯=signn·δx¯+δx¯,
αp=2p·u34p·u12+p·u22,
ρnx= signsin θ cosϕ+16πx11+cos 4πx2+2 cos θ cos 2πx1 cos 2πx2.

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