Abstract

We analyze harmonic generation in a two-dimensional (2D) χ2 photonic crystal and demonstrate the possibility of multiple phase matching and multicolor parametric frequency conversion. We suggest a new type of photonic structure to achieve simultaneous generation of several harmonics; we also present both general analytical results and design parameters for 2D periodically poled LiNbO3 structures.

© 2000 Optical Society of America

Full Article  |  PDF Article

Corrections

Solomon Saltiel and Yuri S. Kivshar, "Phase matching in nonlinear χ(2) photonic crystals: errata," Opt. Lett. 25, 1612-1612 (2000)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-25-21-1612

References

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  1. J. D. Joannopoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  2. J. G. Fleming and S.-Y. Lin, Opt. Lett. 24, 49 (1999).
    [CrossRef]
  3. For an excellent overview of optical applications, see Th. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23, 51 (1999).
    [CrossRef]
  4. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  5. 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]
  6. See, e.g., Y. Takagi and S. Muraki, J. Lumin. 87–89, 865 (2000), and references therein.
    [CrossRef]
  7. See, e.g., K. Koynov and S. Saltiel, Opt. Commun. 152, 96 (1998); Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, Phys. Rev. E 60, R5056 (1999), and references therein.
    [CrossRef]
  8. See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]
  9. See, e.g., A. M. Kossevich, The Crystal Lattice: Phonons, Solitons, and Dislocations (Springer-Verlag, Berlin, 1999).
    [CrossRef]

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]

See, e.g., Y. Takagi and S. Muraki, J. Lumin. 87–89, 865 (2000), and references therein.
[CrossRef]

1999 (2)

J. G. Fleming and S.-Y. Lin, Opt. Lett. 24, 49 (1999).
[CrossRef]

For an excellent overview of optical applications, see Th. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

1998 (2)

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

See, e.g., K. Koynov and S. Saltiel, Opt. Commun. 152, 96 (1998); Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, Phys. Rev. E 60, R5056 (1999), and references therein.
[CrossRef]

1992 (1)

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Bayer, R. L.

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Berger, V.

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

Broderick, N. G. R.

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]

De La Rue, R. M.

For an excellent overview of optical applications, see Th. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

Fejer, M. M.

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Fleming, J. G.

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]

Joannopoulos, J. D.

J. D. Joannopoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Jundt, D. H.

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Kossevich, A. M.

See, e.g., A. M. Kossevich, The Crystal Lattice: Phonons, Solitons, and Dislocations (Springer-Verlag, Berlin, 1999).
[CrossRef]

Koynov, K.

See, e.g., K. Koynov and S. Saltiel, Opt. Commun. 152, 96 (1998); Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, Phys. Rev. E 60, R5056 (1999), and references therein.
[CrossRef]

Krauss, Th. F.

For an excellent overview of optical applications, see Th. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

Lin, S.-Y.

Meade, R. B.

J. D. Joannopoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Muraki, S.

See, e.g., Y. Takagi and S. Muraki, J. Lumin. 87–89, 865 (2000), and references therein.
[CrossRef]

Nagel, G. A.

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

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, 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.

See, e.g., K. Koynov and S. Saltiel, Opt. Commun. 152, 96 (1998); Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, Phys. Rev. E 60, R5056 (1999), and references therein.
[CrossRef]

Takagi, Y.

See, e.g., Y. Takagi and S. Muraki, J. Lumin. 87–89, 865 (2000), and references therein.
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

IEEE J. Quantum Electron. (1)

See, e.g., M. M. Fejer, G. A. Nagel, D. H. Jundt, and R. L. Bayer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

J. Lumin. (1)

See, e.g., Y. Takagi and S. Muraki, J. Lumin. 87–89, 865 (2000), and references therein.
[CrossRef]

Opt. Commun. (1)

See, e.g., K. Koynov and S. Saltiel, Opt. Commun. 152, 96 (1998); Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); Yu. S. Kivshar, A. A. Sukhorukov, and S. Saltiel, Phys. Rev. E 60, R5056 (1999), and references therein.
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

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]

Prog. Quantum Electron. (1)

For an excellent overview of optical applications, see Th. F. Krauss and R. M. De La Rue, Prog. Quantum Electron. 23, 51 (1999).
[CrossRef]

Other (2)

See, e.g., A. M. Kossevich, The Crystal Lattice: Phonons, Solitons, and Dislocations (Springer-Verlag, Berlin, 1999).
[CrossRef]

J. D. Joannopoulos, R. B. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a 2D χ2 photonic crystal with different types of grating structures. The shaded circles mark the regions with the reverse sign of second-order susceptibility.

Fig. 2
Fig. 2

(a) Reciprocal lattice of the 2D crystal shown in Fig. 1; (b) SHG phase-matching wave-vector triangle.

Fig. 3
Fig. 3

DPM for (a) THG, noncollinear SHG, and noncollinear SFM and (b) FHG, noncollinear SHG, and noncollinear 2ω+2ω=4ω processes.

Fig. 4
Fig. 4

Schematric diagram of an asymmetric 2D χ2 photonic crystal. For δ=60° and ϵ=1, it is transformed into the structure shown in Fig. 1.

Fig. 5
Fig. 5

Examples of design parameters ϵ and d for the double- and triple-phase-matching conditions in a 2D LiNbO3 APNC structure.

Equations (8)

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

k22=4k12+Kpq2+4k1Kpq cosαpq-β1,
Kmn2+2k12Kmn cosαmn-β12=k32-k122,
d=2πQpqΔk2ϵ sin δ.
k32-k122Δk22-QmnQpq2=2k12Δk2QmnQpqcos θmnpq,
k42-4k22Δk22-QijQpq2=4k2Δk2QijQpqcos θijpq.
cos δ3ω=p2k32-k122-ϵ2n2Δk222k12Δk2ϵnp,
cos δ4ω=p2k42-4k22-ϵ2j2Δk224k2Δk2ϵjp.
ϵ2=p22jk32-k122k2-nk42-4k22k12nj2jk2-nk12Δk22.

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