Abstract

We present a theoretical analysis for simultaneous optical wavelength interchange and isolation of a pair of collinear input optical signals by use of two concurrent difference-frequency-generation processes in a two-dimensional second-order nonlinear photonic crystal. We have derived a set of relations, including a general nonlinear Bragg condition, that we use to determine the parameters of the nonlinear lattice, given the input wavelengths and desired exit angles of the wavelength-interchanged outputs.

© 2000 Optical Society of America

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  3. A. Yariv, D. Fekete, and D. M. Pepper, Opt. Lett. 4, 52 (1979).
    [CrossRef]
  4. D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
    [CrossRef]
  5. G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]
  6. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
    [CrossRef]
  7. E. Yablonovitch, J. Opt. Soc. Am. B 10, 283 (1993).
    [CrossRef]
  8. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  9. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  10. M. L. Bortz, M. A. Arbore, and M. M. Fejer, Opt. Lett. 20, 49 (1995).
    [CrossRef] [PubMed]
  11. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).

1999 (1)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

1998 (1)

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

1997 (1)

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

1996 (1)

G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

1995 (1)

1993 (1)

1987 (1)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

1979 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Arbore, M. A.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Berger, V.

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

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bortz, M. L.

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Burger, J.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Dapkus, P. D.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Dubovitsky, S.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

M. L. Bortz, M. A. Arbore, and M. M. Fejer, Opt. Lett. 20, 49 (1995).
[CrossRef] [PubMed]

Fekete, D.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Joannopoulos, J. D.

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

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).

Meade, R. D.

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

Pepper, D. M.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Steier, W. H.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Tishinin, D.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Toner, L.

G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Uppal, K.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Winn, J. N.

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

Yablonovitch, E.

Yariv, A.

Zhu, D. X.

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

D. X. Zhu, S. Dubovitsky, W. H. Steier, K. Uppal, D. Tishinin, J. Burger, and P. D. Dapkus, Appl. Phys. Lett. 70, 2082 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Toner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. Lett. (2)

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

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Other (2)

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

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram showing the wavelength-interchange process in a 2-D nonlinear photonic crystal.

Fig. 2
Fig. 2

Reciprocal space representation of a nonlinear lattice designed to perform wavelength interchange λAλB and λBλA. The two Ewald spheres intersect at one common point only. The difference wave vector kp-kA, which overlaps kp-kB, is slightly displaced for purposes of visualization.

Equations (9)

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

2Er,t-n2c22Er,tt2=μ0χ2r2Er,tt2,
Er,t=1/2m=13Amr,t×expiωmt-km·r+c.c.,
k1·A1*=1/2iμ0χ2rω12A2*A3*×exp-ik1-k2-k3·r,k2·A2=-1/2iμ0χ2rω22A1A3*×exp-ik1-k2-k3·r,k3·A3=-1/2iμ0χ2rω32A1A2*×exp-ik1-k2-k3·r.
ω3=ω1-ω2,k3ω3=k1ω1-k2ω2-G,
G=mA+nB,
λ3n3SFG,DFG=2πG1-n1λ2±n2λ1n3λ2±λ12+4n1λ2±n2λ1n3λ2±λ1sin2θ1/2,
ωA=ωp-ωB,kAωA=kpωp-kBωB-GA,ωB=ωp-ωA,kBωB=kpωp-kAωA-GB,
rA,B=2πGA,Bsinϕ,
sinϕ=kA|GA|sin2θA2-kA|GA|sin2θAkB|GB|sin2θB21/2±kB|GB|sin2θB2-kA|GA|sin2θAkB|GB|sin2θB21/2,

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