A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).

[Crossref]

C. M. de Sterke, S. M. Saltiel, and Y. S. Kivshar, “Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal,” Opt. Lett. 26, 539–541 (2001).

[Crossref]

C. Zhang, H. Wei, Y.-Y. Zhu, H.-T. Wang, S.-N. Zhu, and N.-B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).

[Crossref]

S. M. Saltiel and Y. S. Kivshar, “Phase matching in nonlinear χ(2) photonic crystals,” Opt. Lett. 25, 1204–1206 (2000).

[Crossref]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

A. Chowdhury, S. C. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000).

[Crossref]

D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22, 378–380 (1997).

[Crossref]
[PubMed]

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).

[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

N. G. R. Broderick, D. J. Richardson, D. Taverner, and M. Ibsen, “High-power chirped-pulse all-fiber amplification system based on large-mode-area fiber components,” Opt. Lett. 24, 566–568 (1999).

[Crossref]

A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).

[Crossref]

A. Chowdhury, S. C. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000).

[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1953).

A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).

[Crossref]

A. Chowdhury, S. C. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000).

[Crossref]

C. Zhang, H. Wei, Y.-Y. Zhu, H.-T. Wang, S.-N. Zhu, and N.-B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

N. G. R. Broderick, D. J. Richardson, D. Taverner, and M. Ibsen, “High-power chirped-pulse all-fiber amplification system based on large-mode-area fiber components,” Opt. Lett. 24, 566–568 (1999).

[Crossref]

D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22, 378–380 (1997).

[Crossref]
[PubMed]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

N. G. R. Broderick, D. J. Richardson, D. Taverner, and M. Ibsen, “High-power chirped-pulse all-fiber amplification system based on large-mode-area fiber components,” Opt. Lett. 24, 566–568 (1999).

[Crossref]

D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22, 378–380 (1997).

[Crossref]
[PubMed]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

C. Zhang, H. Wei, Y.-Y. Zhu, H.-T. Wang, S.-N. Zhu, and N.-B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

C. Zhang, H. Wei, Y.-Y. Zhu, H.-T. Wang, S.-N. Zhu, and N.-B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

A. Chowdhury, S. C. Hagness, and L. McCaughan, “Simultaneous optical wavelength interchange with a two-dimensional second-order nonlinear photonic crystal,” Opt. Lett. 25, 832–834 (2000).

[Crossref]

A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535–1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. 26, 1353–1355 (2001).

[Crossref]

C. M. de Sterke, S. M. Saltiel, and Y. S. Kivshar, “Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal,” Opt. Lett. 26, 539–541 (2001).

[Crossref]

S. M. Saltiel and Y. S. Kivshar, “Phase matching in nonlinear χ(2) photonic crystals,” Opt. Lett. 25, 1204–1206 (2000).

[Crossref]

N. G. R. Broderick, D. J. Richardson, D. Taverner, and M. Ibsen, “High-power chirped-pulse all-fiber amplification system based on large-mode-area fiber components,” Opt. Lett. 24, 566–568 (1999).

[Crossref]

G. Imeshev, M. Proctor, and M. M. Fejer, “Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings,” Opt. Lett. 23, 673–675 (1998).

[Crossref]

D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-µJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22, 378–380 (1997).

[Crossref]
[PubMed]

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).

[Crossref]

C. Zhang, H. Wei, Y.-Y. Zhu, H.-T. Wang, S.-N. Zhu, and N.-B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).

[Crossref]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

[Crossref]

S.-N. Zhu, Y.-Y. Zhu, Y.-Q. Qin, H.-F. Weng, C.-Z. Ge, and N.-B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997).

[Crossref]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).

[Crossref]

N. G. R. Broderick, H. L. Offerhaus, G. W. Ross, D. J. Richardson, and D. C. Hanna, “HeXLN: a 2-dimensional nonlinear periodic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).

[Crossref]
[PubMed]

Such a calculation should not be taken too seriously, but it does give a rough order-of-magnitude calculation for the efficiencies.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1953).

One can, of course, design crystals in which any desired Fourier coefficients are maximized; however, such crystals are likely to contain fine features that are not easily fabricated. Our decision to look only at low-order Fourier components is based on the fact that the resultant patterns are easily fabricated.