Abstract

Using high-power nanosecond pulses, we measured the second-harmonic conversion efficiency of two-dimensional hexagonally poled lithium niobate as a function of temperature and wavelength. These results were compared with theoretical estimates and with measurements in one-dimensional periodically poled lithium niobate. We found that for a substantial range of parameters a two-dimensional noncollinear interaction has a broader tuning response than a one-dimensional collinear interaction. We also observed and characterized third- and fourth-harmonic generation processes in the same crystal.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. 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]
  3. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
    [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. S. M. Saltiel and Y. S. Kivshar, “Phase matching in nonlinear χ(2) photonic crystals,” Opt. Lett. 25, 1204–1206 (2000).
    [CrossRef]
  9. 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]
  10. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  11. C. Kittel, Introduction to Solid State Physics, 3rd ed. (Wiley, New York, 1953).
  12. 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]
  13. Such a calculation should not be taken too seriously, but it does give a rough order-of-magnitude calculation for the efficiencies.
  14. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  15. 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]
  16. 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]
  17. 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.

2001 (3)

2000 (3)

1999 (1)

1998 (2)

1997 (3)

1962 (1)

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]

Armstrong, J. A.

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]

Berger, V.

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

Bloembergen, N.

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]

Boland, B. F.

Broderick, N. G. R.

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]

Caplen, J. E.

Chowdhury, A.

de Sterke, C. M.

Dong, L.

Ducuing, J.

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]

Fejer, M. M.

Ge, C.-Z.

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]

Hagness, S. C.

Hanna, D. C.

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]

Ibsen, M.

Imeshev, G.

Jundt, D. H.

Kivshar, Y. S.

Kuech, T. F.

McCaughan, L.

Ming, N.-B.

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]

Offerhaus, H. L.

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]

Penty, R. V.

Pershan, P. S.

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]

Proctor, M.

Qin, Y.-Q.

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]

Richardson, D. J.

Ross, G. W.

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]

Saltiel, S. M.

Staus, C.

Taverner, D.

Wang, H.-T.

Wei, H.

Weng, H.-F.

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]

Williams, K.

Zhang, C.

Zhu, S.-N.

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]

Zhu, Y.-Y.

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]

Opt. Lett. (9)

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]

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]

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]

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

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]

Phys. Rev. (1)

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]

Phys. Rev. Lett. (3)

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]

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]

Other (4)

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.

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

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) HeXLN crystal and wave vectors involved in SHG. Period a of the crystal is 18.05 µm, as shown, and is uniform over the whole sample. In our experiments propagation was in the +x direction. (b) Reciprocal lattice for our crystal and possible examples of SHG with different RLVs. Note that propagation in the ΓM direction corresponds to propagation in the +x direction.

Fig. 2
Fig. 2

Temperature dependence of the NPCs. Solid curve, measured efficiency curve for the HeXLN crystal; long-dashed curve, measured PPLN response; short-dashed curve, theoretical efficiency for HeXLN.

Fig. 3
Fig. 3

Contour plot of the second-harmonic conversion efficiency relative to temperature and output angle. The contours that are at every 1-dB level below the peak show the regions of highest-output second-harmonic intensity.

Fig. 4
Fig. 4

QPM diagrams for the cascaded generation of (a) the third and (b) the fourth harmonics.

Fig. 5
Fig. 5

Temperature-tuning curves for the second and the third harmonics. Filled circles, second harmonic; filled triangles, third harmonic. In this and subsequent experiments the fundamental wavelength was 1536 nm.

Fig. 6
Fig. 6

Angle tuning of the type II third-harmonic-generation process. Points, experimental measurements; curves, theoretical model. Here it can clearly be seen that when the fundamental and the second harmonic are vertically polarized no third-harmonic light will be visible.

Fig. 7
Fig. 7

Temperature-tuning curves for the second and the fourth harmonics. Filled circles, second harmonic; filled triangles, fourth harmonic.

Equations (9)

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

k2ω·E2ω(r)=-2i ω2c2χ(2)(r)(Eω)2×exp[i(k2ω-2kω)·(r)],
χ(2)(r)=n,m κn,m exp(iGn,m·r),n, m,
k2ω-2kω-Gn,m=0
2E2ω+n22(2ω)2c2E2ω=(2ω)2c2χ(2)(r)(Eω)2,
G(r; r)=-i4H0(1)(k2ω|r-r|),
sin(t1N1)N1 sin(t1)2sin(t2N2)N2 sin(t2)2,
t1=kfa-ksa2 cos ϑi,
t2=12 3ksa sin ϑi,
dϑidT=-t1Tϑit1ϑiT=2kf-ks cos ϑiks sin ϑi,

Metrics